Abstract:
An RF position tracking system for wirelessly tracking the three dimensional position of a device that transmits a radio signal. The device has an antenna and at least one inertial sensor. The system uses a plurality of receiver antennas to receive the device&#39;s radio signal at each antenna. The device also incorporates an inertial sensor to improve position stability by allowing the system to compare position data from radio signals to data provided by the inertial sensor.

Description:
RELATED APPLICATIONS 
       [0001]    This application is a continuation of co-pending U.S. application No. 13/293,639, filed Nov. 10, 2011, titled “Position Tracking System and Methods Using Radio Signals and Inertial Sensing”, which claims the benefit of and priority to U.S. provisional application No. 61/413,026, filed on Nov. 12, 2010, titled “Position Tracking System and Methods Using Radio Signals and Inertial Sensing,” the entireties of which applications are incorporated by reference herein. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present disclosure relates generally to position tracking of mobile devices. More particularly, the present disclosure relates to a position tracking system and method using radio signals and inertial sensing. 
       BACKGROUND 
       [0003]    In a Global Positioning System (GPS), satellites orbiting the earth transmit signals to passive receivers on the ground. The receivers only receive signals, but they do not transmit signals. One limitation of GPS receivers is that they require an unobstructed view of the sky. As a result, GPS receivers typically are better suited for outdoor use and in areas away from tall buildings or heavy tree cover. A further limitation of GPS location devices is their dependence on an accurate external time reference. 
         [0004]    In a GPS system, each of many GPS satellite transmits a signal that includes data to indicate the satellite&#39;s location and current time. GPS systems use two carrier frequencies (L1 and L2) for transmitting information, including satellite location, ionospheric propagation delays, offsets between satellite clock time and true GPS time. Additionally, GPS measurements are determined from pseudoranges, which are range measurements biased by receiver and satellite clock errors. The GPS satellites are all synchronized to transmit repeating signals at the same time. Because each satellite is located at a different distance from a receiver on the ground, transmitted signals arrive at the GPS receiver at slightly different times. The receiver uses the different receipt times for various signals to calculate the receiver&#39;s location in three dimensions. 
         [0005]    U.S. Pat. Nos. 5,953,683; 7,143,004; and 7,533,569 describe sourceless orientation sensors. For example, U.S. Pat. No. 7,533,569 discloses a method of measuring positional changes of an object by using multiple accelerometers. U.S. Pat. No. 7,236,091 describes a hybrid RF/inertial position tracking system having a “wide resolution” mode for general position tracking, and a “high-resolution” mode that employs kinematic models. In this system, the high-resolution position accuracy is considered to be within the order of meters. U.S. Pat. Nos. 7,409,290; 6,167,347; 6,292,750; 6,417,802; 6,496,778; 5,923,286; 6,630,904; 6,721,657; 7,193,559; and 6,697,736 describe GPS-aided positioning and navigation methods. For example, U.S. Pat. No. 7,409,290 altitude and heading information are used to aid the GPS positioning when satellite signals are not available. 
         [0006]    Unlike GPS, where transmission time is measured from a satellite to a mobile device or receiver, high-accuracy systems that track mobile devices in three dimensional space measure the time that a signal arrives from the mobile device to a system&#39;s connected (either wired or wireless) antennae. These systems do not have the bias errors that GPS has. These time-based, high-accuracy RF positioning systems that use networked antennae for comparing signal time of arrival or difference of arrival measurements consist of receiver hardware having multiple receiver antennae and transmitter hardware having one or more transmitter antennae. To track a single transmitter or transmitter antenna in three dimensions, at least four receiver antennae are required. Similarly, for tracking in two dimensions, at least three receiver antennae are required. 
         [0007]    Also unlike GPS, where the tracking calculation is performed in the mobile device, the RF system&#39;s receiver antennae provide the reference frame in which the mobile antennae are tracked. More receiver antennae provide better coverage and more accuracy, but do so with increased complexity and cost. The receiver antennae must be distinct, fixed, and have a known location in space. More transmitter antennae attached to or embedded in a tracked object allow the object&#39;s orientation to be calculated based on geometric principles. For example, two transmitter antennae, separated by a distance D, yield a pointer, since the two transmitter antennae form a line with known direction. Three transmitter antennae provide enough information to calculate three dimensional position and orientation. The system can be reversed, with the receiver antennae being tracked and the transmitter antennae providing the reference frame. 
         [0008]    The major source of error in RF positioning systems is signal propagation errors, such as multipath. While many methods have attempted to mitigate this problem (antennae diversity, spread spectrum), signal propagation errors are very difficult to totally eliminate. A sourceless navigation system does not have these issues, but does have its own set of problems. Sourceless navigation systems are typically based on inertial sensors, which can consist of accelerometers and gyroscopes, as well as magnetic sensors. The use of small inertial sensors, like gyroscopes and accelerometers, has become commonplace in position tracking. Inertial sensors overcome problems like line-of-sight restrictions that plague tracking systems. Unfortunately, commercial, low-cost devices have drift, bias and scale factor errors and orientation motion and positional motion need to be algorithmically separated. 
         [0009]    A positioning solution is obtained by numerically solving Newton&#39;s equations of motion using measurements of forces and rotation rates obtained from the inertial sensors. The magnetic sensor helps to define azimuth based on the earth&#39;s magnetic field. The accelerometer, gyroscope, and magnetic sensor, and various combinations thereof, together with the associated hardware and electronics comprise the inertial/magnetic devices subsystem (IMDS). 
         [0010]    Angular orientation may be determined by integrating the output from angular rate sensors. A relatively small offset error on the gyroscope signal will introduce large integration errors. Accelerometers measure the vector sum of acceleration of the sensor and the gravitational acceleration (g). In most situations, g is dominant, thus providing inclination information that can be used to correct the drifted orientation estimate from gyroscopes. The principles for measuring orientation of a moving body segment fusing gyroscopes and accelerometers in a Kalman filter have been described in H. J. Luinge,  Inertial Sensing of Human Movement  (Ph.D. Thesis, 2002), and is incorporated by reference herein in its entirety. The magnetic sensor is sensitive to the earth&#39;s magnetic field and it gives information about the heading direction in order to correct drift of the gyroscope about the vertical axis. Methods for integrating these devices are described in E. R. Bachman,  Inertial and Magnetic Tracking of Limb Segment Orientation for Inserting Humans into Synthetic Environments  (Ph.D. Thesis 2000), and E. Foxlin,  Inertial Head - Tracker Sensor Fusion by a Complementary Separate - Bias Kalman Filter  Proc. of VRAIS &#39;96, 185-94 (1996), both incorporated in their entireties by reference herein. 
         [0011]    These Kalman filter implementations use accelerometers and magnetic sensors for low frequency components of the orientation and use gyroscopes to measure faster changes in orientation. Finally, an accelerometer-only based position and orientation tracker is disclosed in “Design and Error Analysis of Accelerometer-Based Inertial Navigation Systems,” by Chin-Woo Tan Sungsu Park for the California Partners for Advanced Transit and Highways (PATH). 
         [0012]    Methods for integrating similar IMDS components with GPS, acoustic, optical and magnetic tracking systems are known in the art. Some examples include “Robust Dynamic Orientation Sensing Using Accelerometers: Model-based Methods for Head Tracking in AR”, by Matthew Stuart Keir, “Accelerometer-based Orientation Sensing for Head Tracking in AR &amp; Robotics,” by Matthew S. Keir, et al, “Using Gravity to Estimate Accelerometer Orientation,” by David Mizell, “Setting up the MMA 7660FC to do Orientation Detection,” Freescale Semiconductor AN3840, “3D Orientation Tracking Based on Unscented Kalman Filtering of Accelerometer and Magnetometer Data,” Benoit Huyghea et al., “Inertial and Magnetic Sensing of Human Movement near Ferromagnetic Materials,” Daniel Roetenberg et al., “An Extended Kalman Filter for Quaternion-Based Orientation Estimation Using MARG Sensors,” Joao Luis Marins et al., “An Improved Quaternion-Based Filtering Algorithm for Real-Time Tracking of Human Limb Segment Motions using Sourceless Sensors,” Eric Bachmann et al., and are incorporated by reference herein in their entireties. In addition to these patents, the general methods for incorporating GPS and sourceless sensors are described in “The Global Positioning System &amp; Inertial Navigation,” by J. Farrell and M. Barth, (McGraw-Hill 1999); “Global Positioning Systems, Inertial Navigation and Integration,” by M. Grewal, L. Weill, and A. Andrew, (John Wiley and Sons 2001); and “Introduction to Random Signals and Applied Kalman Filtering,” by R. Brown and P. Hwang (John Wiley &amp; Sons 1983). These references are also incorporated by reference in their entireties. 
       SUMMARY 
       [0013]    No examples exist of RF-based position tracking systems that use inertial devices in a tracked mobile device to increase stability of the mobile device&#39;s RF signals received at the system&#39;s antennae. Therefore, what is needed is an RF position tracking system that tracks the position of one or more wireless mobile devices in two or three dimensions, improves on the limitations of GPS systems, and effectively integrates inertial sensing information in a combined system that allows the user to obtain a more stabilized and accurate position solution. 
         [0014]    It is an object of the invention to provide a position tracking system that avoids the satellite and receiver clock errors of GPS systems. 
         [0015]    It is also an object of the invention to provide a position tracking system capable of tracking the location of a transmitter in two or three dimensions. 
         [0016]    It is also an object of the invention to provide a system that reduces the signal propagation errors of RF position tracking systems. 
         [0017]    It is also an object of the invention to provide a system that reduces the drift, bias, and scale factor errors of sourceless navigation systems. 
         [0018]    It is also an object of the invention to integrate an inertial/magnetic subsystem (IMDS) in a mobile device to better perform tracking by increasing stability of the system&#39;s received RF signals. 
         [0019]    It is also an object of the invention to integrate an RF positioning system with an inertial/magnetic devices subsystem (IMDS) to provide long-term position stability and accuracy, even when the RF positioning system experiences temporary loss of signal. 
         [0020]    It is also an object of the invention to use Kalman filter implementations in a RF system having accelerometers, magnetic sensors, and/or gyroscopes to measure faster changes in orientation. 
         [0021]    It is also an object of the invention to use inertial sensors to reduce battery consumption allowing the device to transmit its radio signal only when it is moving. 
         [0022]    It is also an object of the invention to use inertial sensors for constant tracking between the device and the system to maintain absolute position monitoring. 
         [0023]    The present invention relates to RF position tracking system that tracks, in two or three dimensions, one or more wireless mobile device(s). The disclosure features utilizing an inertial/magnetic subsystem (IMDS) integrated in the mobile device to better perform tracking by adding stability to the system&#39;s RF signals received at the system&#39;s receiver(s). As RF signals from the mobile device are received at the system receiver, inertial information is also received that helps the system screen interference and multipath by weighting the RF data to best match the inertial data provided by the IMDS. The combined system allows a user to obtain a more stabilized/accurate position solution. 
         [0024]    One embodiment of the invention is a system for wirelessly tracking the physical position of an object. The system has at least one radio frequency (RF) device having an antenna and at least one inertial sensor. The RF device is configured to emit a radio signal. The system has at least three receiver antennae that are each configured to receive a radio signal emitted by the device and transmit that signal to a receiver. The system also has a receiver in communication with the three or more receiver antennae. The receiver is configured to receive the radio signal from each receiver antenna and is further configured to communicate data to a data processor. Another embodiment comprises a positioning and/or navigation method and system thereof, in which the acceleration and/or velocity and/or position and/or heading from an inertial/magnetic navigation subsystem is/are used to supplement the carrier phase tracking of the RF positioning system signals, so as to enhance the performance of the RF positioning system during signal corruption or loss. 
         [0025]    In another embodiment, a positioning and navigation system receives the acceleration, velocity, position, and/or heading measurements from an inertial/magnetic navigation subsystem. The inertial sensor measurement(s) is/are fused in a Kalman filter to supplement the carrier phase tracking of the RF positioning system signals, so as to enhance the performance of the RF positioning system during signal corruption or loss. 
         [0026]    In another embodiment, the present invention provides an automatic power up/power down method that relies on the inertial/magnetic devices subsystem (IMDS). When the IMDS has detected no motion for a period of time, the RF positioning system is powered to a low power state. When motion resumes, the RF positioning system is returned to a full power state. In this way extended battery life may be achieved. 
         [0027]    A method of tracking an object having an inertial sensor and capable of transmitting an RF signal includes each one of at least three antennae receiving an RF signal transmitted from an object to be tracked. The antennae receive an inertial signal from an inertial sensor integrated into or fixed onto the object. The system processes the RF signal and the inertial signal to determine the position of the object. 
         [0028]    Additional advantages and novel features will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and the accompanying drawings or may be learned by production or operation of the examples. The advantages of the present teachings may be realized and attained by practice or use of various aspects of the methodologies, instrumentalities and combinations set forth in the detailed examples discussed below. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0029]    The drawing figures depict one or more implementations in accord with the present teachings, by way of example only, not by way of limitation. In the figures, like reference numerals refer to the same or similar elements. 
           [0030]      FIG. 1  is a block diagram illustrating an embodiment of a positioning and navigation system in which RF-based positioning system measurements and an inertial devices subsystem measurement are blended. 
           [0031]      FIG. 2  is a block diagram illustrating an embodiment of a positioning and navigation system in which RF signal measurements are used to determine the position of a set of transmitter antennae with respect to a set of receiving antennae. 
           [0032]      FIG. 3  is a block diagram showing an embodiment of a positioning and navigation system having a RF position-aided IMDS design. 
           [0033]      FIG. 4  is a block diagram showing an embodiment of a positioning and navigation system having a RF range-aided IMDS design. 
           [0034]      FIG. 5  is a block diagram showing another embodiment of a positioning and navigation system that implements feedback. 
           [0035]      FIG. 6  is a block diagram showing an embodiment of a positioning and navigation system that incorporates acceleration and velocity data in a range-aided or position-aided IMDS design. 
           [0036]      FIGS. 7   a  and  7   b  are flow diagrams for alternate embodiments of a method of tracking an object having an inertial sensor and capable of transmitting an RF signal. 
       
    
    
     DETAILED DESCRIPTION 
       [0037]    In the following detailed description, numerous specific details are set forth by way of examples in order to provide a thorough understanding of the relevant teachings. However, it should be apparent to those skilled in the art that the present teachings may be practiced without such details. In other instances, well known methods, procedures, components, and/or circuitry have been described at a relatively high-level, without detail, in order to avoid unnecessarily obscuring aspects of the present teachings. 
         [0038]      FIG. 1  illustrates one embodiment of a positioning and navigation system  1 . The positioning and navigation system  1  includes inertial/magnetic devices subsystem  10  (IMDS), an RF tracking system  20 , a fusion algorithm processor  30  and a corrected position and orientation output interface  40 . The inertial/magnetic devices subsystem  10  (IMDS) may include gyroscopes  11 , and/or accelerometers  12  and/or magnetic sensors  13 , with their accompanying signal conditioning methods and algorithms processor  14 . INS algorithm block  14  may be based on Kalman filtering techniques. The RF tracking system  20  comprises a set of RF receiving antennae  21 , a set of RF transmitting antennae  22 , RF system hardware  23 , a tracking processor  24 , a fusion algorithm processor  30 , and a corrected position and orientation output interface  40 . 
         [0039]    The gyroscope  11  may be based on fiber optics, ring lasers, vibrating masses, micro-machined devices (MEMS technology), or other technology. A typical three-axis MEMS-based gyroscope  11  is the Analog Devices ADIS 16354, a high precision tri-axis inertial sensor. Multiple, single-axis gyroscopes could also be used. 
         [0040]    The accelerometer  12  may be piezo-electric, capacitive, strain, optical, surface wave, micro-machined (MEMS technology) or one of the many other types of technologies used for measuring acceleration. A typical three-axis MEMS accelerometer  12  is the Analog Devices ADXL325, a three-axis analog accelerometer. The magnetic sensor (magnetometer)  13  can be a Hall effect, GMR, moving coil, magneto resistive, SQUID, spin dependent tunneling, proton precession, flux-gate, or other type of technology. An example of a three-axis magneto resistive magnetometer is the Honeywell HMC1043 three-axis magnetic sensor. 
         [0041]    Finally, IMDS subsystem  10  may also consist of a complete integrated solution, as exemplified by the Razor IMU for Sparkfun Electronics, a 9 degree-of-freedom system that incorporates three devices-an InvenSense ITG-3200 (triple-axis gyro), Analog Devices ADXL345 (triple-axis accelerometer), and a Honeywell HMC5883L (triple-axis magnetometer). The outputs of all sensors  11 ,  12 ,  13  are processed by an on-board Atmel ATmega328 RISC processor  14  and the navigation solution, which is represented by the corrected position and orientation block  40  is output over a serial interface. 
         [0042]    The RF tracking system  20  includes a set of RF receiving antennae  21 , a set of RF transmitting antennae  22 , RF system hardware  23  and a tracking processor  24 . The RF receiving antennae  21  and the transmitter antennae  22  can be a dipole, patch or other antennae appropriate for the particular wavelength. Various combinations of antennae may also be used. The RF system hardware  23  includes RF components that are explained more fully in the description of  FIG. 2 . The processed results from RF system hardware  23  are converted to a position and orientation solution by tracking processor  24 . Tracking processor  24  may include a DSP, embedded processor or other such processing system that runs an algorithm to compute the position and orientation from the processed results. 
         [0043]    As shown in  FIG. 2 , the RF tracking system  20  includes multiple receiver antennae  21 , one or more transmitter antennae  22  and transmitter hardware, and RF system hardware  23 . RF system hardware  23  may consist of amplifiers, limiters, filters, signal sources, demodulators, modulators, and other devices. These devices may be separate entities, may be embedded mathematically in a DSP or processor, or may be a combination of separate and embedded devices. 
         [0044]    The transmitter section  50  consists of a sine wave  220  modulated with a pseudo-random noise sequence  215  by CDMA modulator  210 . This type of modulation may be of the type found in cell phones and other communication devices. The signal is amplified (not shown) and sent to transmitter antenna  22 . 
         [0045]    In the receiver section  60 , the signal is received by the receiver antennae  21  and receiver reference antenna  101 . Receiver antenna  101  is the reference from which the time difference of arrival is measured. The receiver antennae receive the transmitted signal and forward these signals to the receiver circuitry  110  for demodulation using another pseudo-random noise (PN) sequence  115 . PN sequence  115  may be identical to PN sequence  215 , although not synchronized to it in time (in other words, the starting points are not the same). This means that both sequences contain the identical pseudo-random data, but that the data is read from different starting positions. CDMA demodulators  110  retrieve the transmitted sine wave from sine wave generator  220 . Within the tracking processor  24 , which may be a DSP (or microprocessor), the recovered reference sine wave is shifted by 90° so that when the other signals are multiplied by it and then integrated, the reference sine wave provides a measure of phase shift between the reference and the other received signals (i.e., differential phase). The differential phases are used by the position and orientation algorithm in the tracking processor  24  to determine position and orientation  121  of a tracked object. 
         [0046]    Tracking a single transmitter device or transmitter antenna in three dimensions requires at least four receiver antennae  21 ; tracking in two dimensions requires at least three receiver antennae  21 . The receiver antennae  21  provide the reference frame in which the transmitter antennae are tracked. More receiver antennae  21  provide better coverage and more accuracy, but do so with increased complexity and cost. The receiver antennae  21  must be distinct and their respective locations known in space. More transmitter antennae  21  attached to or embedded in a tracked object allow the object&#39;s orientation to be calculated based on geometric principles. 
         [0047]    For example, two transmitter antennae  22 , separated by a distance D, yield a pointer, since the two transmitter antennae  22  form a line with known direction. Three transmitter antennae  22  provide enough information to calculate a three-dimensional orientation. The system  1  can be reversed, with the receiver antennae  21  being tracked and the transmitter antennae  22  providing the reference frame. Recent art can be found in “Communication Systems Engineering,” by Proakis and Salehi, and is incorporated herein. Many variations possible to achieve the same functionality and many of the noted components can be part of an integrated DSP. For example, a DSP might generate sine wave  220  and PN sequence  215 . Discrete multipliers and integrators might be implemented in hardware instead of firmware. 
         [0048]    The inertial/magnetic devices subsystem  10  (IMDS) provides inertial and magnetic field measurements including body angular rates, specific forces, and information on the Earth&#39;s magnetic field direction which are sent to the fusion algorithm processor  30  for minimizing RF tracking system errors during loss or corruption of RF signal. In one embodiment, the position and orientation of the transmitter antennae  22  are calculated in RF algorithm block  24 . 
         [0049]    The position and orientation algorithm is based on solving the underlying range equations. In this phase-based system, the phase is used to measure range. The operating wavelengths of the RF tracking system provide ambiguous phase measurements because phase measurements are modulo 2π numbers. Without further information, only the fractional part of the phase can be determined, making the range incorrect. Equations (1)-(3) illustrate the phase to range measurement relationship. ρ n  is the range, λ is the wavelength (for a fixed frequency), Φn is the measured phase and kn is the integer portion of the phase. Methods exist to determine the additional integer number of wavelengths corresponding to the actual range, but it should be noted that problems due to multipath, line-of-sight issues, and other problems can lead to loss of tracking. 
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     1 
                   
                   = 
                   
                     λ 
                      
                     
                       ( 
                       
                         
                           Φ1 
                           
                             2 
                              
                             π 
                           
                         
                         + 
                         
                           k 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ρ 
                       2 
                     
                     = 
                     
                       λ 
                        
                       
                         ( 
                         
                           
                             Φ2 
                             
                               2 
                                
                               π 
                             
                           
                           + 
                           
                             k 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   … 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     ρ 
                     n 
                   
                   = 
                   
                     λ 
                      
                     
                       ( 
                       
                         
                           
                             Φ 
                              
                             
                                 
                             
                              
                             n 
                           
                           
                             2 
                              
                             π 
                           
                         
                         + 
                         kn 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0050]    One way to measure the phases is against a fixed reference phase. By measuring the transmitter signal&#39;s phase differences recorded at two receiver antennae the distance is calculated. In the following equations, values ρ1-ρ4 represent distances between the receiver antennae positions and the transmitter position and are determined by the phases. Receiver positions are denoted as rcvr_pos receiver number,position coordinate , and are fixed, known quantities. Position coordinate x 1,2,3  represent x,y,z, respectively. 
         [0000]    
       
         
           
             
               
                 
                   
                     p 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 1 
                                 , 
                                 1 
                               
                             
                             - 
                             
                               x 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 1 
                                 , 
                                 2 
                               
                             
                             - 
                             
                               x 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 1 
                                 , 
                                 3 
                               
                             
                             - 
                             
                               x 
                               3 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                      
                     
                         
                     
                      
                     2 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 2 
                                 , 
                                 1 
                               
                             
                             - 
                             
                               x 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 2 
                                 , 
                                 2 
                               
                             
                             - 
                             
                               x 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 2 
                                 , 
                                 3 
                               
                             
                             - 
                             
                               x 
                               3 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                      
                     
                         
                     
                      
                     3 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 3 
                                 , 
                                 1 
                               
                             
                             - 
                             
                               x 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 3 
                                 , 
                                 2 
                               
                             
                             - 
                             
                               x 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 3 
                                 , 
                                 3 
                               
                             
                             - 
                             
                               x 
                               3 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                      
                     
                         
                     
                      
                     4 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 4 
                                 , 
                                 1 
                               
                             
                             - 
                             
                               x 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 4 
                                 , 
                                 2 
                               
                             
                             - 
                             
                               x 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               rcvr_pos 
                               
                                 4 
                                 , 
                                 3 
                               
                             
                             - 
                             
                               x 
                               3 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0051]    Phase differences such as formed from manipulating equations (4)-(7) into differences ρ4−ρ1, ρ3−ρ1, and ρ2−ρ1 provide the same information for determining position while allowing one of the received signals to act as a common reference. 
         [0052]    These four equations are used to solve for x1, x2 and x3, in the RF algorithm  24 , which represents the x,y,z, position of the transmitter, respectively. This can be solved in a least squares algorithm, such as Levenberg-Marquardt or in a Kalman filter, as noted in the references. 
         [0053]    There are many ways to combine the various data streams. According to Gautier in “GPS/INS GENERALIZED EVALUATION TOOL (GIGET) FOR THE DESIGN AND TESTING OF INTEGRATED NAVIGATION SYSTEMS,” a loosely-coupled system calculates position using the RF solution only. The IMDS computes position, velocity and attitude from the raw inertial sensor measurements and uses the RF solution to fix the IMDS errors. A benefit of a loosely coupled system is that the RF system can be treated as a “black box.” In tightly coupled systems, the Kalman filter receives phase measurements of range. Ultra-tightly coupled system utilize contain feedback to the RF system itself. However, in “The Global Positioning system and Inertial Navigation,” by Farrell and Barth, loosely coupled is defined in a more general manner (reference section 7.2.2 and accompanying figures) and allows for some feedback mechanisms to exist. The ultra-tightly coupled method of Gautier is equivalent to Farrell and Barth&#39;s version of tightly coupled. For this reason, and because it is more general, the definition of coupling will be based on Farrell and Barth&#39;s description in what follows. 
         [0054]    Referring to  FIGS. 3-6 , the fusion algorithm processor  30  is shown as a separate processor, which may again take the form of a DSP or microprocessor subsystem. Its job is to combine the inertial/magnetic devices subsystem  10  (IMDS) outputs with those of the RF tracking system algorithm  24  in what might be called an uncoupled form of fusion or unaided inertial solution. Methods of merging the data could require ad-hoc methods to prevent errors from becoming unbounded. Merging these data streams could be done in a Kalman filter. The Kalman filter provides corrected position and orientation outputs  40  by combining the two outputs which could arrive at the fusion processor  32  at different rates. It is also possible to combine algorithm processing  14 ,  30  and  24  into a single processor for all of the algorithms or to combine various portions as necessary. 
         [0055]    This x,y,z position solution from RF algorithm  24  is incorporated into the fusion algorithm processor  30 , which preferably consists of a linearized or extended Kalman filter. The Kalman filter  30  is a recursive filter that estimates the state of a dynamic system. It is commonly used in data fusion applications, among others. The Kalman filter  30  is used to combine, in an optimal manner, the RF tracking system  20  data with those of the IMDS subsystem  10 . If the filter  30  detects short term divergence of the RF and IMDS subsystem, it weights the final solution towards the IMDS information and supplies a corrected position and orientation output  40 . 
         [0056]      FIG. 3  represents different approaches to the second embodiment of the system  1 . When interface  36  is not included, the result is a linearized Kalman filtering approach. When it  36  is there, the result is an extended Kalman filter. Linearized Kalman filters are derived assuming a linearization was performed around the operating point of the filter. Extended Kalman filters utilize non-linear models. Both filters have pros and cons, such as implementation simplicity and speed of processing. 
         [0057]    In this second embodiment, the fusion of RF tracking and inertial tracking is performed in a loosely coupled manner. In loosely-coupled fusion, a link  36  sends the error signal from the Kalman filter  30  to the inertial sensing processor  14  to modify the IMDS  10  output. A feed-forward, complementary filter design, also known as a RF position aided IMDS design, is shown in  FIG. 3 . Many of the main blocks were already defined in  FIG. 1 . At the instant at which the GPS measurement is valid, the IMDS state is saved and used for comparison with the RF data. By driving the Kalman filter  30  with the error between the RF data and the IMDS data (output of block  31 ), it is valid to estimate the navigation error state based on a linearized system model. Second, since the filter is designed based on an error model, all model parameters can be properly defined in a stochastic sense. Third, the responsiveness of the navigation system is determined primarily by the update rate of the IMDS system  10  (assuming it has a faster update rate than the RF system) and the bandwidth of the inertial sensors  11 ,  12 ,  13 . Fourth, because the Kalman filter  30  estimates slowly-varying error quantities, the system  1  can be a low-bandwidth system to attenuate any high-frequency error on the RF aiding signal. This error value is subtracted from the IMDS solution in block  32  to remove errors that occur over time in the IMDS system  10 . 
         [0058]    If link  36  is added, the INS algorithm  14  can be modified to take the error signal generated by Kalman filter  30  and modify the IMDS  10  output at the computation source. This can reduce offsets and biases that are common in inertial hardware  11 ,  12 , and  13 . 
         [0059]    In a third embodiment shown in  FIG. 4 , the fusion of RF tracking and inertial tracking is performed in a loosely-coupled manner. As noted above, loosely-coupled fusion is when link  36  sends the error signal from the Kalman filter  30  to the inertial sensing processor  14  to modify the IMDS  10  output. An example of a feed-forward, complementary filter design, also known as a RF range-aided IMDS design, is shown in  FIG. 4 . Many of the main blocks were already defined in  FIGS. 1 and 3 . The RF algorithm, however, is now incorporated into Kalman filter  30 . Transformation block  35  takes the position solution from the IMDS system  10  and converts it back into range data. Range error is determined in block  31  by subtracting this ranged data from that obtained from RF positioning system  23 . This error range data output of block  31  is now used by Kalman filter  30  to compute a position or position and orientation error solution, which in turn, is used to correct output  40  via block  32 . This embodiment also provides a means to correct phase errors that occur due to multipath, line-of-sight issues, and other sources, since cycle slippage due to the phase being modulo  2 n numbers can be corrected. 
         [0060]    In an alternate embodiment shown in  FIG. 5 , if link  36  is added, the INS algorithm  14  can be modified to receive the error signal generated by Kalman filter  30  and modify the IMDS  10  output at the computation source  14 . This can reduce offsets and biases that are common in inertial hardware  11 ,  12  and  13 . 
         [0061]      FIG. 5  shows another embodiment in which complementary filters may be designed for feedback implementation. In this embodiment, errors between the RF system  20  and the IMDS system  10  are produced by block  31 . These errors are filtered by Kalman filter  30  to produce bias and drift compensation to the inertial components  11 ,  12  and  13 . 
         [0062]      FIG. 6  shows another embodiment of the system  1  in which the fusion of RF tracking and inertial tracking is performed in a tightly-coupled manner. In tightly-coupled fusion, link  36  sends the error signal from the Kalman filter  30  to the inertial sensing processor  14  to modify the IMDS  10  output while interface  37  sends acceleration and velocity data to the RF algorithm  24 . This embodiment has a feed-forward, complementary filter design, also known as a RF-aided IMDS design. This embodiment can be either position- or range-aided, as described previously. A difference in this embodiment is the addition of interface  37 , which provides the RF algorithm  24  with acceleration and velocity data from the inertial hardware  11 ,  12 , and/or  13 . Interface  37  allows RF algorithm  24 , which would preferably be a Kalman filter, to incorporate acceleration and velocity data into its model. This embodiment also provides a means to correct phase errors that occur due to multipath, line-of-sight issues, and other sources, since cycle slippage due to the phase being modulo  2 n numbers, can be corrected. 
         [0063]    An additional use for the accelerometers  12  is as a power-saving device. In this mode of operation, the accelerometer is monitored for periods of no acceleration (hence no velocity or positional changes). During these periods, the RF positioning system, especially the RF transmitters, can be put into a low or no power state. When movement resumes, which would cause an instantaneous acceleration to be measured, the RF transmitters could be powered up to resume RF tracking. Since the fusion algorithm processor  30  mediates this process, it would be able to keep track of the last computed position and orientation  40 , and once acceleration is detected, apply corrections to the position and orientation based on the IMDS subsystem  10  measurements until the RF tracking system  20  comes back on line. 
         [0064]    Depending on total system tracking requirements, including accuracy, cost limitations, or other constraints, one or more components of the inertial/magnetic devices subsystem  10  (IMDS) may or may not be present. Multiple units of each device  11 ,  12 , and/or  13  may be used to sense various directional components. In a minimal embodiment, only one accelerometer  12  may be used to provide positional corrections over short periods of time. Also, while the fusion algorithm processor  30  is expected to run a Kalman filter, other methods for integrating the disparate measurements may be used. 
         [0065]      FIGS. 7   a  and  7   b  show a method  700  of tracking an object having an inertial sensor and capable of transmitting an RF signal. In step  710  of one embodiment, shown in  FIG. 7   a,  each one of at least three antennae receives an RF signal transmitted from an object to be tracked. In step  720  the antennae receive an inertial signal from an inertial sensor integrated into or fixed onto the object. In step  730  the system processes the RF signal and the inertial signal to determine the position of the object. 
         [0066]    In another embodiment of the method, shown  FIG. 7   b,  the method  700  may also comprise the step  725  of merging the received RF signal with the received inertial signal using a Kalman or similar filter. In other embodiments of the method  700 , one or more inertial sensors may be used, including combinations of gyroscopes, accelerometers, and magnetic sensors. Also, the processing step  730  may include applying a fusing algorithm to the received RF signal and the received inertial signal. The method  700  may be used to determine the position of an object in two or three dimensions as explained above regarding the system. Additionally, the processing step  730  may be broken into a first step of pre-processing the received RF signal and a second step of processing the inertial signal. The method  700  may also embody variations and combinations of each embodiment described above. 
         [0067]    Aspects of the position tracking system  1  and method  700  for using radio signals and inertial sensing can be executed on various computing platforms and/or using various programing languages. Program aspects of the technology may be thought of as “products” or “articles of manufacture” typically in the form of executable code and/or associated data that is carried on or embodied in a type of machine readable medium. “Storage” type media include any or all of the memory of the computers, processors or the like, or associated modules thereof, such as various semiconductor memories, tape drives, disk drives and the like, which may provide storage at any time for the software programming. All or portions of the software may at times be communicated through the Internet or various other telecommunication networks. Such communications, for example, may enable loading of the software from one computer or processor into another computer or processor. Thus, another type of media that may bear the software elements includes optical, electrical and electromagnetic waves, such as used across physical interfaces between local devices, through wired and optical landline networks and over various air-links. The physical elements that carry such waves, such as wired or wireless links, optical links or the like, also may be considered as media bearing the software. As used herein, unless restricted to tangible “storage” media, terms such as computer or machine “readable medium” refer to any medium that participates in providing instructions to a processor for execution. 
         [0068]    Hence, a machine readable medium may take many forms, including but not limited to, a tangible storage medium, a carrier wave medium or physical transmission medium. Non-volatile storage media include, for example, optical or magnetic disks, such as any of the storage devices in any computer(s) or the like, such as may be used to implement the data aggregator, the customer communication system, etc. shown in the drawings. Volatile storage media include dynamic memory, such as main memory of such a computer platform. Tangible transmission media include coaxial cables; copper wire and fiber optics, including the wires that comprise a bus within a computer system. Carrier-wave transmission media can take the form of electric or electromagnetic signals, or acoustic or light waves such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media therefore include for example: a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD or DVD-ROM, any other optical medium, punch cards paper tape, any other physical storage medium with patterns of holes, a RAM, a PROM and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave transporting data or instructions, cables or links transporting such a carrier wave, or any other medium from which a computer can read programming code and/or data. Many of these forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution. 
         [0069]    Those skilled in the art will recognize that the present teachings are amenable to a variety of modifications and/or enhancements. 
         [0070]    While the foregoing has described what are considered to be the best mode and/or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications and variations that fall within the true scope of the present teachings.