Patent Publication Number: US-2022214452-A1

Title: Ratio metric position sensor and control system

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATIONS 
     This application is a continuation-in-part of and claims the benefit of priority to U.S. patent application Ser. No. 16/987,828, filed Aug. 7, 2020, the contents of which are incorporated by reference herein. 
    
    
     TECHNICAL FIELD 
     This instant specification relates to ultrasonic position sensors. 
     BACKGROUND 
     Position measurement devices are used for the characterization and operation of fluid control systems. Traditionally, effector (e.g., valve body, piston head) position tracking is achieved through the use of linear variable differential transformers (LVDTs). LVDTs drive system sizing and introduce accuracy and sizing constraints. Specifically, actuation devices generally require the LVDT be installed through the piston rod, driving actuator sizing. 
     Ultrasonic position sensors are a proven industrial technology that can be leveraged for position detection. Existing time of flight ultrasonic position sensors emit acoustic pings and measure the amount of time until reflected echoes of the pings return. The amount of time between the transmission and return of the pings is generally dependent upon the distance between the transceiver and the object being measured, and the speed of sound in the medium through which the pings are being transmitted. That speed of sound is dependent upon the characteristics of the medium, such as its density, temperature, and/or acoustic impedance. Existing time of flight ultrasonic position sensors depend upon on predetermined knowledge or determination of the speed of sound through the medium through which the pings are being transmitted in order to function. In applications such as fuel valves and pressure regulators, the temperatures and types of fuels used can vary, which can cause the speed of sound to vary dynamically during operation. The speed of sound of a medium can be sensed, but the inclusion of these additional sensors adds to the complexity, size, cost, and weight of such systems. 
     SUMMARY 
     In general, this document describes ultrasonic position sensors. 
     In an example embodiment, a position sensor system includes a sensor housing defining a first cavity having a first face, a fluid effector including an actuator housing having an inner surface defining a second cavity, and a moveable body having a second face and configured for reciprocal movement within the second cavity, an acoustic transmitter system configured to emit a first emitted acoustic waveform toward the first face, and emit a second emitted acoustic waveform toward the second face, and an acoustic receiver system configured to detect a first reflected acoustic waveform based on a first reflection of the first emitted acoustic waveform based on the first face, and detect a second reflected acoustic waveform based on a second reflection of the second emitted acoustic waveform based on the second face. 
     Various embodiments can include some, all, or none of the following features. The position sensor system can include a timer configured to determine a first time of flight of the first emitted acoustic waveform and the first reflected acoustic waveform, and determine a second time of flight of the second emitted acoustic waveform and the second reflected acoustic waveform. The position sensor system can include a processor system configured to determine a position of the moveable body within the second cavity based on the first time of flight and the second time of flight. The acoustic transmitter system can be configured to emit one or both of the first emitted acoustic waveform and the second emitted acoustic waveform through a fluid in one or both of the first cavity and the second cavity, and the acoustic receiver system can be configured to receive one or both of the first reflected acoustic waveform and the second reflected acoustic waveform from the fluid in one or both of the first cavity and the second cavity. The acoustic transmitter system can be configured to transmit the second emitted acoustic waveform at a predetermined emitted frequency, and the acoustic receiver system can be configured to determine a reflected frequency of the second reflected acoustic waveform. The position sensor system can include a processor system configured to determine a speed of the moveable body based on the predetermined emitted frequency and the reflected frequency. The fluid effector can be a linear piston effector, the first cavity can be a first tubular cavity having a first longitudinal end and a second longitudinal end defining the first face opposite the first longitudinal end, the second cavity can be a second tubular cavity having a third longitudinal end and a fourth longitudinal end opposite the third longitudinal end, the moveable body can be a piston head configured for longitudinal movement within the second tubular cavity, the acoustic transmitter system can include a first acoustic transmitter arranged at the first longitudinal end and a second acoustic transmitter arranged at the third longitudinal end, and the acoustic receiver system can include a first acoustic receiver arranged at the first longitudinal end and a second acoustic receiver arranged at the third longitudinal end. The position sensor system can include a unified cavity having the first cavity and the second cavity. The first face can be at least partly defined by a shoulder extending between first cavity and the second cavity. The acoustic transmitter system can include a first acoustic emitter configured to emit the first emitted acoustic waveform toward the first face, and a second acoustic emitter configured to emit the second emitted acoustic waveform toward the second face. The second acoustic emitter at least partly concentrically surrounds the first acoustic emitter. The position sensor system can include a phase detector configured to determine a difference between at least one of (1) a first emitted phase of the first emitted acoustic waveform and a first reflected phase of the first reflected acoustic waveform, and (2) a second emitted phase of the second emitted acoustic waveform and a second reflected phase of the second reflected acoustic waveform. The position sensor system can include another moveable body having a third face and configured for reciprocal movement within a third cavity, wherein the acoustic transmitter system is configured to emit a third emitted acoustic waveform toward the third face, and the acoustic receiver system is configured to detect a third reflected acoustic waveform based on a third reflection of the third emitted acoustic waveform based on the third face. 
     In an example implementation, a method of position sensing includes emitting a first emitted acoustic waveform through a fluid having a first acoustic impedance toward a first acoustic interface, emitting a second emitted acoustic waveform through the fluid toward a second acoustic interface, reflecting, by the first acoustic interface, a first reflected acoustic waveform based on the first emitted acoustic waveform, reflecting, by the second acoustic interface, a second reflected acoustic waveform based on the second emitted acoustic waveform, and determining a first position of the second acoustic interface based on the first reflected acoustic waveform and the second reflected acoustic waveform. 
     Various implementations can include some, all, or none of the following features. The method can include determining a first time of flight based on the first emitted acoustic waveform and the first reflected acoustic waveform, and determining a second time of flight based on the second emitted acoustic waveform and the second reflected acoustic waveform, wherein determining a first position of the second acoustic interface is further based on the first time of flight and the second time of flight. Determining the first position of the second acoustic interface based on the first time of flight (t 1 ) and the second time of flight (t 2 ) can be given by an equation: (t 1 −t 2 )/(t 1 +t 2 ). The method can include determining a second position of the second acoustic interface, and determining a speed of the second acoustic interface based on the first position and the second position. The method can include determining a reflected acoustic frequency based on one or both of the first reflected acoustic waveform and the second reflected acoustic waveform, and determining a speed of the second acoustic interface based on the determined reflected acoustic frequency and a predetermined emitted acoustic frequency of the second emitted acoustic waveform. The first acoustic interface can be defined by a first face of a fluid cavity having a second acoustic impedance that is different than the first acoustic impedance, the second acoustic interface can be defined by a second face of a moveable body within a fluid effector and having a third acoustic impedance that is different than the first acoustic impedance, the first emitted acoustic waveform can be emitted toward the first face through the fluid, the second emitted acoustic waveform can be emitted toward the second face through the fluid, the first reflected acoustic waveform can be based on a first reflection of the first emitted acoustic waveform by the first face, and the second reflected acoustic waveform can be based on a second reflection of the second emitted acoustic waveform by the second face. The method can include determining a phase difference between a second emitted phase of the second emitted acoustic waveform and a second reflected phase of the second reflected acoustic waveform, wherein determining a first position of the second acoustic interface can be further based on the determined phase difference. The first emitted acoustic waveform can be emitted through a first fluid cavity toward a face of the first fluid cavity defining the first acoustic interface, and the second emitted acoustic waveform can be emitted through a second fluid cavity toward a second face of a moveable member defining the second acoustic interface. The first emitted acoustic waveform can be emitted through a first portion of a fluid cavity toward a face of the fluid cavity defining the first acoustic interface, and the second emitted acoustic waveform can be emitted through a second portion of the fluid cavity toward a second face of a moveable member defining the second acoustic interface. The method can include emitting a third emitted acoustic waveform through the fluid toward a third acoustic interface, reflecting, by the third acoustic interface, a third reflected acoustic waveform based on the third emitted acoustic waveform, and determining a second position of the third acoustic interface based on the first reflected acoustic waveform and the third reflected acoustic waveform. 
     In another example embodiment, a non-transitory computer storage medium is encoded with a computer program, the computer program having instructions that when executed by data processing apparatus cause the data processing apparatus to perform operations including emitting a first emitted acoustic waveform through a fluid having a first acoustic impedance toward a first acoustic interface, emitting a second emitted acoustic waveform through the fluid toward a second acoustic interface, reflecting, by the first acoustic interface, a first reflected acoustic waveform based on the first emitted acoustic waveform, reflecting, by the second acoustic interface, a second reflected acoustic waveform based on the second emitted acoustic waveform, and determining a first position of the second acoustic interface based on the first reflected acoustic waveform and the second reflected acoustic waveform. 
     The systems and techniques described here may provide one or more of the following advantages. First, a system can determine a position and/or speed of a target object though an acoustic transmission medium. Second, the system can operate without determining the acoustic properties of the transmission medium. Third, the system can have a more efficient and/or economical mechanical design compared to existing mechanical position measurement solutions such as variable differential transformers (VDTs). Fourth, the system can have a more efficient and/or economical electronic design compared to existing ultrasonic position measurement solutions. Fifth, the system can provide a more space efficient option for system sizing. Sixth, the system can improve weight, pump demand, thermal loads, and measurement accuracy. 
     The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic diagram that shows an example of a system for ultrasonic position measurement. 
         FIG. 2  is an internal view of an example of a linear fluid effector. 
         FIG. 3  is an internal view of another example of a linear fluid effector. 
         FIG. 4  is a sectional view of an example of an acoustic interface. 
         FIG. 5  is a sectional view of an example of a rotary fluid effector. 
         FIG. 6  is a conceptual diagram of a transmitted acoustic waveform. 
         FIG. 7  is a graph showing examples of phase shifts in acoustic waveforms. 
         FIG. 8  is a flow diagram of an example process for ultrasonic position sensing. 
         FIG. 9  shows another example of a system for ultrasonic position measurement. 
         FIG. 10  shows another example of a system for ultrasonic position measurement. 
         FIG. 11  is a conceptual sectional view of another example linear fluid effector. 
         FIG. 12  is a conceptual sectional view of another example linear fluid effector. 
         FIG. 13  is an end view of an example transceiver. 
         FIG. 14  is an end view of another example transceiver. 
         FIG. 15  is a schematic diagram of an example fluid effector system. 
         FIG. 16  is a block diagram of an example transducer controller. 
         FIG. 17  is a block diagram of another example transducer controller. 
         FIG. 18  is a block diagram of time-of-flight and ratiometric function blocks. 
         FIG. 19  is a graph of an example log  10  to linear transformation. 
         FIG. 20  is a block diagram of an example analog cross-correlation module. 
         FIG. 21  is a block diagram of an example cross-correlation receiver module. 
         FIG. 22  is a schematic diagram of an example clock circuit. 
         FIG. 23  is a schematic of an example template generator circuit. 
         FIG. 24  is a graph of examples of signal timings. 
         FIG. 25  is a block diagram of an example closed loop control system. 
         FIG. 26  is a flow diagram of another example process for ultrasonic position sensing. 
         FIG. 27  is a schematic diagram of an example of a generic computer system. 
     
    
    
     DETAILED DESCRIPTION 
     This document describes systems and techniques for ultrasonic position sensing, more particularly, for sensing the position of moveable members in fluid environments, such as valve bodies and piston heads. In general, the ultrasonic position sensing systems and techniques described in this document measure the distance from a moveable object to each end of its length of travel to determine a ratiometric position value that can be determined without needing to know or otherwise determine the speed of sound in the medium in which the ultrasonic signals are being transmitted. 
       FIG. 1  is a schematic diagram that shows an example of a system  100  for ultrasonic position measurement (e.g., a position sensor system). The system  100  includes a fluid effector  110 . The fluid effector  110  includes a housing  112  having an inner surface  114  defining a cavity  116  (e.g., a cylindrical cavity), and a moveable body  118 . The moveable body  118  has a face  120  and a face  122  opposite the face  120 , and is configured for reciprocal movement within the housing  112 . The moveable body  118  is configured to contact the inner surface  114  and subdivide the cavity  116  to define a fluid chamber  124  at the face  120  and define a fluid chamber  126  at the face  122 , and is configured for longitudinal movement within the cavity  116 . 
     The fluid effector  110  includes an acoustic transceiver  130   a . The acoustic transceiver  130   a  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  132   a  in a first direction toward the face  120 . The acoustic transceiver  130   a  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  133   a  based on a first reflection of the emitted acoustic waveform  132   a  based on the moveable body  118 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     The fluid effector  110  also includes an acoustic transceiver  130   b . The acoustic transceiver  130   b  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  132   b  in a second direction opposite the first direction toward the face  122 . The acoustic transceiver  130   a  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  133   b  based on a second reflection of the emitted acoustic waveform  132   b  based on the moveable body  118 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     A signal processor  150  is configured to process signals from the acoustic transceiver  130   a  and the acoustic transceiver  130   b  to determine the position of the moveable body  118  within the cavity  116 . A controller  160  (e.g., a computer) is configured to receive position information from the signal processor  150  and perform functions based on the position information (e.g., control a process, present information to a user, transmit information to another system, record a log). In some embodiments, the signal processor  150  can include a timer (e.g., to measure the times of flight of emitted and reflected signals). In some embodiments, the signal processor  150  can include a phase detector (e.g., to determine phase and/or Doppler shifts in reflected signals). 
     In general, the fluid effector  110  is configured as a ratiometric position-sensing device. A transmit-receive transducer is located on either end of the effector. Both transmitters can send a pulse echo and receive an echo upon reflection from the effector piston. Time measurements of the two transducers can independently determine the position of a moveable body when sound speed is known. However, when coupling two transducers into a system, sound speed is cancelled and a ratiometric ultrasound position sensor is obtained. In some implementations, if either transducer fails, redundancy can be obtained through measurement or approximation of sound speed. The techniques for processing the signals, and several embodiments of the fluid effector  110 , will be discussed in the descriptions of  FIGS. 2-8 . 
       FIG. 2  is an internal view of an example of a linear fluid effector  200 . In some implementations, the linear fluid effector  200  can be the example fluid effector  110  of  FIG. 1 . 
     The fluid effector  200  includes a housing  212  having an inner surface  214  defining a cavity  216  (e.g., a tubular cavity), and a moveable body  218 . The housing  212  is generally tubular, having a first longitudinal end  213   a  and a second longitudinal end  213   b  opposite the first longitudinal end  213   a , and a length represented by arrow  270 . 
     The moveable body  218  has a face  220   a  and a face  220   b  opposite the face  220   a . The moveable body  218  is configured for reciprocal movement within the housing  212 . The moveable body  218  is configured to contact the inner surface  214  and subdivide the cavity  216  to define a fluid chamber  224   a  on the side of the face  220   a  and define a fluid chamber  224   b  on the side of the face  220   b.    
     In some embodiments, the fluid effector  200  can be configured as a valve. For example, the housing  212  can be a valve housing and the moveable body  218  can be a valve body configured to slide longitudinally within the valve housing to control fluid flow. In some embodiments, the fluid effector  200  can be configured as a pressure regulator or sensor, in which fluid pressure in one or both of the fluid chambers  224   a - 224   b  can urge movement of the moveable body  218  within the housing. In some embodiments, the fluid effector  200  can be configured as a fluid actuator. For example, the housing  212  can be a hydraulic cylinder and the moveable body  218  can be a piston head that can be moved within the cavity  216  to urge a fluid flow, or a piston head that can be moved within the cavity  216  by fluid pressure within the fluid chambers  224   a - 224   b . In some embodiments, the fluid effector  200  can be configured as any appropriate form of device in which a moveable body moves linearly within a fluid-filled cavity. 
     The fluid effector  200  includes an acoustic transceiver  230   a . The acoustic transceiver  230   a  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  232   a  toward the face  220   a  through a medium (e.g., a fluid) filling the fluid chamber  224   a . The acoustic transceiver  230   a  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  233   a  based on a reflection of the emitted acoustic waveform  232   a  off the moveable body  218 . 
     The fluid effector  200  includes an acoustic transceiver  230   b . The acoustic transceiver  230   b  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  232   b  toward the first face  220   b  through a medium filling the fluid chamber  224   b . The acoustic transceiver  230   b  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  233   b  based on a reflection of the emitted acoustic waveform  232   b  off the moveable body  218 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     The acoustic transceivers  230   a - 230   b  are configured to be activated by an external system such as the example signal processor  150  of  FIG. 1 , and provide signals based on the reflected acoustic waveforms  233   a - 233   b  to the external system for processing. In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitters and the acoustic receivers can be discrete components. 
     The medium through which the acoustic waveforms  232   a  and  233   a  travel has a speed of sound (C 1 ). In the illustrated example, the measured time (t 1 ) (e.g., a first time-of-flight) in conjunction with the sound speed (C 1 ) defines a distance L 1  (represented by arrow  260   a ) from the acoustic transceiver  230   a  to the face  220   a  of the moveable body  218 : 
     
       
         
           
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       L 
                       1 
                     
                   
                   = 
                   
                     
                       t 
                       1 
                     
                     * 
                     
                       C 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     The medium through which the acoustic waveforms  232   b  and  233   b  travel has a speed of sound (C 2 ). In the illustrated example, the measured time (t 2 ) (e.g., a second time-of-flight) in conjunction with the sound speed (C 2 ) defines a distance L 2  (represented by arrow  260   b ) from the acoustic transceiver  230   b  to the face  220   b  of the moveable body  218 : 
     
       
         
           
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       L 
                       2 
                     
                   
                   = 
                   
                     
                       t 
                       2 
                     
                     * 
                     
                       C 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The acoustic transceivers  230   a  and  230   b  and the moveable body  218  can be configured such that the signals are used to determine a ratiometric value for the position of the moveable body  218  within its range of motion (e.g., the distance L 1 +L 2 , or the length  270  minus the longitudinal thickness of the moveable body  218 ): 
     
       
         
           
             
               
                 
                   Position 
                   ∼ 
                   
                     
                       
                         t 
                         1 
                       
                       - 
                       
                         t 
                         2 
                       
                     
                     
                       
                         t 
                         1 
                       
                       + 
                       
                         t 
                         2 
                       
                     
                   
                   ∼ 
                   
                     
                       
                         
                           2 
                           ⁢ 
                           
                             L 
                             1 
                           
                         
                         
                           C 
                           1 
                         
                       
                       - 
                       
                         
                           2 
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                         
                           C 
                           2 
                         
                       
                     
                     
                       
                         
                           2 
                           ⁢ 
                           
                             L 
                             1 
                           
                         
                         
                           C 
                           1 
                         
                       
                       + 
                       
                         
                           2 
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                         
                           C 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     In use, the speed of sound in the fluid that fills the cavity  216  does not need to be known or determined. Since both sides of the cavity  216  are filled with the same type of fluid under substantially the same conditions (e.g., temperature), the speed of sound in the fluid will be the same on both sides of the cavity  216 , and the speed of sound becomes cancelled out of Equation 3. And since the speed of sound drops out of Equation 3, the relative position of the moveable body  218  within the cavity  216  becomes a unitless ratiometric value. An absolute position of the moveable body  218  can be determined, if needed, based on the ratiometric value and a predetermined value for the range of motion (e.g., L 1 +L 2 ). For example, if the range of motion is known to be 10 cm, and the position is determined to be 0.63 (e.g., based on t 1  and t 2 ), then the absolute position of the moveable body  218  within the cavity  216  can be determined. 
     For example, the transducers may sit flush with the bore of the cylinder on both ends (e.g., if the piston head sits on the wall time is zero on the face). In this example, if the piston is precisely in the middle, then t 1 =t 2 , which is 50% of stroke. However, Equation 3 is Position˜(t 1 −t 2 )/(t 1 +t 2 )→(t 1 =t 2 ) (e.g., the numerator goes to zero). As the piston strokes in one direction, t 1  decreases and t 2  increases, driving the ratio negative. Conversely, as the piston strokes in the opposite direction, the ratio increases. So at one stop the position output is −1 in this example, and at the opposite stop the position output is +1. In another example, for an Equation 3 measurement of 0.63 this would fall between −1 (e.g., retract) and +1 (e.g., extend). The percentage of total stroke here becomes (0.63−(−1))/(1−(−1))→1.63/2→81.5% of total stroke. For a piston configuration having a total stroke of 10 cm, the actual position from the housing stop would be (L 1 +L 2 )*81.5%=10 cm*81.5%=8.15 cm, and the distance from the opposing stop would be 10 cm−8.15 cm=−1.85 cm. 
     Since the ratiometric value is based on the distances between the acoustic transceivers  230   a  and  230   b  and the faces  220   a  and  220   b , the thickness of the moveable body  218  (e.g., the distance between the faces  220   a  and  220   b ) does not directly affect the ratiometric value. In some implementations, the absolute positions of the faces  220   a  and  220   b  can be determined based on a determined absolute position of the moveable body  218  and the predetermined thickness of the moveable body  218  (e.g., the absolute position of the face  220   a - 220   b  can be offset from the absolute position of the center of the moveable body  218  by plus or minus one-half the distance between the faces  220   a  and  220   b  or another predetermined offset distance). 
     The described technique can be extended to perform additional functions. For example, by pinging the two sides of the moveable body  218 , the position of the moveable body  218  can be determined. By pinging the two sides of the moveable body  218  again to determine a second position of the moveable body, the difference in the two positions and the amount of time between the two measurements can be used to determine a speed of the moveable body  218 . The determined speed of the moveable body  218  and predetermined knowledge of the mechanical configuration of the fluid effector  200  can be used to determine a linear velocity of the moveable body  218  (e.g., the speed can be determined, and the moveable body  218  is known to move linearly). In another example, multiple positions and/or velocities can be measured and/or determined, and such information can be used to determine an acceleration of the moveable body  218 . 
     In the example fluid effector  200 , the acoustic waveforms  232   a  and  232   b  are reflected off the faces  220   a  and  220   b . The reason that the acoustic waveforms  232   a  and  232   b  are reflected is because the moveable body  218  defines an acoustic interface at the faces  220   a  and  220   b . The fluid in the fluid chambers  224   a  and  224   b  has an acoustic impedance, and the moveable body  218  has a different acoustic impedance. As in many types of signal transmission systems, an impedance mismatch can cause a transmitted signal to be reflected. In the illustrated example in which ultrasonic signals are being transmitted, the locations of these impedance mismatches define the locations of acoustic interfaces. In the illustrated example, the face  220   a  and the face  220   b  define the locations of the acoustic impedance mismatches and their corresponding acoustic interfaces. Other examples of using acoustic interfaces for determining the location of a moveable body are discussed in further detail in the descriptions of  FIGS. 3-5 . 
       FIG. 3  is an internal view of another example of a linear fluid effector  300  (e.g., a linear piston effector). In some implementations, the linear fluid effector  300  can be the example fluid effector  110  of  FIG. 1 . In general, this embodiment also relies on time of flight, but uses transverse waves propagating within the cylinder wall of the actuator instead of the hydraulic working fluid. 
     The linear fluid effector  300  includes a housing  312  having an inner surface  314  defining a cavity  316 . A moveable body  318  (e.g., a piston head in the illustrated example) is configured to move longitudinally within the cavity  316  to actuate a piston rod  319 . The housing  312  is generally tubular, having a first longitudinal end  313   a  and a second longitudinal end  313   b  opposite the first longitudinal end  313   a.    
     The moveable body  318  has a face  320   a  and a face  320   b  opposite the face  320   a . The moveable body  318  is configured for reciprocal movement within the housing  312  with a total stroke (represented by arrow  370 ). The moveable body  318  is configured to contact the inner surface  314  and subdivide the cavity  316  to define a fluid chamber  324   a  on the side of the face  320   a  and define a fluid chamber  324   b  on the side of the face  320   b.    
     The linear fluid effector  300  includes an acoustic transceiver  330   a . The acoustic transceiver  330   a  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  332   a  through the housing  312  toward a first side  320   a  of an acoustic interface  321 . The acoustic transceiver  330   a  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  333   a  based on a reflection of the emitted acoustic waveform  332   a  off the acoustic interface  321 . 
     The linear fluid effector  300  includes an acoustic transceiver  330   b . The acoustic transceiver  330   b  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  332   b  through the housing  312  toward a second side  320   b  of the acoustic interface  321 . The acoustic transceiver  330   b  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  333   b  based on a reflection of the emitted acoustic waveform  332   b  off the acoustic interface  321 . 
     The acoustic transceivers  330   a - 330   b  are configured to be activated by an external system such as the example signal processor  150  of  FIG. 1 , and provide signals based on the reflected acoustic waveforms  333   a - 333   b  to the external system for processing. In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     Transverse waves and/or surface acoustic waves are generated by acoustic transceivers  330   a - 330   b  located on opposing ends of the cylinder wall in intimate acoustic contact with the housing  312 . In some embodiments, the acoustic transceivers  330   a - 330   b  can be formed of bonded bulk ceramic, bulk single-crystal, or deposited piezoelectric layers, material films, or any other appropriate material that can form an integral part of the housing  312 . The acoustic transceivers  330   a - 330   b  are configured to generate a hoop stress in the housing  312  which propagates in the axial direction along the housing  312 . Transverse waves and surface acoustic waves cannot propagate within fluidic masses, substantially eliminating the effects of reverberation and cross coupling within the fluid that may otherwise interfere with measurement accuracy. The waves are reflected when they reach the moveable body  318 , being in intimate contact with the housing  312 , produces an abrupt acoustic impedance change in the propagation path. 
     In some implementations, this embodiment can be used in applications that cannot accommodate transducers in contact with the hydraulic fluid medium, cannot accommodate the required pressure ports into the hydraulic cylinder, would otherwise benefit from reduced size and location of the transducers, or require higher measurement accuracy than previous position indicators. In some implementations, sensor accuracy may not be substantially impacted compared to the echoes in the fluid. The acoustic transceivers  330   a - 330   b  may further be located within the inner diameter of the housing  312  in contact with the fluid, or externally on the outside of housing  312 . In some embodiments, the acoustic transceivers  330   a - 330   b  can be fashioned as removable transducers. For example, the use of removable transducers can enable the techniques described in this document to be applied or retrofitted to hydraulic or pneumatic fluidic actuators not originally designed or conceived to possess position sensing functionality at the time of manufacture. 
     The process of determining the position of the moveable member  318  is similar to that of the process described in relation to the example fluid effector  200  of  FIG. 2 , except that instead of transmitting and receiving the acoustic waveforms  232   a ,  232   b ,  233   a , and  233   b  though fluid in the fluid chambers  224   a  and  224   b  as in the example fluid effector  200 , the acoustic waveforms  332   a ,  332   b ,  333   a , and  333   b  are transmitted through the housing  312 . The emitted acoustic waveforms  332   a  and  332   b  are reflected by the acoustic interface  321  as the reflected acoustic waveforms  333   a  and  333   b.    
     In use, the times of flight of the emitted acoustic waveforms  332   a  and  332   b , and their return as the reflected acoustic waveforms  333   a  and  333   b  can be measured (e.g., times-of-flight) and used to determine the ratiometric position (and by extension, the absolute position) of the moveable member  318  and the piston rod  319 . For example, equations 1-3 discussed above can also be used with the times-of-flight determined from the linear fluid effector  300 . 
       FIG. 4  is a sectional view of an example of an acoustic interface  400 . In some examples, the acoustic interface  400  can be the example acoustic interface  321  of  FIG. 3 . In the illustrated example, a housing  412  includes an inner surface  414  that defines a cavity  416 . A seal  419  is configured to contact the inner surface  414  and a moveable body  418  to subdivide the cavity  416  into a fluid chamber  424   a  and a fluid chamber  424   b . The seal  419  contacts the housing  412  at a contact area  420 . 
     Acoustic impedance is defined as Z=ρ B V P , where P B  is the bulk density of the medium and is the longitudinal velocity of the wave in the medium. The housing  412  is made out a material that has a natural acoustic impedance, for example, due to the temperature, density, and other properties of the material from which the housing  412  is formed. In the illustrated example, the regions of the housing  412  having the natural acoustic impedance are represented by a light dither pattern and the identifier  450 . For example, the acoustic impedance of aluminum is about 17.10 g/cm 2 -sec×10 5 , and the acoustic impedance of 347 stainless steel is about 45.40 g/cm 2 -sec×10 5 . These are just two examples of acoustic impedances for two different materials. The techniques described in this document make it unnecessary to know, determine, or estimate the acoustic impedance of a material. 
     The housing  412  also includes a region of modified acoustic impedance represented by a denser dither pattern and the identifier  460 . In some embodiments, the effective acoustic impedance of a material can be affected by mechanical contact with or proximity to another object at or around the point of contact or proximity. For example, mechanical contact between the seal  419  and the housing  412  can acoustically dampen the housing  412  at or around the contact area  420  and increase the acoustic density of the housing  412  at or near the contact area  420 . In such examples, the region  460  can have a relatively higher acoustic impedance than the regions  450 . In another example, the seal  419  may have a lower acoustic impedance than the housing  412 , and mechanical contact between the seal  419  and the housing  412  can provide a path of lesser acoustic impedance for acoustic vibrations travelling along the housing  412  at or near the contact area  420 , effectively lowering the acoustic impedance of the acoustic transmission pathway in the region  460  relative to the regions  450 . 
     In general, when two sections of a transmission medium have different impedances, an impedance mismatch is presented. The boundaries between differing acoustic impedances define the locations of acoustic impedance mismatches, which are also called acoustic interfaces. In the illustrated example, acoustic waves traverse at the interface of the fluid and the housing (e.g., along the inner surface  414 ). The mismatch in impedance occurs when the fluid becomes the seal. The junctions where the inner surface  414 , the fluid, and the seal  419  coincide one another define an acoustic interface  470   a  and an acoustic interface  470   b.    
     As in many types if signal transmission processes, a signal that propagates along a transmission pathway and then encounters an impedance mismatch can result in at least a portion of the signal to be reflected back along the transmission pathway. Similarly, acoustic signals (e.g., the emitted acoustic waveforms  332   a  and  332   b ) can be reflected back toward their sources by acoustic interfaces. 
     In the illustrated example, the locations of the acoustic interfaces  470   a  and  470   b  within the housing  412  are defined by the location of the moveable body  418  within the cavity  416  (e.g., the moveable body  418  defines the location of the seal  419 , which defines the location of the region  460 , which defines the locations of the acoustic interfaces  470   a  and  470   b ). Movement of the moveable body  418  causes the acoustic interfaces  470   a  and  470   b  to move as well. 
     Returning briefly to  FIG. 3 , movement of the moveable body  318  causes corresponding movements of acoustic interfaces (e.g., the acoustic interfaces  470   a  and  470   b ) within the housing  312 . As the moveable body  318  moves, the distances between the acoustic transceivers  330   a  and  330   b  and their respective acoustic interfaces change as well, which causes proportional changes in the times-of-flight of the emitted acoustic waveforms  332   a  and  332   b  and the reflected acoustic waveforms  333   a  and  333   b . As discussed above, the times of flight can be used to determine the ratiometric position of the acoustic interfaces along the housing  312 , and therefore determine the position of the moveable member  318  within the cavity  316 . As also discussed above, these locations can be determined without knowing or determining the acoustic properties of the housing (e.g., the acoustic impedances of the housing or of regions of modified acoustic impedance, which can change dynamically with temperature). 
       FIG. 5  is a sectional view of an example of a rotary fluid effector  500 . In some implementations, the rotary fluid effector  500  can be the example fluid effector  110  of  FIG. 1 . The rotary fluid effector  500  includes a housing  512  having an inner surface  514  defining a cavity  516  that is generally cylindrical. A moveable body  518  (e.g., a rotary vane in the illustrated example) is configured to move semi-elliptically (e.g., rotate, pivot) about a central axis  511  of a shaft  519  within the cavity  516 . In some embodiments, the moveable body  518  can be configured to urge rotation of the shaft  519 . 
     The moveable body  518  is configured to contact the inner surface  514  (e.g., directly or through a seal) along a contact area  520  at or along an axial position of the generally cylindrical housing  512 . The materials used to form the housing  512  have an acoustic impedance, and the contact between the moveable body  518  and the housing  512  modified the acoustic impedance of the housing  512  at or around the contact area  520  to define a region  560  having a modified acoustic impedance. The region  560  presents an acoustic impedance mismatch within the housing  512 , having an acoustic interface  570   a  and an acoustic interface  570   b.    
     The rotary fluid effector  500  includes an acoustic transceiver  530 . The acoustic transceiver  530  includes an acoustic transmitter system configured to emit an emitted acoustic waveform  532   a  through the housing  512  toward the acoustic interface  570   a . The acoustic transceiver  530  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  533   a  based on a reflection of the emitted acoustic waveform  532   a  off the acoustic interface  570   a.    
     The acoustic transceiver  530  is also configured to emit an emitted acoustic waveform  532   b  through the housing  512  toward the acoustic interface  570   b  of the region  560 . The acoustic transceiver  530  also includes an acoustic receiver system configured to detect a reflected acoustic waveform  533   b  based on a reflection of the emitted acoustic waveform  532   b  off the acoustic interface  570   b . In the illustrated example, the acoustic transceiver  530  is configured to perform the transmission and receipt of the acoustic waveforms  532   a ,  532   b ,  533   a , and  533   b  (e.g., by “ringing” the housing  512  at a single location and having the emitted waveforms  532   a - 532   b  propagate away from both sides), but in some embodiments separate acoustic transceivers can be used (e.g., one configured to ring the periphery of the housing  512  in a clockwise direction and another configured to ring the periphery in a counter-clockwise direction). 
     The acoustic transceiver  530  is configured to be activated by an external system such as the example signal processor  150  of  FIG. 1 , and provide signals based on the reflected acoustic waveforms  533   a - 533   b  to the external system for processing. In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     The process of determining the position of the moveable body  518  is similar to that of the process described in relation to the example linear fluid effector  300  of  FIG. 3 , except that instead of transmitting and receiving the acoustic waveforms  332   a ,  332   b ,  333   a , and  333   b  along the longitudinal length of the housing  312  as in the example linear fluid effector  300 , the acoustic waveforms  532   a ,  532   b ,  533   a , and  533   b  are transmitted circumferentially (e.g., orbitally) about the housing  512 . The emitted acoustic waveforms  532   a  and  532   b  are reflected by the acoustic interface  521  as the reflected acoustic waveforms  533   a  and  533   b.    
     In use, the times of flight of the emitted acoustic waveforms  532   a  and  532   b , and their return as the reflected acoustic waveforms  533   a  and  533   b  can be measured (e.g., times-of-flight) and used to determine the ratiometric position (and by extension, the absolute position) of the moveable body  518  and the shaft  519 . For example, equations 1-3 discussed above can also be used with the times-of-flight determined from the rotary fluid effector  500 . 
     In some embodiments, the rotary fluid effector  500  can be a rotary vane actuator (RVA) or a rotary valve. In some embodiments, the rotary fluid effector can be modified to be a rotary piston actuator (RPA). For example, emitted waveforms can be transmitted circumferentially about a tubular housing toward the end of a rotary piston that is configured to move about the axis of the housing and define an acoustic interface within a portion of the housing, and the acoustic interface can reflect a portion of the waveforms for use in determining the rotary position of the rotary piston. 
       FIG. 6  is a conceptual diagram  600  of a transmitted acoustic waveform  610 .  FIG. 7  is a graph  700  showing examples of phase shifts in acoustic waveforms. In addition to time based measurement (e.g., as discussed above), time and phase are related to one another as a function of frequency and wavelength. In the illustrated example, the transmitted acoustic waveform  610  is transmitted by an acoustic transceiver  620  as a continuous wave of single frequency f. The transmitted acoustic waveform  610  is broadcast toward a moveable reflector  630  positioned at some distance D from the reflector. The transmitted acoustic waveform  610  is reflected back toward the acoustic transceiver  620 , and reaches the acoustic transceiver  620  after making a round trip of length L=2D. 
     The acoustic transceiver  620  travels some whole number n of wavelengths plus a fraction, where wavelength is given by: 
     
       
         
           
             
               
                 
                   
                     λ 
                     = 
                     
                       
                         
                           c 
                           / 
                           f 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         where 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         c 
                       
                       = 
                       
                         sound 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         speed 
                       
                     
                   
                   , 
                   
                     f 
                     = 
                     
                       wave 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       frequency 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     Using Equation 4, the round trip distance to target can be written as: 
     
       
         
           
             
               
                 
                   D 
                   = 
                   
                     
                       ( 
                       
                         
                           n 
                           1 
                         
                         + 
                         
                           ϕ 
                           
                             2 
                             ⁢ 
                             π 
                           
                         
                       
                       ) 
                     
                     × 
                     
                       λ 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     1 
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         1 
                       
                       ⁢ 
                       
                         T 
                         1 
                       
                     
                     = 
                     
                       
                         4 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           1 
                         
                         ⁢ 
                         
                           d 
                           1 
                         
                       
                       c 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     1 
                   
                   = 
                   
                     
                       ϕ 
                       1 
                     
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     2 
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                       ⁢ 
                       
                         T 
                         2 
                       
                     
                     = 
                     
                       
                         4 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           2 
                         
                         ⁢ 
                         
                           d 
                           2 
                         
                       
                       c 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     2 
                   
                   = 
                   
                     
                       ϕ 
                       2 
                     
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
     Where the ϕ/2π term is equivalent to time as shown in Equations 7 and 9. If n 1 =0, Equation 2 is unambiguous and since the frequency f and fluid sound speed are known apriori, D can be determined by direct measurement of the phase of the received signal relative to the transmitted signal. 
     When n 1 &gt;1, D is ambiguous as the measured phase values repeat at intervals of 2πf. The value n 1  can be extracted from the measured data based on the idea that the differential phase shift of two simultaneously propagating waves of differing frequencies will generate progressively larger phase shifts; the value of the increase is a constant φ d  as the travel time increases. This is shown in  FIG. 7 . Detecting the two signals at some distance D and knowing they began traveling at the same time the measured phase can be divided by φ d  to extract the number of complete wave periods that occurred to generate the measured phase difference. Mathematically: 
     
       
         
           
             
               
                 
                   
                      
                     
                       
                         ϕ 
                         1 
                       
                       - 
                       
                         ϕ 
                         2 
                       
                     
                      
                   
                   = 
                   
                     
                       D 
                       ⁡ 
                       
                         ( 
                         
                           
                             1 
                             
                               λ 
                               1 
                             
                           
                           - 
                           
                             1 
                             
                               λ 
                               2 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ϕ 
                       
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     The phase difference embodiment modifies the time difference embodiment by applying a fixed frequency f 1  to the phase measurement in one of the fluid chambers, and another fixed frequency f 2  to the other fluid chamber. The exact frequency values of f 1  and f 2  are not critical to the function of the invention, however it is critical that the frequencies are selected to ensure that n 1 =n 2  or n 1 =n 2 +1. This relationship ensures that the value of god remains constant over the entire measurement range. 
     Rewriting Equation 3, using Equations 7 and 9: 
     
       
         
           
             
               
                 
                   
                     Stroke 
                     ∼ 
                     
                       
                         
                           t 
                           1 
                         
                         - 
                         
                           t 
                           2 
                         
                       
                       
                         
                           t 
                           1 
                         
                         + 
                         
                           t 
                           2 
                         
                       
                     
                     ∼ 
                     
                       
                         
                           
                             ϕ 
                             1 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               1 
                             
                           
                         
                         - 
                         
                           
                             ϕ 
                             2 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             ϕ 
                             1 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               1 
                             
                           
                         
                         + 
                         
                           
                             ϕ 
                             2 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               2 
                             
                           
                         
                       
                     
                   
                   = 
                   
                     
                        
                       
                         
                           ϕ 
                           1 
                         
                         - 
                         
                           
                             
                               f 
                               1 
                             
                             
                               f 
                               2 
                             
                           
                           ⁢ 
                           
                             ϕ 
                             2 
                           
                         
                       
                        
                     
                     
                        
                       
                         
                           ϕ 
                           1 
                         
                         + 
                         
                           
                             
                               f 
                               1 
                             
                             
                               f 
                               2 
                             
                           
                           ⁢ 
                           
                             ϕ 
                             2 
                           
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
     The phase embodiment maintains the same ratiometric benefits of mechanical length and sound speed insensitivity as the time of flight embodiment. The frequency f 1  is related to f 2  by a fixed ratio. This condition ensures the relative phase difference remains constant with circuit aging and temperature change. Other embodiments can remove this restriction with the result of reduced aging performance and temperature compensation without substantively altering the method. 
     Ultrasonic pulses are emitted periodically as is prescribed for position measurement. Following each emission, the returned echo signal is sampled at a fixed delay after the emission. From Equations 13 and 14, this delay defines the depth. 
     As the actuator moves between the successive emissions the sampled values taken at time T s  will change over the time. As the speed information is available only periodically, the technique is limited by the Nyquist theorem. This means that a maximum speed exists for each pulse repetition frequency (F prf ): 
     
       
         
           
             
               
                 
                   
                     V 
                     max 
                   
                   = 
                   
                     
                       
                         F 
                         prf 
                       
                       * 
                       C 
                     
                     
                       4 
                       * 
                       
                         F 
                         e 
                       
                       * 
                       cos 
                       ⁢ 
                       δ 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ) 
                 
               
             
           
         
       
     
     The maximum measurable depth is also defined by the pulsed repetition frequency: 
     
       
         
           
             
               
                 
                   
                     P 
                     max 
                   
                   = 
                   
                     C 
                     
                       2 
                       * 
                       
                         F 
                         prf 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ) 
                 
               
             
           
         
       
     
     Therefore the product of P max  and V max  is constant, and is given by: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       max 
                     
                     * 
                     
                       V 
                       max 
                     
                   
                   = 
                   
                     
                       C 
                       2 
                     
                     
                       8 
                       * 
                       
                         F 
                         s 
                       
                       * 
                       cos 
                       ⁢ 
                       δ 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 8  is a flow diagram of an example process  800  for ultrasonic position sensing. In some implementations, the process  800  can be performed by all or part of the example system  100  of  FIG. 1 , the example fluid effector  110 , the example linear fluid effector  200  of  FIG. 2 , the example linear fluid effector  300  of  FIG. 3 , or the example rotary fluid effector  500  of  FIG. 5 . 
     At  810 , a first emitted acoustic waveform is emitted in a first direction through an acoustic medium having a first acoustic impedance toward a first side of an acoustic interface. For example, the acoustic transceiver  130   a  can emit the emitted acoustic waveform  132   a  toward the face  120  of the moveable body  118  through a fluid in the cavity  116 . In another example, the acoustic transceiver  530  can emit the emitted acoustic waveform  532   a  toward the acoustic interface  570   a  of the moveable body  518  through the housing  512 . 
     At  820 , a second emitted acoustic waveform is emitted in a second direction, opposite the first direction, through the acoustic medium toward a second side of the acoustic interface opposite the first side. For example, the acoustic transceiver  130   b  can emit the emitted acoustic waveform  132   b  toward the face  122  of the moveable body  118  through a fluid in the cavity  116 . In another example, the acoustic transceiver  530  can emit the emitted acoustic waveform  532   b  toward the acoustic interface  570   b  through the housing  512 . 
     At  830 , a first reflected acoustic waveform is reflected by the acoustic interface in the second direction based on the first emitted acoustic waveform. For example, the face  120  can reflect the reflected acoustic waveform  133   a  back toward the acoustic transceiver  130   a . In another example, the acoustic interface  570   a  can reflect the reflected acoustic waveform  533   a  back toward the acoustic transceiver  530 . 
     At  840 , a second reflected acoustic waveform is reflected by the acoustic interface in the first direction based on the second emitted acoustic waveform. For example, the face  122  can reflect the reflected acoustic waveform  133   b  back toward the acoustic transceiver  130   b . In another example, the acoustic interface  570   b  can reflect the reflected acoustic waveform  533   b  back toward the acoustic transceiver  530 . 
     At  850 , a first position of the acoustic interface is determined based on the first reflected acoustic waveform and the second acoustic waveform. For example, measurements based on the emitted acoustic waveforms  132   a ,  132   b ,  133   a , and  133   b , or the acoustic waveforms  532   a ,  532   b ,  533   a , and  533   b  can be used with Equations 1-14 to determine the positions of the moveable bodies  118  or  518 . 
     In some implementations, the process  800  can also include determining a first time of flight based on the first emitted acoustic waveform and the first reflected acoustic waveform, and determining a second time of flight based on the second emitted acoustic waveform and the second reflected acoustic waveform, where determining a first position of the acoustic interface is further based on the first time of flight and the second time of flight. In some implementations, determining the first position of the acoustic interface based on the first time of flight (t 1 ) and the second time of flight (t 2 ) is given by an equation: (t 1 −t 2 )/(t 1 +t 2 ). For example, Equation 3 shows an example of how times of flight of reflected acoustic waveforms can be used to determine a ratiometric position of the acoustic interface that caused the reflections. 
     In some implementations, the process  800  can also include determining a second position of the acoustic interface, and determining a speed of the acoustic interface based on the first positon and the second position. For example, by determining a first position of the moveable body  118 , a second position of the moveable body  118 , and the amount of time between the two positions, a speed at which the moveable body  118  is moving can be determined. 
     In some implementations, the process  800  can include determining a reflected acoustic frequency based on one or both of the first reflected acoustic waveform and the second acoustic waveform, and determining a speed of the acoustic interface based on the determined reflected acoustic frequency and a predetermined emitted acoustic frequency of one or both of the first emitted acoustic waveform and the second emitted acoustic waveform. For example, the emitted acoustic waveforms  132   a  and  132   b  can be emitted at a predetermined emitted frequency, and movement of the example moveable body  118  can cause a Doppler shift in the reflected acoustic waveforms  133   a  and  113   b . The degree of the Doppler shift can be measured to determine a speed of the moveable body  118  relative to the acoustic transceivers  130   a  and  130   b.    
     In some implementations, the acoustic medium can be a fluid having a first acoustic impedance, the acoustic interface can be defined by a moveable body within a fluid effector and having a second acoustic impedance that is different than the first acoustic impedance, the first emitted acoustic waveform can be emitted toward a first face of the moveable body through the fluid, the second emitted acoustic waveform can be emitted toward a second face of the moveable body, arranged opposite the first face, through the fluid, the first reflected acoustic waveform can be based on a first reflection of the first emitted acoustic waveform by the first face, and the second reflected acoustic waveform can be based on a second reflection of the second emitted acoustic waveform by the second face. For example, the emitted acoustic waveforms  132   a  and  132   b  can travel through a fluid in the cavity  116  to the face  120  and the face  122 , and be reflected back through the fluid to the acoustic transceivers  130   a  and  130   b.    
     In some implementations, the acoustic medium can be a housing of a fluid effector, the housing having a first acoustic impedance and defining a cavity, and also including contacting a portion of the housing with a moveable body configured for movement within the cavity, and modifying, based on the contacting, the first acoustic impedance of the contacted portion of the housing to define a portion of the housing having a second acoustic impedance that is different from the first acoustic impedance, where the contacted portion of the housing defines the acoustic interface. For example, contact between the example seal  419  and the example housing  412  can develop the region of modified acoustic impedance  460 . 
     In some implementations, the process  800  can also include determining a phase difference between at least one of (1) a first emitted phase of the first emitted acoustic waveform and a first reflected phase of the first reflected acoustic waveform, and (2) a second emitted phase of the second emitted acoustic waveform and a second reflected phase of the second reflected acoustic waveform, wherein determining a first position of the acoustic interface is further based on the determined phase difference. For example, the differences in phase between the emitted acoustic waveform  132   a  and the reflected acoustic waveform  133   a  can be used (e.g., in the example Equations 4-14) to determine a position of the moveable body  118 . 
     All of the embodiments described can provide, in addition to position, direct measurement of actuator speed by the incorporation of signal processing to extract Doppler shift information (e.g., reflected frequency) from the transducer(s) signals. While only one of the plurality of transducers is required to be processed, Doppler processing of two transducers can provide higher accuracy by a factor of about 1.4× over the use of a single channel. 
       FIG. 9  shows an example of a system  900  for ultrasonic position measurement (e.g., a position sensor system). The system  900  includes a fluid effector  910 . The fluid effector  910  includes a sensor housing  912  defining a cavity  920  having a face  922 . The fluid effector  910  also includes an actuator housing  914  having an inner surface  931  defining a cavity  930 . The cavities  920  and  930  are fluidically connected by a passage  980 . A moveable body  938  is configured for reciprocal movement within the cavity  930 . The moveable body  938  has a face  932 . 
     In the illustrated example, the sensor housing  912  and the actuator housing  914  are a unified housing that includes both of the cavities  920  and  930 . As will be discussed in the description of  FIG. 15 , the sensor housing and the actuator housing may be separate housings. 
     The system  900  includes an acoustic transceiver  940   a  that is configured as an acoustic transmitter or acoustic emitter to emit an emitted acoustic waveform  942   a  toward the face  922 . The acoustic transceiver  940   a  is also configured as an acoustic receiver configured to detect a reflected acoustic waveform  944   a  based on a reflection of the emitted acoustic waveform  942   a  off the face  922 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     The system  900  includes an acoustic transceiver  940   b  that is configured as an acoustic transmitter or acoustic emitter to emit an emitted acoustic waveform  942   b  toward the face  932 . The acoustic transceiver  940   b  is also configured as an acoustic receiver configured to detect a reflected acoustic waveform  944   b  based on a reflection of the emitted acoustic waveform  942   b  off the face  932 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     A signal processor  960  is configured to process signals from the acoustic transceiver  940   a  and the acoustic transceiver  940   b  to determine the position of the moveable body  938  within the cavity  930 . A controller  970  (e.g., a computer) is configured to receive position information from the signal processor  960  and perform functions based on the position information (e.g., control a process, present information to a user, transmit information to another system, record a log). In some embodiments, the signal processor  960  can include a timer (e.g., to measure the times of flight of emitted and reflected signals). In some embodiments, the signal processor  960  can include a phase detector (e.g., to determine phase and/or Doppler shifts in reflected signals). 
     In general, the fluid effector  910  is configured as a ratiometric position-sensing device. The acoustic transceiver  940   a  is configured to sound a known, fixed distance  950   a  to the face  922 , whereas the acoustic transceiver  940   b  is configured to sound the variable distance  950   b  to the face  932  of the moveable body  938 . Time measurements of the two acoustic transceivers  940   a ,  940   b  can be used to determine the position of the moveable body  938  when sound speed is known. However, when coupling two transducers into a system, sound speed is cancelled and a ratiometric ultrasound position sensor is obtained. The passage  980  is provided to improve equalization of fluid temperatures in the cavities  920 ,  930  to improve equalization of the speed of sound in the fluids that occupy the cavities  920 ,  930 . In some implementations, if either transducer fails, redundancy can be obtained through measurement or approximation of sound speed. The techniques for processing the signals, and several embodiments of the fluid effector  910 , will be discussed in the descriptions of  FIGS. 16-26 . 
     In the illustrated example shown in  FIG. 9 , the fluid effector is configured as a linear (e.g., piston) actuator.  FIG. 10  shows another example of a system  1000  for ultrasonic position measurement. The system  1000  is substantially similar to the example system  900 , except the system  1000  includes a fluid effector  1010  that is configured as a valve. 
     The fluid effector  1010  includes the sensor housing  1012  defining a cavity  1020  having a face  1022 . The fluid effector  1010  also includes an actuator housing  1014  having an inner surface  1031  defining a cavity  1030 . A moveable body  1038  is configured for reciprocal movement within the cavity  1030 . The moveable body  1038  has a face  1032 . In the illustrated example, the moveable body  1038  is configured as a valve body. 
     In the illustrated example, the sensor housing  1012  and the actuator housing  1014  are a unified housing that includes both of the cavities  1020  and  1030 . As will be discussed in the description of  FIG. 15 , the sensor housing and the actuator housing may be separate housings. 
     The system  1000  includes an acoustic transceiver  1040   a  that is configured as an acoustic transmitter or acoustic emitter to emit an emitted acoustic waveform  1042   a  toward the face  1022 . The acoustic transceiver  1040   a  is also configured as an acoustic receiver configured to detect a reflected acoustic waveform  1044   a  based on a reflection of the emitted acoustic waveform  1042   a  off the face  1022 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     The system  1000  includes an acoustic transceiver  1040   b  that is configured as an acoustic transmitter or acoustic emitter to emit an emitted acoustic waveform  1042   b  toward the face  1032 . The acoustic transceiver  1040   b  is also configured as an acoustic receiver configured to detect a reflected acoustic waveform  1044   b  based on a reflection of the emitted acoustic waveform  1042   b  off the face  1032 . In some embodiments, a single transducer (e.g., a piezo element) can perform the functions of both the acoustic transmitter and the acoustic receiver. In some embodiments, the acoustic transmitter and the acoustic receiver can be discrete components. 
     A signal processor  1060  is configured to process signals from the acoustic transceiver  1040   a  and the acoustic transceiver  1040   b  to determine the position of the moveable body  1038  within the cavity  1030 . A controller  1070  (e.g., a computer) is configured to receive position information from the signal processor  1060  and perform functions based on the position information (e.g., control a process, present information to a user, transmit information to another system, record a log). In some embodiments, the signal processor  1060  can include a timer (e.g., to measure the times of flight of emitted and reflected signals). In some embodiments, the signal processor  1060  can include a phase detector (e.g., to determine phase and/or Doppler shifts in reflected signals). 
       FIG. 11  is a conceptual sectional view of an example linear fluid effector  1100 . In the illustrated example, the effector  1100  is defined by a housing  1102  with an inner surface  1104  that defines a cavity  1106 . 
     A moveable member  1110  is configured for axial movement within a portion  1120  of the cavity  1106 . The portion  1120  is sized to contact the moveable body  1110  and partly define a fluid chamber having a cross-sectional area  1121 , and can be pressurized to urge linear movement of the moveable body  1110 . 
     A portion  1122  of the cavity  1106  is arranged axially adjacent to the portion  1120 , and has an axial cross-sectional area  1123  that is larger than the cross-sectional area  1121  of the portion  1120 . A face portion  1130  is defined by an axial shoulder transition between the cross-sectional area  1121  and the cross-sectional area  1123 . 
     The portion  1120  and the portion  1122  together define a unified cavity in which fluid (e.g., fuel) is free to move between the portions  1120 ,  1122  and maintain a substantially even distribution of temperatures throughout the cavity  1106 . In the illustrated example, the portion  1122  is coaxially larger than the portion  1120  in cross-section. In some embodiments, the portion  1122  may be axially offset asymmetrically from the portion  1122 . In some embodiments, the portion  1122  may be at least partly discontinuous from the portion  1120 . 
     An acoustic transceiver  1140  is arranged at an axial end of the housing  1102 . The acoustic transceiver  1140  is configured to emit an emitted acoustic signal  1150  toward both the moveable body  1110  and the face portion  1130 . The face portion  1130  reflects a portion of the emitted acoustic signal  1150  back toward the acoustic transceiver  1140  as a reflected acoustic signal  1152 . The face portion  1112  of the moveable body  1110  reflects another portion of the emitted acoustic signal  1150  back toward the acoustic transceiver  1140  as a reflected acoustic signal  1154 . 
     In operation, a signal processor (e.g., the example signal processor  960  of  FIG. 9 ) can activate the acoustic transceiver  1140  to emit the emitted acoustic signal  1150  and use the acoustic transceiver  1140  to sense the reflected acoustic signals  1152  and  1154 . The signal processor can determine a time of flight for both the reflected acoustic signals  1152  and  1154  to determine the position of the moveable body  1110  within the cavity  1106 . The techniques for processing the signals will be discussed in the descriptions of  FIGS. 16-26 . 
       FIG. 12  is a conceptual sectional view of another example linear fluid effector  1200 . In general, the linear fluid effector  1200  is a modification of the example linear fluid effector  1100  of  FIG. 11 , in which the acoustic transceiver  1140  has been replaced by an acoustic transceiver  1240 . 
       FIG. 13  is an end view of the example acoustic transceiver  1240  of  FIG. 12 . The acoustic transceiver  1240  includes an acoustic transceiver portion  1242  that at least partly coaxially surrounds an acoustic transceiver portion  1244 . The acoustic transceiver portion  1242  is sized based on the cross-sectional area  1123 , and the acoustic transceiver portion  1244  is sized based on the cross-sectional area  1121 . The acoustic transceiver portion  1244  is configured to emit an emitted acoustic signal  1250  toward the moveable body  1110 , and the acoustic transceiver portion  1242  is configured to emit an emitted acoustic signal  1251  toward the face portion  1130 . The face portion  1130  reflects a portion of the emitted acoustic signal  1251  back toward the acoustic transceiver portion  1242  as a reflected acoustic signal  1252 . The face portion  1112  of the moveable body  1110  reflects a portion of the emitted acoustic signal  1250  back toward the acoustic transceiver portion  1244  as a reflected acoustic signal  1254 . 
     The acoustic transceiver portions  1242 ,  1244  are separately operable and readable by a signal processor (e.g., the example signal processor  960  of  FIG. 9 ). The signal processor can determine a time of flight for both the reflected acoustic signals  1252  and  1254  to determine the position of the moveable body  1110  within the cavity  1106 . The techniques for processing the signals will be discussed in the descriptions of  FIGS. 16-26 . 
       FIG. 14  is an end view of another example acoustic transceiver  1400 . In some embodiments, the acoustic transceiver  1400  can be substituted for the example acoustic transceiver  1240  of  FIGS. 12-13 . 
     The acoustic transceiver  1400  includes an acoustic transceiver portion  1242  that is radially offset from an acoustic transceiver portion  1444 . The acoustic transceiver portion  1442  is sized based on the cross-sectional area  1121 , and the acoustic transceiver portion  1444  is sized based on the cross-sectional area  1123 . The acoustic transceiver portion  1444  is configured to emit an emitted acoustic signal toward the example moveable body  1110 , and the acoustic transceiver portion  1442  is configured to emit an emitted acoustic signal toward the example face portion  1130 . The face portion  1130  reflects a portion of the acoustic signal emitted by the acoustic transceiver portion  1442  back toward the acoustic transceiver portion  1442  as a reflected acoustic signal. The face portion  1112  of the moveable body  1110  reflects a portion of the acoustic signal emitted by the acoustic transceiver portion  1444  back toward the acoustic transceiver portion  1444  as a reflected acoustic signal. 
     The acoustic transceiver portions  1442 ,  1444  are separately operable and readable by a signal processor (e.g., the example signal processor  960  of  FIG. 9 ). The signal processor can determine a time of flight for both the reflected acoustic signals to determine the position of the moveable body  1110  within the cavity  1106 . The techniques for processing the signals will be discussed in the descriptions of  FIGS. 16-26 . 
     The acoustic transceiver  1440  also includes an acoustic transceiver portion  1446  that is radially offset from an acoustic transceiver portion  1444 . The acoustic transceiver portion  1444  is sized based on the cross-sectional area  1123 . The acoustic transceiver portion  1446  is configured to emit an emitted acoustic signal toward the example face portion  1130 . The face portion  1130  reflects a portion of the acoustic signal emitted by the acoustic transceiver portion  1446  back toward the acoustic transceiver portion  1446  as a reflected acoustic signal. In some embodiments, the acoustic transceiver portions  1442  and  1146  are part of a single acoustic transceiver device that is separately operable and measurable from the acoustic transceiver portion  1444 . In some embodiments, the acoustic transceiver portion  1446  is separately operable and measurable from the acoustic transceiver portion  1442  and  1144 . For example, the acoustic transceiver portion  1446  can be used redundantly in cooperation with the acoustic transceiver portion  1442 . 
       FIG. 15  is a schematic diagram of an example fluid effector system  1500 . The system  1500  includes an acoustic fluid measurement module  1502   a  and an acoustic fluid measurement module  1502   b . Each of the acoustic fluid measurement modules  1502   a ,  1502   b  includes a sensor housing  1504  that defines a cavity  1505  having a predetermined length and a face  1507 , and an acoustic transceiver  1506  configured to perform a time-of-flight measurement of the length of the cavity  1505 . The acoustic fluid measurement modules  1502   a ,  1502   b  are operable and readable by a signal processor  1560  and a controller  1570  to determine time of flight of acoustic signals within the acoustic fluid measurement modules  1502   a ,  1502   b . In some embodiments, the acoustic fluid measurement modules  1502   a ,  1502   b  can provide functionality similar to that of the example acoustic transceivers  940   a  and/or  1040   a  of  FIGS. 9 and 10 . 
     The system  1500  also includes a collection of fluid effectors  1510   a - 1510   c , each having an actuator housing  1512  defining a cavity  1516  in which a moveable body  1514  having a face  1517  is configured to move axially. In various embodiments, each of the fluid effectors  1510   a - 1510   c  can be any appropriate form of fluid effector, such as a linear fluid actuator or a fluid actuated valve. Each of the fluid effectors  1510   a - 1510   c  also includes an acoustic transceiver  1518  configured to perform a time-of-flight measurement of the length of the cavity  1516 . The acoustic transceivers  1518  are operable and readable by the signal processor  1560  and the controller  1570  to determine times of flights of acoustic signals within fluid effectors  1510   a - 1510   c . In some embodiments, the acoustic transceivers  1518  can provide functionality similar to that of the example acoustic transceivers  940   b  and/or  1040   b  of  FIGS. 9 and 10 . 
     In the illustrated example, the system  1500  is shown with two acoustic fluid measurement modules and three fluid effectors, though any appropriate number of one or more acoustic fluid measurement modules and any appropriate number of one or more fluid effectors can be used. For example, a single acoustic fluid measurement module can be used to provide a baseline measurement, or multiple acoustic fluid measurement modules can be used to provide redundancy. In another example, one or more baseline measurements from one or a collection of acoustic measurement modules can be used with one, two, three, five, ten, twenty, or any other appropriate number of fluid effectors. 
     In very general terms, the acoustic fluid measurement modules  1502   a ,  1502   b  can be used to provide (e.g., redundant) baseline measurements against which the measurements by the acoustic transceivers  1518  can be compared to determine the positions of the moveable bodies  1514 . In operation, operative fluid (e.g., fuel) flows along a supply passage  1540 , through the acoustic fluid measurement modules  1502   a ,  1502   b  to the fluid effectors  1510   a - 1510   c , and out through a return passage  1542 . The signal processor  1560  can activate the acoustic transceivers  1506  to emit emitted acoustic signals and use the acoustic transceivers  1506  to sense the reflected acoustic signals. The signal processor can determine a time of flight of the reflected acoustic signals within the known lengths of the cavities  1505 . The signal processor  1560  can activate the acoustic transceivers  1518  to emit emitted acoustic signals and use the acoustic transceivers  1518  to sense the reflected acoustic signals to determine the times of flights of the signals due to the positions of the moveable bodies  1514  within the cavities  1516 . The signal processor  1560  can compare the times of flights from the acoustic fluid measurement modules  1502   a ,  1502   b  to the times of flights from the fluid effectors  1510   a - 1510   c  to determine the positions of the moveable bodies  1514  within the cavities  1516 . The techniques for processing the signals will be discussed in the descriptions of  FIGS. 16-26 . 
       FIGS. 16-26  show examples of various systems that can be used to perform positional measurement and control using apparatus such as the examples shown and described above. 
     To improve system sizing, two ultrasound sensors are implemented on either chamber of a fluid effector. The ultrasound sensor transmits a signal which reflects off the effector and is received by the transducer. The measured time in conjunction with the sound speed defines the distance to the effector (see Equation 1). When coupling two transducers together the other chamber follows the same form (see Equation 2). 
     The transducers and the effector can be configured such that the signals are used as a ratio metric device, rather: 
     
       
         
           
             
               
                 
                   Stroke 
                   ∼ 
                   
                     
                       
                         t 
                         1 
                       
                       - 
                       
                         t 
                         2 
                       
                     
                     
                       
                         t 
                         1 
                       
                       + 
                       
                         t 
                         2 
                       
                     
                   
                   ∼ 
                   
                     
                       
                         
                           L 
                           1 
                         
                         
                           C 
                           1 
                         
                       
                       - 
                       
                         
                           L 
                           2 
                         
                         
                           C 
                           2 
                         
                       
                     
                     
                       
                         
                           L 
                           1 
                         
                         
                           C 
                           1 
                         
                       
                       + 
                       
                         
                           L 
                           2 
                         
                         
                           C 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ) 
                 
               
             
           
         
       
     
     Since C 1 ˜C 2 , as a ratio metric device, the effects of sound speed characteristics are cancelled out and not required for evaluation of position. In addition to time based measurement, time, and phase are related to one another as a function of frequency and wavelength. A continuous wave of single frequency f is broadcast toward a moveable reflector positioned at some distance D from the reflector. The wave is reflected back toward the transducer and reaches the transducer after making a round trip of length L=2D. The wave travels some whole number n of wavelengths plus a fraction, where wavelength is given by: 
     
       
         
           
             
               
                 
                   λ 
                   = 
                   
                     c 
                     f 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ) 
                 
               
             
           
         
       
     
     Where c=sound speed, and f=wave frequency. Using Equation 16, the round trip distance to target can be written as: 
     
       
         
           
             
               
                 
                   D 
                   = 
                   
                     
                       ( 
                       
                         
                           n 
                           1 
                         
                         + 
                         
                           ϕ 
                           
                             2 
                             ⁢ 
                             π 
                           
                         
                       
                       ) 
                     
                     × 
                     
                       λ 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     1 
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         1 
                       
                       ⁢ 
                       
                         T 
                         1 
                       
                     
                     = 
                     
                       
                         4 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           1 
                         
                         ⁢ 
                         
                           d 
                           1 
                         
                       
                       c 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     1 
                   
                   = 
                   
                     
                       ϕ 
                       1 
                     
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     2 
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                       ⁢ 
                       
                         T 
                         2 
                       
                     
                     = 
                     
                       
                         4 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           2 
                         
                         ⁢ 
                         
                           d 
                           2 
                         
                       
                       c 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     2 
                   
                   = 
                   
                     
                       ϕ 
                       2 
                     
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ) 
                 
               
             
           
         
       
     
     Where the ϕ/2π term is equivalent to time as per (19) and (21). If n 1 =0, (15) is unambiguous and since the frequency f and fluid sound speed are known a priori D can be determined by direct measurement of the phase of the received signal relative to the transmitted signal. 
     When n 1 &gt;1, D is ambiguous as the measured phase values repeat at intervals of 2πf. The value n 1  can be extracted from the measured data based on the idea that the differential phase shift of two simultaneously propagating waves of differing frequencies will generate progressively larger phase shifts; the value of the increase is a constant φ d  as the travel time increases. Detecting the two signals at some distance D and knowing they began traveling at the same time the measured phase can be divided by φ d  to extract the number of complete wave periods that occurred to generate the measured phase difference. 
     Mathematically, 
     
       
         
           
             
               
                 
                   
                      
                     
                       
                         ϕ 
                         1 
                       
                       - 
                       
                         ϕ 
                         2 
                       
                     
                      
                   
                   = 
                   
                     
                       D 
                       ( 
                       
                         
                           1 
                           
                             λ 
                             1 
                           
                         
                         - 
                         
                           1 
                           
                             λ 
                             2 
                           
                         
                       
                       ) 
                     
                     = 
                     
                       Δϕ 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ) 
                 
               
             
           
         
       
     
     The phase difference embodiment modifies the time difference embodiment by applying a fixed frequency f 1  to the phase measurement in one of the fluid chambers, and another fixed frequency f 2  to the other fluid chamber. The exact frequency values of f 1  and f 2  are not critical to the function of the invention, however it is critical that the frequencies are selected to ensure that n 1 =n 2  or n 1 =n 2 +1. This relationship ensures that the value of φ d  remains constant over the entire measurement range. 
     Rewriting (15) using (19), (21): 
     
       
         
           
             
               
                 
                   
                     Stroke 
                     ~ 
                     
                       
                         
                           
                             ϕ 
                             1 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               1 
                             
                           
                         
                         - 
                         
                           
                             ϕ 
                             2 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             ϕ 
                             1 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               1 
                             
                           
                         
                         + 
                         
                           
                             ϕ 
                             2 
                           
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               2 
                             
                           
                         
                       
                     
                   
                   = 
                   
                      
                     
                       
                         
                           ϕ 
                           1 
                         
                         - 
                         
                           
                             
                               f 
                               1 
                             
                             
                               f 
                               2 
                             
                           
                           ⁢ 
                           
                             ϕ 
                             2 
                           
                         
                       
                       
                         
                           ϕ 
                           1 
                         
                         + 
                         
                           
                             
                               f 
                               1 
                             
                             
                               f 
                               2 
                             
                           
                           ⁢ 
                           
                             ϕ 
                             2 
                           
                         
                       
                     
                      
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ) 
                 
               
             
           
         
       
     
     The phase embodiment maintains the same ratiometric benefits of mechanical length and sound speed insensitivity as the time of flight embodiment. The frequency f 1  is related to f 2  by a fixed ratio. This condition ensures the relative phase difference remains constant with circuit aging and temperature change. Other embodiments can remove this restriction with the result of reduced aging performance and temperature compensation without substantively altering the method. 
     As an extension of the linearized ratio metric position sensors of  FIG. 1-8 , a modification can be made to place the transceiver elements in more preferential locations. In the examples of  FIGS. 9-15 , this is achieved by positioning a transceiver element (XDCR 1 ) in reflective communication with an effector, and a second transceiver element (XDCR 2 ) located in a static chamber sharing common fluid (e.g., fuel), and therefore approximate physical properties with the first transceiver element (XDCR 1 ). The result of a static reference is a logarithmic differential/sum output which will be outlined below. The transceiver element XDCR 1  transmits a signal which reflects off the effector and is received by the transceiver. The measured time in conjunction with the sound speed defines the distance to the effector: 
     
       
         
           
             
               
                 
                   
                     L 
                     1 
                   
                   = 
                   
                     
                       t 
                       1 
                     
                     × 
                     
                       C 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ) 
                 
               
             
           
         
       
     
     The transceiver element XDCR 2  of the static chamber follows a similar form: 
     
       
         
           
             
               
                 
                   
                     L 
                     2 
                   
                   = 
                   
                     
                       t 
                       2 
                     
                     × 
                     
                       C 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     25 
                   
                   ) 
                 
               
             
           
         
       
     
     The fuel of the second transceiver element XDCR 2  in the static chamber is supplied from a shared source as the first transceiver element XDCR 1 . The transducers and the effector can be configured such that the signals are used as a ratiometric device, rather: 
     
       
         
           
             
               
                 
                   Stroke 
                   ~ 
                   
                     
                       
                         t 
                         1 
                       
                       - 
                       
                         t 
                         2 
                       
                     
                     
                       
                         t 
                         1 
                       
                       + 
                       
                         t 
                         2 
                       
                     
                   
                   ~ 
                   
                     
                       
                         
                           L 
                           1 
                         
                         
                           C 
                           1 
                         
                       
                       - 
                       
                         
                           L 
                           2 
                         
                         
                           C 
                           2 
                         
                       
                     
                     
                       
                         
                           L 
                           1 
                         
                         
                           C 
                           1 
                         
                       
                       + 
                       
                         
                           L 
                           2 
                         
                         
                           C 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ) 
                 
               
             
           
         
       
     
     Since C 1 ˜C 2 , as a ratio metric device, the effects of sound speed characteristics are cancelled out and not required for evaluation of position. XDCR 1  monitors the dynamical position of an effector while XDCR 2  acts as a constant distance reference. In some configurations XDCR 1  and XDCR 2  can be the same transceiver element, with output energy divided between appropriate surfaces. As a result, the output of equation 26 is logarithmic. A sample logarithmic output is provided in  FIG. 19 . 
     All of the embodiments described can provide, in addition to position, direct measurement of actuator velocity and/or actuator acceleration by the incorporation of signal processing using multiple position samples and/or by extracting Doppler shift information from the transducer(s) signals. Only one of the plurality of transducers is required to be processed, however. Doppler processing of two transducers provides higher accuracy by a factor of 1.4× over a single channel. 
     Ultrasonic pulses are emitted periodically as is prescribed for position measurement. Following each emission, the returned echo signal is sampled at a fixed delay after the emission. From equations (25) and (26), this delay defines the depth. 
     As the actuator moves between the successive emissions, the sampled values taken at time T s  will change over the time. Unfortunately, as the velocity information is available only periodically, the technique is limited by the Nyquist theorem. This means that a maximum velocity exists for each pulse repetition frequency (F prf ): 
     
       
         
           
             
               
                 
                   
                     V 
                     
                       
                           
                       
                       ⁢ 
                       
                         m 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ax 
                       
                     
                   
                   = 
                   
                     
                       
                         F 
                         prf 
                       
                       ⁢ 
                       C 
                     
                     
                       4 
                       ⁢ 
                       
                         F 
                         e 
                       
                       ⁢ 
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       δ 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     27 
                   
                   ) 
                 
               
             
           
         
       
     
     The maximum measurable depth is also defined by the pulsed repetition frequency: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       m 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ax 
                     
                   
                   = 
                   
                     C 
                     
                       2 
                       ⁢ 
                       
                         F 
                         prf 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     28 
                   
                   ) 
                 
               
             
           
         
       
     
     Therefore the product of P max  and V max  is constant, and is given by: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       
                         ma 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         x 
                       
                     
                     × 
                     
                       V 
                       
                         m 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ax 
                       
                     
                   
                   = 
                   
                     C 
                     
                       8 
                       ⁢ 
                       
                         F 
                         θ 
                       
                       ⁢ 
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       δ 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     29 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 16  is a block diagram of an example transducer controller  1600 . The illustrated example outlines a digital solution to achieving time transits and signal processing. In the sample provided, a digital core  1610  (e.g., a DSP) outputs a signal RX burst signal and a TX enable signal. An RF amplifier  1612  is energized and amplifies the RX burst signal to appropriate voltages for the respective sensing system. The amplified signal then passes through a directional coupler  1614  and excites a pair of transceiver elements  1620   a ,  1620   b . In some implementations, a directional coupler or some other blocking circuit can be placed in the transmission line to block or limit the echo signals from each transducer from feeding back to the opposite transducer or to the pulse generator. The desired signals returning from a pair of reflective surfaces  1622   a ,  1622   b  is passed through the direction coupler  1614 , through a T/R switch  1630  and amplified through a pre-amp  1632  to usable voltage levels prior to receipt at the digital core  1610 . Within the digital core  1610  digital signal processing is completed for determination of time transits and ultimately ratio metric position of the effector, linear or logarithmic. With the digital core  1610  accessible, complex DSP tasks can be performed enabling the determination of effector parameters such as velocity, acceleration, and health monitoring prognostics. 
     However, in certain aerospace and other high-temperature harsh-environment applications, ambient temperatures can exceed the capabilities of silicon-based semiconductors. In some embodiments, DSP-based correlation processors, memory, ADC/DAC, and other standard components needed to support such a system may not currently exist in a form that can withstand such harsh environmental conditions. An advantage of an analog correlator is that it can process signals in real time and provide a continuous voltage output at low frequency, and can reduce or eliminate the need for an ADC, sampled data processing, memory, and/or discrete arithmetic methods. Analog correlators can therefore be well suited for high-temperature implementation in wide-bandgap (WBG) semiconductor processes. This opens the potential for implementation of a complete time-of-flight correlation system using WBG semiconductors capable of supporting the required level of device integration with existing IC process technologies. 
       FIG. 17  is a block diagram of another example transducer controller  1700 . The illustrated example shows an embodiment of a transducer controlling circuit using an analog approach in the time domain. This circuit excites transducers  1701   a ,  1701   b  simultaneously and then measures the time difference between return echoes from the two transducers. The output from the circuit is the difference as a ratio metric voltage proportional to the relative position of the two targets. A detailed description of the functional blocks follows. 
     A pulse generator  1710  is triggered by a pulse repetition rate (PRR) signal synchronized with the behavior of a time of flight (TOF) difference over sum block  1712  and governed by the TOF physics of the mechanical system. The electrical pulse generated is simultaneously sent to both transducers  1701   a ,  1701   b  over a bifurcated transmission line. A pair of directional couplers  1714   a ,  1714   b  or some other blocking circuit is placed in the transmission line to block or limit the echo signals from each transducers  1701   a ,  1701   b  from feeding back to the opposite transducer or to the pulse generator  1710 . The pulse is transformed by each transducer to an ultrasonic incident wave,  11  and  12  respectively. The reflected wave from each transducer, R 1  and R 2  respectively is transformed back to small voltage signals. 
     The remaining description will focus on one path of the signal condition circuitry shown in  FIG. 17 . Both paths behave substantially identically. 
     A low noise RF amplifier (LNA)  1720  amplifies the weak signal before passing it to a band pass filter  1722  which is designed to allow only the frequencies of interest to be forwarded to the remaining circuit. 
     An envelope detector  1724  is an amplitude demodulator configured to extract a baseband envelope pulse from a high frequency AC signal. The envelope is then passed through a constant fraction discriminator  1730  (CFD) circuit to a timer  1740  to obtain an amplitude invariant zero-crossing time stamp for the return echo signal. 
     Signals from both paths shall now again be used for the remainder of this description. 
       FIG. 18  is a block diagram  1800  of time-of-flight and ratiometric function blocks. The circuit in the illustrated example provides a basis for a description of the example timer  1740  and TOF difference over sum blocks  1712  of  FIG. 17 . 
     A free running oscillator  1810  provides a time-based trigger to both a pulse generator  1812  and a reset signal to two ramp generators  1814   a ,  1814   b . A linear voltage ramp is fed to sample and hold (S-H) function  1816   a ,  1816   b  to start a sampling timer running. When a CFD output signal  1820   a  from transducer  1  crosses zero, a comparator  1822   a  output activates the hold on the S-H  1816   a  stopping the timer and latching the echo return time t 1  as a specific voltage level on its output. Similarly, the echo return time t 2  voltage equivalent is processed and latched on the output of the S-H function  1816   b  based on a CFD output signal  1820   b  from transducer  2  and a comparator  1822   b  output. 
     These voltages (times) are continually updated with each successive pulse-echo cycle at the rate set by the PRR frequency. In so doing, the change in position of the target is recorded as a continuous sequence of t 1  and t 2  times. 
     The two voltages values, t 1  and t 2 , are then simultaneously fed into a difference amplifier  1830  to get a differential time t 1 −t 2 , and a summing amplifier  1832  to get t 1 +t 2 . These difference and sum voltages are then input to an amplifier  1834  that performs a division and arrives at the difference over sum ratio-metric output, (t 1 −t 2 )/(t 1 +t 2 ). 
     If two opposing transducers are used on either side of the moving target, an output  1840  will be a linear relationship of seconds/second vs position. If one of the two transducers is fixed, the resulting difference over sum relationship will be a logarithmic (log  10 ) profile instead of a linear one. To make subsequent use of this output easier to use, the logarithmic signal can be linearized by an antilog circuit  1844 . An inverse exponential or anti-log can be realized by the equation 10x=e 2.3x . An exponential amplifier can be accomplished with an analog circuit. By setting the logarithmic difference over sum voltage from the stationary target set-up=x, a three-step process can arrive at a linear ramp on output  1842  substantially equal in range to the natural linear ramp at output  1840  that occurs for an opposing transducer set-up. First multiply x by 2.3, then pass it through the exponential amplifier to realize the e 2.3x  operation. Finally, a linear scaling and offset function, y=mx+b, can fit the linear ramp to the desired range.  FIG. 19  is a graph of an example log  10  to linear transformation. In some implementations, a notional circuit could be used to perform this function. The log  10  and resulting linear signals are shown in  FIG. 19 . 
     In yet another embodiment, the ToF sensor can consist of a transmitter and correlation matched-filter receiver along with a voltage to frequency converter that produces a continuous frequency output proportional to the measured ToF. The transmitter can be a simple pulse generator that periodically charges and dumps an accumulated charge on the piezo transducer, exciting the crystal step response. A system functional block diagram of an example analog cross-correlation module  2000  is shown in  FIG. 20 . 
     In this illustrated embodiment, the previously described CFD and ramp timer can be replaced with a frequency domain correlator or matched filter in the receiver. A correlation time-of-flight receiver would consist of a correlator  2010 , a low-noise amplifier (LNA)  2012 , a comparator  2014 , a ramp or sawtooth generator  2016 , a zero-order sample hold  2018 , and a voltage-controlled oscillator. A received signal is amplified by the LNA  2012  and correlated with a local template impulse during a pulse repetition period (PRP), and its output is sampled and held to detect whether there is a signal in the PRP observation window. The analog correlator  2010  includes a standard Gilbert cell (GC), load capacitor, and other supporting circuits. An example embodiment of such an analog correlator is presented as  FIG. 21 . 
     After a fixed post TX dead-band interval, the standard GC multiplies the received signal with the template, and the product is integrated by the load capacitor. To evaluate the performance and describe the operation of the correlator, a two-tone signal model is also described. 
     The correlator  2010  is used to detect the presence of signals with a known waveform in a noisy background. The output is nearly zero if only noise is present; otherwise, the energy of the received signal is integrated with the local template waveform over a fixed time interval to obtain a voltage output above a predefined threshold. The cross-correlation function can be described by the following equation: 
     
       
         
           
             
               
                 
                   
                     C 
                     c 
                   
                   = 
                   
                     
                       
                         ∫ 
                         
                           t 
                           ⁢ 
                           0 
                         
                         
                           
                             t 
                             ⁢ 
                             0 
                           
                           + 
                           T 
                         
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ω 
                                 1 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               φ 
                               1 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               φ 
                               2 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                       d 
                       ⁢ 
                       t 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30 
                   
                   ) 
                 
               
             
           
         
       
     
     Where LO(t) is the local template signal, RF(t) is the input F frequency signal of the correlator, and T is the integration period. 
     The correlation process can be divided into two steps. The first step involves multiplication of the received signal and the reference waveform (local template signal) using a GC. The second step involves integration of the output current via a capacitor. 
     An example of a correlator  2100  is depicted in  FIG. 21 . A GC multiplier  2110 , as a current-mode element, outputs a differential current  2120 . The typical resistive or inductive load of a standard Gilbert mixer is replaced by two current sources  2130   a ,  2130   b , and a capacitor  2132  across the differential output nodes. Because the common-mode part of the output current is absorbed by the current source load, the differential output current is directly fed into the load capacitor. As a result, the capacitor integrates the current and outputs a step-like voltage. A switch  2134  controlled by an internal clock is used to determine the integration interval and to clear the charge in the capacitor  2132  at the end of each interval. 
     Clocking is achieved using a ramp generator and comparators configured to trigger at voltage set points along the ramp waveform. An example of such a circuit  2200  is shown in  FIG. 22 . Relative timing between clock events is maintained ratio metrically using a fixed voltage divider having constant current source bias. A ramp  2202  is generated by charging a timing capacitor  2204  using a mirror  2212  of a divider current source  2210 . In some implementations, use of mirroring can at least partly cancel relative drift between the voltage set points and the PRP ramp voltage, minimizing timing drift over circuit element and IC process variation. 
     The sequence of control gates is shown in  FIG. 22 . The PRP ramp  2202  is a free-running oscillator. A cycle begins when the timing capacitor  2204  is reset and the PRP ramp voltage is zero. As the capacitor  2204  charges, the ramp voltage increases, triggering a TX Gate comparator  2220  and firing the transducer driver circuit. A dead-band interval is built-in to the timing to disable the receiver during a short blanking interval. This dead-band prevents reverberations and other false signal returns from triggering the correlator prematurely. After the dead-band delay an Xcorr Gate comparator  2222  fires, allowing the integration switch on the GC to open and charge the load capacitor. The integrated load capacitor voltage represents the time cross-correlation of the template signal and the receiver signal. 
     The point in time of the measurement interval at which the correlator output voltage switches is determined by the ToF of the receiver input signal. Once the correlator switches the voltage on the load capacitor will begin to decay as soon as the receive echo passes, which will degrade accuracy. To prevent this, the PRP ramp and correlator output are compared by an SH Gate comparator  2224  to generate a SH Gate. The SH Gate activates a zero-order (sample) hold that captures the load capacitor voltage at the moment the correlator fires. The SH Gate can activate any time after the correlator is enabled by the Xcorr Gate, but not before, as the PRP ramp voltage ensures monotonic sequencing of the gates. When the end of the ToF interval is reached the final PRP End Gate is triggered by a PRP End Gate comparator  2226 , resetting the timing capacitor  2204 , and starting the cycle all over again. 
     Referring again to  FIG. 20 , the output of the sensor uses the voltage to frequency (VCO) converter  2020  to map the output of the sample-hold output voltage to a scaled frequency proportional to time. The VCO scaling can be adjusted to produce a suitable range as needed by a specific application. 
     VCO drift with temperature is a common problem that has a deleterious effect on accuracy in aerospace and other harsh-environment applications. Those familiar with the art will recognize that there are several approaches to managing temperature-induced VCO frequency and gain scaling drift, none of which fundamentally alter the operation principles of the system described here. One example method involves using combinations of components having complementary temperature coefficients in ways that cancel overall frequency drift, gain scaling, or both. Another example method employs a pair of VCOs that have close, but not identical gain scaling functions. As the frequencies drift apart with temperature, the measured gains and the two output frequencies can be combined as a system of two equations and two unknowns, allowing the drift to be compensated. Many other methods beyond those described are known in the art and will not be enumerated further here. 
     Due to the integration applied to the TOF through correlation, phase noise is typically not a significant error term of the correlation. Phase noise, when significant in this embodiment, is an artifact of the specific VCO implementation, not correlation. Presented above are methods to determine the position of a dynamic effector that either produce or can generate a ratio metric position through linear or logarithmic methods. In addition to the physical implementation, outlined are digital and analog solutions for determination of the ratio metric output of the device. This output signal can then be used for communication with a PID controller and command source. The ratio metric output signal can be used as a feedback variable for a PID controller and for reporting the position of an effector at the higher-level system command source. 
       FIG. 23  is a schematic of an example template generator circuit  2300 . In some implementations, the template generator circuit  2300  can be used to produce a matching step response to a transducer by using matching piezo material as a resonant element. 
       FIG. 24  is a graph of examples of signal timings  2400  provided by the example circuit  2200  of  FIG. 22 . In general, PRP ramp-based timing can provide ratiometric delays from a single-timing capacitor and current source, while addition of hysteresis on PRP timing capacitor reset can reduce supply and temperature induced time jitter. 
       FIG. 25  is a block diagram of an example closed loop control system  2500 . The system  2500  includes a command source  2510 , an end effector  2520 , and an electronic closed loop controller  2530 . In some embodiments, the command source  2510  may be an engine controller. The command source  2510  provides a position request to the electronic controller  2530 , and the electronic controller  2530  is configured to move the end effector  2520  via an actuation device. 
     The end effector  2520  includes a linear feedback sensor  2522 . Examples of linear feedback sensors can include the ratio metric ultrasound position sensors presented herein, a linear variable differential transformer, a linear hall sensor, an optical sensor, or any other appropriate linear feedback sensor. 
     Example actuation devices may include but are not limited to direct drive valves, a pumping system, an electro-hydraulic servo valve, a solenoid, a solid-state actuator, a solid-state pump, or any appropriate actuation devices. 
     End effectors for position monitoring may include but are not limited to metering valves, regulating valves, equal area actuators, dual area actuators, and any other appropriate translation device. 
     The higher-level system controller  2530  is in communication with a PID controller (not shown). The PID controller is configured to activate an actuation device and cause the translation of the end effector  2520 . In some implementations, the PID controller can be configured to adjust the command to the actuation device based on a comparison of the current position and the commanded position. 
     The electronic controller  2530  receives from the end effector  2520  a feedback signal  2524 . The position of the end effector  2520  can then be determined by a feedback conditioner  2532  and a feedback controller  2534 . In some implementations, the conditioner  2532  and the controller  2534  may be the digital or analog systems discussed in the descriptions of  FIGS. 16-23 . 
     The determined position is passed to an outer loop feedback module  2536  as a position status for health monitoring and outer loop feedback to the command source  2510 . The determined position is also passed to a summing junction  2538  where the current position is compared to the commanded position defined by the command source  2510  and a signal conditioner  2540 . The difference in the request position and current position is provided to a controller  2550 , such as a PID controller, and actuates an actuator  2552 , such as a brushless DC motor, to move the position of the end effector  2520 . The PID controller (not shown) actively adjusts the actuator based on the current position compared to the commanded position. 
     Provided in  FIG. 25  is an example configuration of a control system. The ratio metric position sensing solutions and respective circuitry of  FIGS. 1-24  may be in any number of control systems. The ratio metric sensors and digital or analog controller can be applied to many system solutions, including others not specifically described in this document. 
       FIG. 26  is a flow diagram of another example process  2600  for ultrasonic position sensing. In some implementations, the process  2600  may be performed by all or parts of the systems and circuits discussed in the descriptions of  FIGS. 9-25 . 
     At  2610  a first emitted acoustic waveform is emitted through a fluid having a first acoustic impedance toward a first acoustic interface. For example, the example acoustic transceiver  940   a  of  FIG. 9  can emit the emitted acoustic waveform  942   a  toward the face  922 . 
     At  2620 , a second emitted acoustic waveform is emitted through the fluid toward a second acoustic interface. For example, the acoustic transceiver  940   b  can emit the emitted acoustic waveform  942   b  toward the face  932   
     At  2630 , the first acoustic interface reflects a first reflected acoustic waveform based on the first emitted acoustic waveform. For example, the face  922  can reflect the emitted acoustic waveform  942   a  as the reflected acoustic waveform  944   a.    
     At  2640 , the second acoustic interface reflects a second reflected acoustic waveform based on the second emitted acoustic waveform. For example, the face  932  can reflect the emitted acoustic waveform  942   b  as the reflected acoustic waveform  944   b.    
     At  2650 , a first position of the second acoustic interface is determined based on the first reflected acoustic waveform and the second reflected acoustic waveform. For example, the example signal processor  960  can process signals from the acoustic transceiver  940   a  and the acoustic transceiver  940   b  to determine the position of the moveable body  938  within the cavity  930 . 
     In some implementations, a first time of flight can be determined based on the first emitted acoustic waveform and the first reflected acoustic waveform, and determining a second time of flight based on the second emitted acoustic waveform and the second reflected acoustic waveform, wherein determining a first position of the acoustic interface is further based on the first time of flight and the second time of flight. For example, the signal processor  960  can be configured to perform processing based on the example equations 15-30 above. 
     In some implementations, the process  2600  can include determining the first position of the acoustic interface based on the first time of flight (t 1 ) and the second time of flight (t 2 ) can be given by an equation: (t 1 −t 2 )/(t 1 +t 2 ) (e.g., equation 15). 
     In some implementations, the process  2600  can also include determining a second position of the second acoustic interface, and determining a speed of the second acoustic interface based on the first position and the second position. For example, two successive position measurements of the example moveable body  938  to determine a speed of the moveable body  938 . 
     In some implementations, the process  2600  can include determining a reflected acoustic frequency based on one or both of the first reflected acoustic waveform and the second reflected acoustic waveform, and determining a speed of the second acoustic interface based on the determined reflected acoustic frequency and a predetermined emitted acoustic frequency of the second emitted acoustic waveform. For example, the signal processor  960  can include a phase detector (e.g., to determine phase and/or Doppler shifts in reflected signals). 
     In some implementations, the first acoustic interface can be defined by a face of a fluid cavity having a second acoustic impedance that is different than the first acoustic impedance, the second acoustic interface can be defined by a second face of a moveable body within a fluid effector and having a third acoustic impedance that is different than the first acoustic impedance, the first emitted acoustic waveform can be emitted toward the first face through the fluid, the second emitted acoustic waveform can be emitted toward the second through the fluid, the first reflected acoustic waveform can be based on a first reflection of the first emitted acoustic waveform by the first face, and the second reflected acoustic waveform can be based on a second reflection of the second emitted acoustic waveform by the second face. For example, the sensor housing and the moveable body  938  can be made of materials that have acoustic impedances that are different from the acoustic impedance of the fluid in the cavities  920  and  930 . The mismatches in acoustic impedances can cause reflections of the emitted acoustic signals  942   a  and  942   b  off the faces  922  and  932 . 
     In some implementations, the process  2600  can include determining a phase difference between a second emitted phase of the second emitted acoustic waveform and a second reflected phase of the second reflected acoustic waveform, wherein determining a first position of the acoustic interface can be further based on the determined phase difference. For example, distance can be determined based on example equation 23. 
     In some implementations, the first emitted waveform can be emitted through a first fluid cavity toward a face of the first fluid cavity defining the first acoustic interface, and the second emitted waveform can be emitted through a second fluid cavity toward a second face of a moveable member defining the second acoustic interface. For example, the example emitted acoustic waveform  942   a  can be emitted through the cavity  920 , and the example emitted acoustic waveform  942   b  can be emitted through the cavity  930 . 
     In some implementations, the first emitted waveform can be emitted through a first portion of a fluid cavity toward a face of the fluid cavity defining the first acoustic interface, and the second emitted waveform can be emitted through a second portion of the fluid cavity toward a second face of a moveable member defining the second acoustic interface. For example, the example emitted acoustic signal  1150  of  FIG. 11  can be emitted toward the face portion  1130  and the face portion  1112 . 
     In some implementations, the process  2600  can include emitting a third emitted acoustic waveform through the fluid toward a third acoustic interface, reflecting, by the third acoustic interface, a third reflected acoustic waveform based on the third emitted acoustic waveform, and determining a second position of the third acoustic interface based on the first reflected acoustic waveform and the third reflected acoustic waveform. For example, in the example system  1500 , a first acoustic signal can be emitted by one of the acoustic transceivers  1506  toward the face  1507 , a second acoustic signal can be emitted by one of the acoustic transceivers  1518  toward a corresponding face  1517 , and a third acoustic signal can be emitted by another one of the acoustic transceivers  1518  toward another corresponding one of the faces  1517 . 
       FIG. 27  is a schematic diagram of an example of a generic computer system  2700 . The system  2700  can be a data processing apparatus (e.g., processor system) used for the operations described in association with the process  800  according to one implementation. For example, the system  2700  may be included in either or all of the signal processors  150 ,  960 ,  1060 ,  1560 , or the controllers  160 ,  970 ,  1070 , or  1570 . 
     The system  2700  includes a processor  2710 , a memory  2720 , a storage device  2730 , and an input/output device  2740 . Each of the components  2710 ,  2720 ,  2730 , and  2740  are interconnected using a system bus  2750 . The processor  2710  is capable of processing instructions for execution within the system  2700 . In one implementation, the processor  2710  is a single-threaded processor. In another implementation, the processor  2710  is a multi-threaded processor. The processor  2710  is capable of processing instructions stored in the memory  2720  or on the storage device  2730  to display graphical information for a user interface on the input/output device  2740 . 
     The memory  2720  stores information within the system  2700 . In one implementation, the memory  2720  is a computer-readable medium. In one implementation, the memory  2720  is a volatile memory unit. In another implementation, the memory  2720  is a non-volatile memory unit. 
     The storage device  2730  is capable of providing mass storage for the system  2700 . In one implementation, the storage device  2730  is a computer-readable medium. In various different implementations, the storage device  2730  may be a floppy disk device, a hard disk device, an optical disk device, or a tape device. 
     The input/output device  2740  provides input/output operations for the system  2700 . In one implementation, the input/output device  2740  includes a keyboard and/or pointing device. In another implementation, the input/output device  2740  includes a display unit for displaying graphical user interfaces. In another implementation, input/output device  2740  includes a serial link, (e.g., Ethernet, CAN, RS232, RS485, optical fiber), for example, to interface to a remote host and/or to send measurement results, either in a command/response protocol, or at some periodic update rate after a short initialization period (e.g., &lt;1 sec). In another implementation the input/output device  2740  includes a data bus connection to a second computer system or processor. 
     The features described can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The apparatus can be implemented in a computer program product tangibly embodied in an information carrier, e.g., in a machine-readable storage device for execution by a programmable processor; and method steps can be performed by a programmable processor executing a program of instructions to perform functions of the described implementations by operating on input data and generating output. The described features can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. 
     Suitable processors for the execution of a program of instructions include, by way of example, both general and special purpose microprocessors, and the sole processor or one of multiple processors of any kind of computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer will also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits). 
     To provide for interaction with a user, the features can be implemented on a computer having a display device such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor for displaying information to the user and a keyboard and a pointing device such as a mouse or a trackball by which the user can provide input to the computer. 
     The features can be implemented in a computer system that includes a back-end component, such as a data server, or that includes a middleware component, such as an application server or an Internet server, or that includes a front-end component, such as a client computer having a graphical user interface or an Internet browser, or any combination of them. The components of the system can be connected by any form or medium of digital data communication such as a communication network. Examples of communication networks include, e.g., a LAN, a WAN, and the computers and networks forming the Internet. 
     The computer system can include clients and servers. A client and server are generally remote from each other and typically interact through a network, such as the described one. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 
     Although a few implementations have been described in detail above, other modifications are possible. For example, the logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. In addition, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Accordingly, other implementations are within the scope of the following claims.