Abstract:
Embodiments of the present invention provide improved systems and methods for estimating N-dimensional parameters while sensing fewer than N dimensions. In one embodiment a navigational system comprises a processor and an inertial measurement unit (IMU) that provides an output to the processor, the processor providing a navigation solution based on the output of the IMU, wherein the navigation solution includes a calculation of an n-dimensional parameter. Further, the navigational system includes at most two sensors that provide an output to the processor, wherein the processor computes an estimate of an n-dimensional parameter from the output of the at most two sensors for bounding errors in the n-dimensional parameter as calculated by the processor when the trajectory measured by the IMU satisfies movement requirements, wherein “n” is greater than the number of the at most two sensors.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 61/442,263, filed on Feb. 13, 2011 (hereinafter the &#39;263 Application). The &#39;263 Application is incorporated herein by reference. 
     
    
     BACKGROUND 
       [0002]    Inertial navigation systems (INS) are used to determine parameters such as position, orientation, and velocity in a moving platform such as an aircraft, a spacecraft, a watercraft or a guided missile. The INS calculates these parameters using dead reckoning without the need for external references. 
         [0003]    At the heart of the INS is an inertial measurement unit (IMU). The IMU typically includes three motion sensors (accelerometers) and three rotation sensors (gyroscopes). The three motion sensors are placed such that their measuring axes are orthogonal to each other. Similarly, the rotation sensors are also placed in a mutually orthogonal relationship to each other. The IMU provides measurements of motion and rotation to the INS to derive a navigation solution composed of position, orientation and velocity. 
         [0004]    One known problem with an INS is error accumulation. Each measurement made by the IMU has an inherent error. Over time, the INS adds current measurements from the IMU to prior navigation solutions. Thus, with the addition of each measurement, the INS accumulates additional errors in the produced navigation solution. 
         [0005]    The accuracy of the INS is improved by using outputs of additional sensors that effectively bound the error of the INS. For example, INS systems typically include one or more of global positioning system (GPS), Doppler, and other sensors that provide inputs to the INS to offset the accumulated errors. 
         [0006]    In a recent development, personal navigation systems are being developed based on an INS platform. Such personal navigation systems can be used by emergency responders so that the position and movement of each responder in a three-dimensional structure can be instantaneously displayed in a command center. However, several problems are inherent in the design of personal navigation systems. First, an INS platform typically has a high power requirement due to the IMU and the other sensors required for accurate position, velocity and orientation information. Further, the size of a typical INS may be larger than desirable for personal navigation systems. 
       SUMMARY 
       [0007]    The Embodiments of the present disclosure provide methods and systems for reducing the size and power requirements of an inertial navigation system with a reduction in the number of additional sensors used to reduce accumulated errors and will be understood by reading and studying the following specification. 
         [0008]    Embodiments of the present invention provide improved systems and methods for estimating N-dimensional parameters while sensing fewer than N dimensions. In one embodiment a navigational system comprises at least one processor and an inertial measurement unit (IMU) that provides an output to the at least one processor, the at least one processor providing a navigation solution based on the output of the IMU, wherein the navigation solution includes a calculation of an n-dimensional parameter. Further, the navigational system includes at most two sensors that provide an output to the at least one processor, wherein the at least one processor computes an estimate of an n-dimensional parameter from the output of the at most two sensors for bounding errors in the n-dimensional parameter as calculated by the at least one processor when the trajectory measured by the IMU satisfies movement requirements, wherein “n” is greater than the number of the at most two sensors. 
     
    
     
       DRAWINGS 
         [0009]    Embodiments of the present invention can be more easily understood and further advantages and uses thereof more readily apparent, when considered in view of the description of the preferred embodiments and the following figures in which: 
           [0010]      FIG. 1  is a block diagram of one embodiment of a system that estimates an n-dimensional parameter using a sensor that measures less than n dimensions. 
           [0011]      FIG. 2  is a functional block diagram of one embodiment of a system that estimates an n-dimensional parameter using a velocity sensor that measures less than n dimensions. 
           [0012]      FIGS. 3A and 3B  are block diagrams of personal navigation systems that estimate a multi-dimensional velocity using single-axis sensors that are fewer in number than the dimensions of the multi-dimensional velocity. 
           [0013]      FIG. 4  is a block diagram of a system that displays the location of personal navigation systems in a three-dimensional space in which the personal navigation systems estimate a three-dimensional velocity using one or two single-axis sensors. 
           [0014]      FIG. 5  is a flow diagram of a method for estimating an n-dimensional parameter using a sensor that measures less than n dimensions. 
       
    
    
       [0015]    In accordance with common practice, the various described features are not drawn to scale but are drawn to emphasize features relevant to the present invention. Reference characters denote like elements throughout figures and text. 
       DETAILED DESCRIPTION 
       [0016]    In the following detailed description, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of specific illustrative embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that logical, mechanical and electrical changes may be made without departing from the scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense. 
         [0017]    Embodiments of the present invention describe a system and method for an n-dimensional estimation of a system motion parameter using fewer than n single-axis sensors. In one example, a 3-dimensional velocity estimation is accomplished in an inertial navigation system (INS) using one or two velocity sensors. Conventionally, INS systems use more than one velocity sensor for platform velocity estimation. Typically, such systems use three or more velocity sensors to determine the three dimensional platform velocity that is used to adjust accumulated errors in the navigation solution of an inertial measurement unit (IMU). In contrast, it has been discovered that, in systems with a platform trajectory that moves in at least one of pitch, roll and yaw, velocity errors in the IMU can be bounded with fewer sensors than the dimension number of the velocity vector. For example, a solitary single-axis velocity sensor can be used to bound three dimensional velocity errors when the trajectory of the platform movement includes appropriate motion in two of pitch, roll, and yaw that provides measurements in three dimensions. Further, two single-axis velocity sensors can be used to bound three-dimensional velocity errors when there is appropriate motion in one of pitch, roll, or yaw that provides measurements in three dimensions. In such systems, it has been shown that the integrated INS platform, aided by fewer than three velocity sensors, exhibits bounded velocity error under the dynamics of the trajectory. 
         [0018]    Embodiments of the present disclosure solve the problem of unbounded INS velocity error by exploiting platform dynamics to acquire earth-referenced velocity in more than one dimension using a solitary single-axis velocity sensor. These multi-dimensional measurements are obtained by changing the direction (i.e. attitude) of the platform, which in turn changes the direction of observation of the velocity sensor. Thus, the growth of the INS system velocity error will be a function of the quality of the inertial sensors, the velocity sensor specifications, and the rate at which the velocity sensor&#39;s line-of-sight spans the three-dimensional space of the platform&#39;s local-vertical coordinate system. Specifically, the quality of the inertial sensors, the quality of the velocity sensor(s), and the velocity sensor(s)&#39; measurement rates will determine the rate at which the platform must rotate in order to bound the velocity error growth. 
         [0019]      FIG. 1  is a block diagram of a navigation system, indicated generally at  100 , that estimates an n-dimensional parameter using a sensor  102  that measures motion parameters along less than n-dimensions. In one implementation, system  100  uses sensors  102  that are single-axis sensors. Alternatively, sensors  102  are sensors that measure in multiple dimensions. In at least one embodiment, sensors  102  are velocity sensors. When sensors  102  are velocity sensors, the measurements from the velocity sensors are used to estimate the 3-dimensional earth reference velocity of a platform when the platform experiences motion in either pitch, roll, or yaw. For example, the measurements from the velocity sensors can estimate the 3-dimensional velocity on a platform that is a personal navigation system, which is illustrated in  FIGS. 3A and 3B  described in more detail below. 
         [0020]    System  100  generates a navigation solution  130  based on sensed parameters. To form navigation solution  130 , in certain embodiments, system  100  includes an IMU  104 . In certain embodiments, IMU  104  includes three sensors that measure motion along three orthogonal axes such as accelerometers that measure acceleration along three orthogonal axes. IMU  104  also includes three sensors that measure rotation about three orthogonal axes such as three gyroscopes that measure rotation about three orthogonal axes. 
         [0021]    Also, IMU  104  is coupled to an inertial navigation processor  106  and provides motion and rotation measurements to inertial navigation processor  106 . Inertial navigation processor  106  generates a navigation solution, which includes position, velocity and attitude data of the platform of system  100  based on the motion and rotation measurements received from IMU  104 . Further navigation processor  106  provides the navigation solution to a processor  116 . As shown in  FIG. 1 , Navigation processor  106  and processor  116  are separate processors, however a single processor is able to perform both the functionality of navigation processor  106  and processor  106 . Also, processor  116  receives motion information from sensors other than IMU  104 , like sensors  102 . Processor  116  processes the motion information received from both IMU  104  and sensors  102  to bound errors in the navigation solution. 
         [0022]    Processor  116  includes a Kalman filter  118 . In some implementations, the processor  116  converts raw sensor data into a common time base and coordinate frame. Further, from the conversion of the raw sensor data, processor  116  forms a navigation measurement  117  for Kalman filter  118 . When processor  116  forms the navigation measurement  117  for Kalman filter  118 , processor  116  writes the navigation measurement  117  as a linear function of the states of Kalman filter  118 . This is known as forming the “H matrix” of a Kalman filter. In addition, if the states are modeled as navigation errors (which they typically are), the navigation measurement  117  sent to the Kalman filter  118  is usually a “measurement difference”, i.e. it is a difference between a quantity derived directly from the navigation solution and the output of the sensors  102  used to bound the errors in the navigation solution. 
         [0023]    Kalman filter  118 , executing on processor  116 , processes the navigation measurement  117 , which in some implementations includes the data from sensors  102 . Kalman filter  118  determines a set of resets, based on the data processed by processor  116 , that are provided to navigation processor  106 . Since the platform experiences appropriate motion in either pitch, roll, or yaw, Kalman filter  118  is able to provide appropriate resets to navigation processor  106  to keep the error bounded even with sensors  102  that sense in fewer dimensions than the dimensions, e.g., 3, of the error bounded in the navigation solution for the platform. 
         [0024]    As an additional benefit, when sensors  102  are velocity sensors, movement of the platform containing system  100  in pitch, roll, or yaw allows processor  116  to use data from sensors  102  to estimate measurements for the accelerometers in IMU  104  in all three body axes of the system  100  via Kalman filter  118 . Kalman filter  118  maintains correlations between states that are modeled in the Kalman filter  118 . During times in which the platform containing system  100  is static or has little to no attitude rate, or movement in pitch, roll, or yaw, Kalman filter  118  estimates a large level of correlation between body-fixed inertial sensor errors and local-vertical frame fixed velocity errors. When the platform containing system  100  moves in pitch, roll, or yaw such that the sensors  102  sense along the appropriate dimensions of motion, sensors  102  provide measurements that allows processor  116  and Kalman filter  118  to correct local-vertical frame velocity errors, that were unobservable before the movement in pitch, roll, or yaw. Kalman filter  118  will be able to correct inertial sensor errors that were correlated with the local-vertical frame velocity error. Similarly, Kalman filter local-vertical position errors are also correlated with the local vertical velocity error, thus platform movement in pitch, roll, or yaw also enables Kalman filter  118  to correct for a portion of the position error that accumulated during the period of unobserved velocity error. 
         [0025]    In some embodiments, the processing of measurements from both IMU  104  and sensors  102  is implemented in software that executes on processor  116 . Also, the software that executes on processor  116  is portable to a variety of different platforms. For example, the platform may be an embedded system or a simulation-based platform. Further, a filtering scheme that uses the approach described and that estimates earth-referenced velocity, will observe bounded velocity error provided the platform dynamics meet the requirement defined by the sensors, where the requirements for a single-axis sensor require that the platform moves in at least two of pitch, roll, and yaw. Further, when the requirements are for two single-axis sensors, the platform moves in one of pitch, roll, and yaw. 
         [0026]      FIG. 2  is a functional block diagram illustrating the functions of elements within a system, indicated generally at  200 , that estimates an n-dimensional parameter using fewer than n single-axis velocity sensors  202 . System  200  is similar to system  100  in  FIG. 1 , however, system  200  further includes additional navigational aides to compensate for error accumulation in the data from the IMU  204 . For example, system  200  includes a number of sensors that generate data used to bound the accumulated error in the navigation solution. In one embodiment, system  200  includes magnetic sensors  208 , altimeter  210 , global positioning system (GPS)  212 , and ranging and communication sensor  214 . Each of these sensors measures a parameter related to the motion or position of the platform associated with system  200 . Magnetic sensors  208  measure compass heading of the platform. Altimeter  210  measures the altitude of the platform. GPS  212  measures the current position of the platform. Ranging sensor  214  measures range and other node information for the platform. Each of these sensors provides input to a processor  216 . 
         [0027]    In certain embodiments, processor  216  receives input from motion classification circuit  217 . Motion classification circuit  217  is coupled to IMU  204 , magnetic sensors  208  and altimeter  210 . Motion classification circuit  217  provides motion information (such as the distance traveled, gait, and other motion information) to processor  216 . 
         [0028]    In a further embodiment, processor  216  provides data to a Kalman filter  218  via a prefilter  220 . Processor  216 , implementing prefilter  220 , receives the raw sensor data acquired by the multiple sensors and converts it into a common time base and common coordinate frame. Further, processor  216  and prefilter  220  form a measurement for Kalman filter  218 . As described above in relation to  FIG. 1 , forming a measurement for Kalman filter  218  involves writing the measurement as a linear function of the states of the Kalman filter  218 . The writing of the measurements as a linear function is known as forming the “H matrix” of a Kalman filter. In addition, if the navigation states calculated by processor  216  are modeled as navigation errors, processor  216  calculates a measurement difference that is used by Kalman filter  218 . The “measurement difference” with multiple aiding sensors is a difference between a quantity derived directly from the navigation solution calculated by navigation processor  206  and the sensor output received from sensors  208 ,  210 ,  212 ,  202 , and  214 . When Kalman filter  218  calculates correcting information using the measurement from processor  216  and measurement prefilter  220 , Kalman filter  218  transmits information to navigation processor  206  that corrects the navigation solution. Kalman filter  218 , processor  216 , navigation processor  206 , and prefilter  220 , as described above, refer to functionality and exists as functions performed by a single processor or multiple processors that are communicatively coupled to one another. 
         [0029]      FIGS. 3A and 3B  are block diagrams of personal navigation systems that estimate a multi-dimensional velocity using single-axis sensors that are fewer in number than the dimensions of the multi-dimensional velocity that is estimated. In  FIG. 3A , personal navigation system  300  includes two single-axis velocity sensors  302  and  304 . Velocity sensors  302  and  304 , in one embodiment, comprise Doppler-based velocity sensors. System  300  further includes an inertial measurement unit (IMU)  306 , a processor  308 , and a ranging radio  310 . Processor  308  perform similar functions to the functionality described for processors  106  and  116  of  FIG. 1 , respectively. Personal navigation system  300  further includes a battery  312  to provide power for the various components of the system. Further, personal navigation system  300  also includes an antenna  314  that is used in conjunction with processor  310  to communicate the navigation solution from processor  308  to an external base station such as the base station described below and shown in  FIG. 4 . This embodiment presumes that the trajectory of system  300  will have some motion in either roll, pitch, or yaw so that the velocity fed to processor  310  will have elements of all three dimensions included even though there are only two velocity sensors. In a further example, personal navigation system  300   a  includes one single-axis velocity sensor  302   a , e.g., a Doppler sensor. In this embodiment, the personal navigation system  300   a  is able to estimate the 3-dimensional velocity with only one single-axis sensor if the system  300   a  moves in at least two of roll, pitch and yaw. 
         [0030]      FIG. 4  is a block diagram of a system, indicated generally at  400 , that displays the location of personal navigation systems  402 - 1 , . . . ,  402 -M, in a three-dimensional space in which the personal navigation systems estimate a three-dimensional velocity using one or two single-axis sensors. In one embodiment, personal navigation systems  402 - 1 , . . . ,  402 -M are constructed as described above with respect to either one or more of  FIGS. 1 ,  2 ,  3 A, and  3 B. System  400  further includes a base station  404  that communicates with the personal navigation systems  402 - 1 , . . . ,  402 -M. Base station  404  receives the respective navigation solutions from each of personal navigation systems  402 - 1 , . . . ,  402 -M and plots the data on display  406 . Thus, the current location of each personal navigation systems  402 - 1 , . . . ,  402 -M is readily viewable on display  406 . Such a system  400  could be used at a command center to identify the location of each emergency responder at the scene of an accident, explosion, fire, or the like. 
         [0031]      FIG. 5  is a flow diagram of a method  500  for estimating an n-dimensional parameter using a sensor that measures less than n dimensions. Method  500  begins at  502  where a navigation solution is calculated for a platform based on measurements from an IMU. For example, the IMU provides measurements of rotation about three orthogonal axes and acceleration along three orthogonal axes to a navigation processor. Upon receiving the measurements from the IMU, the navigation processor calculates the navigation solution, which contains information describing the position, heading, velocity, and attitude of the platform. Method  500  proceeds at  504  where a measurement from at most two sensors is received, wherein the at most two sensors are used to provide an estimated motion parameter in less than n dimensions. In certain exemplary embodiments, the at most two sensors are single axis velocity sensors that provide estimated measurement of velocity along two axis to a processor, where the processor receives the navigation solution from the navigation processor. 
         [0032]    Method  500  proceeds at  506  where an estimate is calculated of accumulated error for a motion parameter in n dimensions based on the estimated motion parameter when the trajectory of platform motion satisfies movement requirements. For example, the processor, having received an estimate of velocity in two dimensions from the sensors, calculates a three dimensional estimate of the velocity when the trajectory of the platform motion has moved in at least one of pitch, roll, and yaw. Method  500  proceeds at  508  where the motion parameter in n dimensions is corrected based on the estimate of accumulated error. For example, the processor determines the difference between the motion parameter in the navigation solution received from the navigation processor and provides the difference as an output to a Kalman filter. The Kalman filter transmits a correction of the motion parameter to the navigation processor to correct the navigation solution. 
         [0033]    Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement, which is calculated to achieve the same purpose, may be substituted for the specific embodiment shown. This application is intended to cover any adaptations or variations of the present invention. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof.