Abstract:
A full fusion positioning method, which can be implemented in the existing hardware, but is more amenable to the emerging wafer-scale integration hardware, comprises the steps of injecting a global positioning system signal received by a global positioning system antenna and a predicted pseudorange and delta range from a data fusion, and converting and tracking said global positioning system signal to obtain pseudorange and delta range measurement and errors of said pseudorange and delta range measurement, which are passed to said data fusion; receiving a vehicle angular rate and an acceleration signal/data from an inertial measurement unit and solving inertial navigation equations for obtaining a referencing navigation solution, including position, velocity, and attitude, which are passed to a data fusion; and fusing said pseudorange and delta range measurement and said errors of said pseudorange and delta range measurement of said global positioning system and said referencing navigation solution to obtain predicted pseudorange and delta range, optimal estimates of said referencing navigation solution errors and inertial sensor errors, and optimal position information.

Description:
This is a regular application of a provisional application having an application number of 60/110,096, filed on Nov. 27, 1998. The present invention relates to a positioning method, and more particularly to a full fusion positioning method for vehicle, wherein signals from global positioning system, inertial angular sensors, and inertial acceleration sensors are processed in full fusion to obtain improved performance in some stress applications such as long-term accuracy, high degree of tolerance to heavy jamming and high dynamics. 
    
    
     FIELD OF THE PRESENT INVENTION 
     Background of the Present Invention 
     Although vehicle positioning systems have become widely known only during the last few decades, their historical roots go much deeper. The world&#39;s first vehicle positioning system was the “south-point-chariot”, an automatic direction-keeping system developed by the Chinese around 200-300AD (possible earlier according to some legendary accounts), almost 1000 years before the magnetic compass was invented. Its operation was based on the phenomenon that as a vehicle changing heading, the outer wheels travel farther than the inner wheels by a distance that is a simple mathematical function of the change in heading. When changing heading, a gear driven by the outer wheel of the south-point chariot automatically engaged and rotated a horizontal turntable to exactly offset the change in heading. Thus, a figure mounted on the turntable continuously pointed an outstretched arm in the same direction, like a compass needle, regardless of which way the chariot turned. As technologies in positioning systems and in other fields are improved and expanded, Newsday, there are various types of the positioning system. 
     The new technology development in positioning system, which will lead to a low cost, small size, and high accurate positioning system, will have broad applications in the commercial community. The applications of vehicle positioning systems are spreading like wildfire, to car, taxi, busses, trains, robotics, to mining/construction, and to the paging and data portions of the personal communications services market as well as cellular emergency 911 service. 
     The ability to determinate vehicle location is the most fundamental requirement of advanced commercial vehicle tracking systems, automobile navigation and route guidance systems, and intelligent vehicle highway systems. 
     Developments of Intelligent vehicle highway systems are major worldwide movement to improve the efficiency, safety, and environmental aspects of road traffic through the application of information, communication, positioning, and control technologies. 
     Generally, some conventional methods for determining the position of a vehicle are to employ dead reckoning systems, radio positioning systems, and hybrid systems. The method of the present invention is a hybrid, fully fusion method for determining position and attitude of a vehicle. 
     A dead reckoning system based on inertial angular rate sensors and acceleration sensors can provide the position and attitude information of a vehicle. It consists of an inertial measurement unit (IMU) and a processor. The inertial measurement unit consists of three orthogonally or more than three skewed mounted accelerometers, which serve as acceleration sensors to measure the vehicle acceleration, and three orthogonally or more than three skewed mounted gyros, which serve as angular rate sensors to measure the vehicle angular rate, and associated hardware and electronics. These components provide the necessary information to stabilize the navigation reference frame for the purpose of providing isolation from vehicle rotation motions, either physically, in a gimbaled inertial system, or analytically, in a strapdown inertial system. The processor processes the platform&#39;s acceleration and angular rate from the inertial measurement unit. After initializing the starting position and initiating an alignment procedure, a continuous output of position, velocity, and attitude data from the processor is available, independent of any outside agency and environmental conditions. 
     The dead reckoning system based on inertial angular rate sensors and acceleration sensors, which is often referred to inertial navigation system, or inertial positioning system, or inertial reference system has the advantage, over all other positioning methods, that it is totally self-contained and that it outputs the full solution and that it offers wide bandwidth. 
     However, an inertial positioning system is expensive and subjects to drift over an extended period of time. This is primarily caused by its sensor error sources, such as gyro drift, accelerometer bias, and scale factor errors. 
     Generally, the ways of improving accuracy of inertial positioning systems include employing highly accurate inertial sensors and aiding an inertial positioning system using an external sensor. 
     The global positioning system (GPS) is a satellite-based, worldwide, all-weather radio positioning and timing system. The system is originally designed to provide precise position, velocity, and timing information on a global common grid system to an unlimited number of adequately equipped users. 
     A specific receiver is the key for a user to access the global positioning system. A conventional, single antenna receiver of the global positioning system supplies world-wide, highly accurate three dimensional position, velocity, and timing information, but not attitude, by processing so-called pseudo range and delta range measurements from the code tracking loops and the carrier tracking loops respectively. In a benign radio environment, the signal propagation errors and satellites errors, including selective availability, serve as the bounds for positioning errors the global positioning system. However, the signals of the global positioning system may be intentionally or unintentionally jammed or spoofed, and the receiver antenna may be obscured during vehicle attitude maneuvering, and the performance degrades when the signal-to-noise ratio of the global positioning system signal is low and the vehicle is undergoing highly dynamic maneuvers. 
     As both the cost and size of high performance receiver of the global position system are reduced in the past decade, a multiple-antenna receiver of the global positioning system can provide both position and attitude solution of a vehicle, using interferometric techniques. This technology utilizes measurements of carrier phase difference on the multiple-antenna to obtain highly accurate relative position measurements. Then, the relative position measurements are converted to the attitude solution. The advantages of this approach are long-term stability of the attitude solution and relative low cost. However, this system remains the characterization of low bandwidth and being susceptible to shading and jamming, and requires at least 3 antennas configurations for a three-axis attitude solution, and requires antenna separation enough for high attitude resolution. 
     Because of the inherent drawbacks of a stand-alone inertial positioning system and a stand-alone receiver of the global positioning system, a stand-alone inertial positioning system or a stand-alone receiver of the global positioning system can not meet mission requirements under some constraints such as low cost, long-term high accuracy, continuous output, etc. 
     Performance characteristics of the mutually compensating stand-alone global positioning system receiver and the stand-alone inertial positioning system suggest that, in many applications, an integrated global positioning/inertial system, combining the best properties of both systems, will provide superior accurate continuous navigation capability. This navigation capability is unattainable in either one of the two systems alone. Many public papers exist on the topic of an integrated global positioning/inertial positioning system. Numerous global positioning/inertial systems have been commonly used since the concept of the global positioning system was initiated in 1973. 
     The benefits offered by an integrated global positioning/inertial positioning system are outlined as follow: 
     (1) The aiding of the global positioning system receiver signal-tracking loop process with inertial data allows the effective bandwidth of the loops to be reduced, resulting in an improved tracking signal in a noisy and dynamic environment. 
     (2) An inertial positioning system not only provides navigation information when the signal of the global positioning system is lost temporarily, but also reduce the search time required to reacquire the signal of the global positioning system. 
     (3) Inertial positioning system errors and inertial sensor errors can be calibrated while the signal of the global positioning system is available, so that the inertial positioning system can provide more accurate position information after the signal of the global positioning system is lost. 
     (4) The global positioning system enables and provides on-the-fly alignment of an inertial positioning system by means of maneuvering, eliminating the static self-alignment pre-mission requirements of the stand-alone inertial positioning system. 
     But, the above mentioned benefits can not be achieved through any level of integration of global positioning/inertial system hardware and software. There are several possible levels of hardware and software integration configurations of global positioning/inertial system: 
     (1) The first integration approach, and also the simplest from an implementation viewpoint, is to reset the position and velocity derived by the inertial positioning system with the position and velocity derived by a global positioning system receiver. 
     (2) The second integration approach is called cascaded integration and is sometimes referred to as loose integration. It uses the position and velocity derived by a global positioning system receiver (the output of the Kalman filter of the global positioning system receiver) as measurements in an integration Kalman filter, hence the name “cascaded ” (a Kalman filter driven by a Kalman filter). 
     (3) The third integration approach is called a tightly coupled global positioning/inertial positioning system. An integration Kalman filter processes the raw measurements (pseudo-range and delta range) of the global positioning system receiver to provide optimal inertial system error estimates, inertial sensor errors, and the receiver clock offset. The data from the inertial positioning system are used to aid the receiver signal tracking loops to improve the signal tracking performance in heavy jamming and highly dynamic environments. 
     The tightly coupled global positioning/inertial positioning system is an effort to more realize the above mentioned advantages offered potentially by an integrated global positioning/inertial positioning system. 
     Unfortunately, the conventional tightly coupled integration approach may be insufficient for achieving optimal performance of an integrated global positioning/inertial positioning system due to the minimal data exchange between the inertial positioning system and the global positioning system, and the potential instability, though it is commonly adopted to obtain improve performance. 
     The reasons for the potential instability in the conventional tightly coupled global positioning/inertial system approach include: 
     (1) The time constant of the inertial-aided tracking loops which uses a narrow bandwidth is much bigger than the update interval of the integration Kalman filter, and the inertial aiding errors are slowly filtered out. The tracking errors are time-correlated, and they are also correlated with the inertial errors, which are modeled by an integration Kalman filter. The statistic characteristic of the pseudo range and delta range measurements, which is disturbed by the tracking errors, is not compatible with measurement requirements of the integration Kalman filter. 
     (2) There is a positive feedback signal loop in the conventional tightly coupled global positioning/inertial systems. The accuracy degradation of the inertial aiding data increases the signal tracking errors. Because the measurements may severely affect the Kalman filter, which is well tuned for a low accuracy inertial positioning system, increasing the tracking errors fed to the global positioning/inertial processing may cause further inertial positioning system aiding data accuracy degradation. 
     In addition to the instability, conventional tightly coupled global positioning/inertial positioning methods can not efficiently detect and isolate the malfunction of the satellite of global positioning system, because the all measurements are processed in a centralized integration Kalman filter. 
     SUMMARY OF THE PRESENT INVENTION 
     A main objective of the present invention is to provide a full fusion positioning method, in which signals from the global positioning system, inertial angular sensors, and inertial acceleration sensors are processed in full fusion to obtain improved performance in some stress applications such as long-term accuracy, high degree of tolerance to heavy jamming and high dynamics, which can be implemented in the existing hardware, but is more amenable to the emerging wafer-scale integration hardware. 
     Another objective of the present invention is to provide a full fusion positioning method, in which an entirely digital, multistage signal/data processing procedure is employed. 
     Another objective of the present invention is to provide a full fusion positioning method, in which conventional phase locked loop-based signal tracking processing method of the global positioning system is replaced by the “tracking loops-in-all system” signal tracking processing method of the present invention. The signal tracking processing of the global positioning system is implemented in entire full fusion of the global positioning/inertial positioning system to overcome potential instability of traditional tightly coupled global positioning/inertial system and to enhance the signal tracking performance of the global positioning system during high dynamics and a heavy jamming environment. 
     Another objective of the present invention is to provide a full fusion positioning method, in which a maximum likelihood estimator provides the tracking errors of the pseudorange and delta range of the global positioning system receiver to the fusion filter to compensate the correlated noise of pseudorange and delta range measurements of the global positioning system receiver, while the optimal navigation solution provided by the full fusion method is used to compute the predicted pseudorange and delta range measurements of the global positioning system receiver to enclose the signal tracking process of the global positioning system. 
     Another objective of the present invention is to provide a full fusion positioning method, in which a dual-function fusion filter is used to fuse data of the global positioning system and inertial sensors and to perform the function of the GPS signal tracking loop filter. 
     Another objective of the present invention is to provide a full fusion positioning method, in which the dual-function fusion filter uses a parallel, decentralized Kalman filtering structure for reconfiguration, as a response to occurrences of malfunctions of satellites of the global positioning system. 
     Another objective of the present invention is to provide a full fusion positioning method, in which multi-level fault tolerance design is employed to improve reliability of the full fusion positioning solution. 
     Another objective of the present invention is to provide a full fusion positioning method, in which multi-level fault tolerance design is employed to perform the integrity monitoring of the global positioning system. 
     Accordingly, in order to accomplish the above objectives, the present invention provides a full fusion positioning method which comprises the steps of: 
     (a) injecting a global positioning system signal received by a global positioning system antenna and a predicted pseudorange and delta range from a data fusion, and converting and tracking said global positioning system signal to obtain pseudorange and delta range measurement and errors of said pseudorange and delta range measurement, which are passed to said data fusion; 
     (b) receiving a vehicle angular rate and an acceleration signal/data from an inertial measurement unit and solving inertial navigation equations for obtaining a referencing navigation solution, including position, velocity, and attitude, which are passed to a data fusion; and 
     (c) fusing said pseudorange and delta range measurement and said errors of said pseudorange and delta range measurement of said global positioning system and said referencing navigation solution to obtain predicted pseudorange and delta range, optimal estimates of said referencing navigation solution errors and inertial sensor errors, and optimal position information. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram illustrating a full fusion positioning method for vehicle. 
     FIG. 2 is a block diagram illustrating the pre-processing of signals of the global positioning system. 
     FIG. 3 is a block diagram illustrating the digital signal processing of the pre-processing of signals of the global positioning system. 
     FIG. 4 is a block diagram illustrating the pre-processing of signals of the inertial measurement unit. 
     FIG. 5 is a block diagram illustrating the approach 1 of the data fusion. 
     FIG. 6 is a block diagram illustrating the approach 2 of the data fusion. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention relates to a full fusion method of signals of the global positioning system and inertial sensors for continuously determining the position of a vehicle. Referring to FIGS. 1 to  6 , the full fusion positioning method for vehicle of the present invention comprises the following steps. 
     1. Inject global positioning system signal received by a global positioning system antenna  5  for converting and pre-processing the received radio frequency signal of the global positioning system to obtain the global positioning system measurement data, such as pseudorange and delta range measurements, which are passed to a data fusion  80 . 
     2. Receive the vehicle angular rate and acceleration signal/data measured by an inertial measurement unit  10  and solve inertial navigation equations for obtaining a referencing navigation solution, such as position, velocity, and attitude, and pass the referencing positioning solution to the data fusion  80 . 
     3. Fuse the measurement data of the global positioning system and the referencing navigation solution to obtain an optimal fusing positioning solution. 
     To obtain improved performance, in step 1, the signal tracking processing of the global positioning system is implemented in open-loop, and is enclosed in the data fusion  80  to improve degree of tolerance to heavy jamming and high dynamics. 
     To obtain improved performance, in step 2, the optimal estimates of errors of the referencing navigation solution from the data fusion  80  is used to remove the errors of the referencing navigation solution. 
     Referring to FIG. 2, the step 1 further comprises the following steps. 
     (1-1) The L band radio frequency (RF) signals received by the global positioning system antenna  5  are input to a RF/IF converter  21 . The input RF signals are mixed with the local signals from the local numerically controlled oscillator  24 . Then, the mixed signals are band-pass filtered into the Intermediate Frequency (IF) signals. The IF signals are sent to the IF/baseband converter  22 . 
     The global positioning system satellites transmit the radio frequency (RF) coarse acquisition (C/A) signal and precision (P) at L1 band. The ith global positioning system satellite transmits the L1 signal as follows. 
     
       
         S i   L1 (t)={square root over (2+L P c +L )}CA(t) i D(t) i cos(ω 1 t+φ)+{square root over (2+L P p +L )}P(t) i D(t) i sin(ω 1 t+φ) 
       
     
     Where, ω 1 : the L1 radian carrier frequency. 
     φ: a small phase noise and oscillator drift component. 
     P c : the C/A signal power. 
     P p : the P signal power. 
     CA(t): the C/A code. 
     P(t): the P code. 
     D(t): the navigation data. 
     The global positioning system satellites transmit the radio frequency signal and precision (P) at L2 band. The ith global position system satellite transmits the L2 signal as follows. 
     
       
         S i   L2 (t)={square root over (2+L P 2 +L )}P(t) i D(t) i cos(ω 2 +φ 2 ), 
       
     
     where, 
     ω 2 : the L2 radian carrier frequency. 
     P 2 : the L2-P signal power. 
     φ 2 : a small phase noise and oscillator drift component 
     P(t): the P code. 
     D(t): the navigation data. 
     These signals travel at the speed of light and arrive at the antenna of the global position system receiver, as follows:                L1        :                                      S   i   L1          (   t   )       =                    2        P   c            C                     A   i          (     t   -     τ   i       )              D   i          (   t   )            cos              [         (       ω   1     +     ω   id       )        t     +   φ     )         ]     +                                2        P   p                P   i          (   t   )              D   i          (   t   )            sin              [         (       ω   1     +     ω   id       )        t     +   φ     )       ]                 L2        :                                      S   i   L2          (   t   )       =                    2        P   2                P   i          (     t   -     τ   i       )              D   i          (   t   )            cos              [         (       ω   2     +     ω   id       )        t     +     φ   2       )         ]     ,                                
     where, τ: the code delay. 
     ω d : the Doppler radian frequency. 
     i: i th satellite of the global positioning system. 
     The global positioning system signals received by the antenna  5  is sent to the RF/IF converter  21  of the pre-processing of the global positioning system  20 . 
     (1-2) The IF signals from the RF/IF converter  21  are received by the IF/baseband converter  22 . The IF signals are mixed with the local signals from the local numerically controlled oscillator  24 . Then, the mixed signals are amplified, low-pass filtered, and transformed onto baseband signals. The bandwidth of the low-pass (LP) filter is 1.023 MHz, for the C/A code channels, and 10.23 MHz, for the P code channels. The baseband signals are sent to the A/D converter  23 . 
     (1-3) The baseband signals form the IF/Baseband converter  22 , which are analog signals, are received by the A/D converter  23 . The analog baseband signals are sampled to form digital signals, with sampling rates approximately twice as those of the pseudo-random noise (PRN) code (2.1518 MHz for the C/A code signal and 21.5 18 MHz or the P code signals). The digital signals are output to the baseband processor  25 . The L1C/A digital signal ith satellite from the A/D converter  23  is 
     
       
         r i (n)=A i CA i [(1+ζ i )nT S −ξ i T P ]COS[(ω b +ω id )n+φ 0 ]+N(n) 
       
     
     where, 
     A: the signal amplitude. 
     CA[.]: a ±1-valued PRN code with rate, R, delayed by τ=ξT p , with respect to GPS system time (T P  is the code chip width). The code rate is equal to (1+ζ)R 0 , 
     where        ζ   =       f   d       f   L                              
     and F L  is the RF frequency, and R 0 is the code rate without the Doppler shift. 
     T s : the sampling period. 
     ω b : 2πƒ b T s , is the digital radial frequency of the base-band frequency, ƒ b . 
     ω d : 2πƒ d T s , is the digital radial frequency of Doppler shift, ƒ d . 
     φ 0 : the initial carrier phase at n=0. 
     N(n): the equivalent input Gaussian noise at base-band . 
     (1-4) Referring to FIGS. 2 and 3) the digital baseband signals from the A/D converter  23  and the predicted code delay and carrier Doppler shift from the data fusion  80  are received by the digital signal processing  25 , and are used to derive the pseudorange and delta range measurements, and the tracking errors of the pseudorange and delta range for each tracked satellite, which are input to the data fusion  80 . 
     The local reference signals provided by the numerically controlled oscillator  24  are input to the RF/IF converter  21 , IF/baseband converter  22 , and the digital signal processing  25 . 
     Referring to FIG. 3, the digital signals from the (A/D) converter  23  are received by the Mixer  26 , and are mixed with the local in-phase(I) and quadraphase (Q) from the sine-cosine generator  29 . The mixed local in-phase(I) and quadraphase (Q) are output to the correlation  27 . 
     The mixed local in-phase (I) and quadraphase (Q) from the mixer  26  and local code from the code generator  30  are received by the correlation  27 , and are used to perform correlation computation. The results of the correlation computation are output to the Maximum-Likelihood Estimator  28 . 
     N samples of the results of the correlation computation from the correlation are collected by the Maximum Likelihood Estimation  28 . Assuming that the tracking errors of the code delay and the carrier Doppler shift are constant quantities over a small observation interval, the maximum likelihood estimates of the code delay and carrier phase Doppler shift are made by the Maximum Likelihood Estimation  28 , and are transformed to the tracking errors of the pseudorange and delta range respectively, which are sent to the data fusion  80 . 
     The predicted carrier Doppler shift from the data fusion  80  is accepted by the code oscillator  31 , and is used to compute code rate. The generated PRN(pseudo random noise) code with the computed rate is input to the code generator  30 . 
     The PRN code with the computed rate from the code oscillator  31  and the predicted code delay from the data fusion  80  are accepted by the code generator  30 , and are used to generate the local prompt code, which is sent to the correlation  27 , and to compute pseudorange measurements, which are output to the data fusion  80 , and to perform demodulation of satellite ephemeris, which are output to the data fusion  80 . 
     The predicted carrier Doppler from the data fusion  80  are received by the sine-cosine generator  29 , and are used to generate the local I and Q signals, which are sent to the mixer  26 , and to compute delta range measurements, which are sent to the data fusion  80 . 
     Referring to FIG. 4, the step 2 has two operational modes: 
     (1) Feedback compensation; 
     (2) Feedforward compensation. 
     The vehicle angular rate and acceleration information can be provided by the following two types of inertial measurement unit: 
     1) The inertial measurement unit comprises three orthogonally mounted gyros and three orthogonally mounted accelerometers to output three axis angular rates and accelerations; 
     2) The inertial measurement unit comprises more than three skewed mounted gyros and more than three skewed mounted accelerometers to output redundant angular rates and accelerations. 
     Therefore, the step 2 further can be implemented by the following options: 
     2(A) The pre-processing of the inertial measurement unit  50  is implemented in the feedback compensation mode. The threes axis angular rates and accelerations from the inertial measurement unit with three orthogonally mounted gyros and three orthogonally mounted accelerometers and the optimal estimates of inertial sensor errors from the data fusion  80  are input to the error compensation  54  are input to the error compensation  52  of the pre-processing of the inertial measurement unit  50 . 
     The errors of the three axis angular rates and accelerations are compensated with the optimal estimates of inertial sensor errors. The compensated three axis angular rates are output to the attitude matrix computation  53 , and the compensated three axis accelerations are output to the coordinate transformation  54 . 
     The compensated vehicle angular rates from the error compensation  52 , the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame) from the earth and vehicle rate computation  26 , and the optimal estimates of referencing navigation solution errors from the data fusion  80  are received by the attitude matrix computation  53 , and are used to perform the update of a attitude matrix from the body frame (b frame) to the navigation frame (n frame) and to remove the error of the attitude matrix. The obtained attitude matrix is output to the coordinate transformation  54  and the referencing navigation computation  56   
     The way to update the attitude matrix is the Euler method, or the direction cosine method, or the quaternion method. 
     The compensated accelerations from the error compensation  52 , which are expressed in the body frame, and the attitude matrix from the attitude matrix computation  53  are accepted by the coordinate transformation  54  and are used to transform the acceleration expressed in the body frame to the acceleration expressed in the navigation frame. The accelerations expressed in the navigation frame are output to the referencing navigation computation  56 . 
     The acceleration expressed in the navigation frame from the coordinate transformation  54 , and the attitude matrix obtained from the attitude matrix computation  53 , and the optimal estimates of the referencing navigation errors from the data fusion  80  are received by the referencing navigation computation  56 , and are used to compute the referencing position, velocity, and attitude, and to remove the errors of the position and velocity solution. The referencing navigation solution such as position, velocity, and attitude are output to the Earth and vehicle rate computation  55  and the data fusion  80 . 
     The referencing navigation solution from the referencing navigation computation  56  are received by the Earth and vehicle rate computation  55 , and are used to compute the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame), which is output to the attitude matrix computation  53 . 
     2(B) The pre-processing of the inertial measurement unit  50  is implemented in the feedforward compensation mode. The threes axis angular rates and accelerations from the inertial measurement unit with three orthogonally mounted gyros and three orthogonally mounted accelerometers are input to the pre-processing of the inertial measurement unit  50 . The input three axis angular rates are output to the attitude matrix computation  53 , and the input three axis accelerations are output to the coordinate transformation  54 . 
     The input vehicle angular rates from the inertial measurement unit  10  and the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame) from the earth and vehicle rate computation  26  are received by the attitude matrix computation  53 , and are used to perform the update of a attitude matrix from the body frame (b frame) to the navigation frame (n frame). The obtained attitude matrix is output to the coordinate transformation  54  and the referencing navigation computation  56   
     The way to update the attitude matrix is the Euler method, or the direction cosine method, or the quaternion method. 
     The input accelerations from the inertial measurement unit  10 , which are expressed in the body frame, and the attitude matrix obtained from the attitude matrix computation  53  are accepted by the coordinate transformation  54  and are used to transform the acceleration expressed in the body frame to the acceleration expressed in the navigation frame. The accelerations expressed in the navigation frame are output to the referencing navigation computation  56 . 
     The input acceleration expressed in the navigation frame from the coordinate transformation  54  and the updated attitude matrix from the attitude matrix computation  53  are received by the referencing navigation computation  56 , and are used to compute the referencing position, velocity, and attitude. The referencing navigation solution such as position, velocity, and attitude are output to the Earth and vehicle rate computation  55  and the data fusion  80 . 
     The referencing navigation solution from the referencing navigation computation  56  are received by the Earth and vehicle rate computation  55 , and are used to compute the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame), which is output to the attitude matrix computation  53 . 
     2(c) The pre-processing of the inertial measurement unit  50  is implemented in the feedback compensation mode. The redundant angular rates and accelerations from the inertial measurement unit with more than three skewed mounted gyros and more than three skewed mounted accelerometers and the optimal estimates of inertial sensor errors from the data fusion  80  are input to the FDIR  51  the pre-processing of the inertial measurement unit  50 , and used to perform failure detection, isolation and recovery processing on the input the redundant angular rates and accelerations to obtain reliable three axis angular rates and accelerations. The obtained three axis angular rates and accelerations are output to the error compensation  54 . 
     The obtained three axis angular rates and accelerations from the FDIR  51  and the optimal estimates of inertial sensor errors from the data fusion  80  are input to the error compensation  54 . The errors of the three axis angular rate and acceleration are compensated with the optimal estimates of inertial sensor errors. The compensated three axis angular rates are output to the attitude matrix computation  53 , and the compensated three axis accelerations are output to the coordinate transformation  54 . 
     The compensated vehicle angular rates from the error compensation  52 , and the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame) from the earth and vehicle rate computation  26  and the optimal estimates of referencing navigation solution errors from the data fusion  80  are received by the attitude matrix computation  53 , and are used to perform the update of a attitude matrix from the body frame (b frame) to the n frame and to remove the error of the attitude matrix. The obtained attitude matrix is output to the coordinate transformation  54  and the referencing navigation computation  56   
     The way to update the attitude matrix is by the Euler method, or the direction cosine method, or the quaternion method. 
     The compensated accelerations from the error compensation  52 , which are expressed in the body frame, and the attitude matrix obtained from the attitude matrix computation  53  are accepted by the coordinate transformation  54  and are used to transform the acceleration expressed in the body frame to the acceleration expressed in the navigation frame. The accelerations expressed in the navigation frame are output to the referencing navigation computation  56 . 
     The acceleration expressed in the navigation frame from the coordinate transformation  54 , and the attitude matrix obtained from the attitude matrix computation  53 , and the optimal estimates of inertial sensor errors from the data fusion  80  are received by the referencing navigation computation  56 , and are used to compute the referencing position, velocity, and attitude, and to remove the errors of the position and velocity solution. The referencing navigation solution such as position, velocity, and attitude are output to the Earth and vehicle rate computation  55  and the data fusion  80 . 
     The referencing navigation solution from the referencing navigation computation  56  are received by the Earth and vehicle rate computation  55 , and are used to compute the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame), which is output to the attitude matrix computation  53 . 
     2(d) The pre-processing of the inertial measurement unit  50  is implemented in the feedforward compensation mode. The redundant angular rates and accelerations from the inertial measurement unit from the inertial measurement unit with more than three skewed mounted gyros and more than three skewed mounted accelerometers are input to the FDIR  51  of the pre-processing of the inertial measurement unit  50 , and used to perform failure detection, isolation and recovery processing on the input the redundant angular rates and accelerations to obtain reliable three axis angular rates and accelerations. The obtained reliable three axis angular rates are output to the attitude matrix compensation  53 . The obtained reliable three axis accelerations are output to the coordinate transformation  54 . 
     The input vehicle angular rates from the FDIR and the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame) from the earth and vehicle rate computation  26  are received by the attitude matrix computation  53 , and are used to perform the update of a attitude matrix from the body frame (b frame) to the navigation frame (n frame). The attitude matrix is output to the coordinate transformation  54  and the referencing navigation computation  56   
     The way to update the attitude matrix is the Euler method, or the direction cosine method, or the quaternion method. 
     The input accelerations from the FDIR  10 , which are expressed in the body frame, and the attitude matrix obtained from the attitude matrix computation  53  are accepted by the coordinate transformation  54  and are used to transform the acceleration expressed in the body frame to the acceleration expressed in the navigation frame. The accelerations expressed in the navigation frame are output to the referencing navigation computation  56 . 
     The input acceleration expressed in the navigation frame from the coordinate transformation  54  and the updated attitude matrix from the attitude matrix computation  53  are received by the referencing navigation computation  56 , and are used to compute the referencing position, velocity, and attitude. The referencing navigation solution such as position, velocity, and attitude are output to the Earth and vehicle rate computation  55  and the data fusion  80 . 
     The referencing navigation solution from the referencing navigation computation  56  are received by the Earth and vehicle rate computation  55 , and are used to compute the rotation rate vector of the local navigation frame (n frame) relative to the inertial frame (i frame), which is output to the attitude matrix computation  53 . 
     Referring to FIGS. 5 and 6, the step 3 has two approaches: 
     3(A) centralized Kalman filter-based approach 
     3(B) decentralized Kalman filter-based approach, such as Federated Kalman filter. 
     Referring to FIGS. 5 and 6, the step 3(a) further comprises the following steps: 
     3(a)-1. Referring to FIG. 5, If the pre-processing of inertial measurement unit  50  is implemented in the feedback compensation mode, the switcher  90  is closed to the pre-processing of inertial measurement unit  50 . The referencing navigation solution from the pre-processing of inertial measurement unit  50 , which is compensated with the feedback optimal estimates of the errors of the referencing navigation solution from the centralized filter  81 , is accepted by the subtractor  82  and is passed to the predicted pseudorange and delta range computation  83 , and is output as the full fusion positioning solution. 
     If the pre-processing of inertial measurement unit  50  is implemented in the feedforward compensation mode, the switcher  90  is closed to the subtractor  82 . The referencing navigation solution from the pre-processing of inertial measurement unit  50  and the optimal estimates of the errors of the referencing navigation solution from the centralized filter  81  is accepted by the subtractor  82  and are used to compensate the errors of the referencing navigation solution with and the optimal estimates of the errors of the referencing navigation solution from the centralized filter  81 . The compensated referencing navigation solution is passed to the predicted pseudorange and delta range computation  88  and are output as full fusion positioning solution. 
     The satellite ephemeris from each digital signal processing  25  of each tracked satellite channel, the referencing navigation solution from the substractor  90 , and the optimal estimates of receiver clock offset and offset rate of the global positioning system are accepted by the predicted pseudorange and delta range computation  83 . 
     The predicted pseudorange and delta range for each tracked satellite channel is calculated from: the global positioning system satellite position and velocity, the position and velocity of the inertial measurement unit, the Kalman estimated receiver clock offset and offset rate, the deterministic clock correction of the global positioning system satellite, and the computed atmospheric delays. 
     The predicted pseudorange and delta range for each tracked satellite channel is output to the centralized filter  81 , and is transformed to the predicted code delay and carrier Doppler shift of the global positioning system signal, which is output to the digital signal processing  25  of each tracked satellite channel to enclose each signal tracking loop of the global positioning system receiver. 
     3(a)-2. The dynamics of the referencing navigation parameter errors such as 3 position errors, 3 velocity errors 3 attitude errors, and inertial sensor errors such as accelerometer measurement errors, gyro measurement errors, and receiver clock errors are modeled by the centralized filter as follows: 
     
       
         X(t)=F(t)X (t)+G (t)W (t) 
       
     
     The measured pseudorange and delta range measurement and tracking error of the pseudorange and delta range measurement from the digital signal processing  25  for all tracked satellite channel, the predicted pseudorange and delta range measurement for all tracked satellite channels and satellite ephemeris and the referencing inertial navigation solution from the predicted pseudorange and delta range computation  83  are output to the centralized filter  81 , and used to perform the following steps: 
     Updating the parameters of the system and measurement equations; 
     Computing the parameters for discrete model of the system equation; 
     Computing the parameters for the linear model of the measurement equation; 
     Computing the time propagation of the state estimation and covariance matrix; 
     Differencing the measured pseudorange and delta range measurement with the predicted pseudorange and delta range measurement. The differences are compensated with the tracking error of the pseudorange and delta range measurement and are used as the measurements of the centralized filter  81 . 
     Computing measurement residuals; 
     Updating the state estimation and covariance matrix; 
     The updated state estimation is output to the substractor  82  and the pre-processing of inertial measurement unit  50 . 
     3(a)-3. The measurement residuals from the centralized filter  81  are input to the FDIR  84 , and are used to perform the test-statistical distribution of the input measurement residuals to detect and isolation possible failure of the input pseudorange and delta range measurements caused by the malfunction of the satellite of the global positioning system. If a failure is detected, an indication of the malfunction satellite is output by the FDIR to the centralized filter  81  to isolate the malfunction or update the centralized filter  81 . 
     3(b)-1. Referring to FIG. 6, If the pre-processing of inertial measurement unit  50  is implemented in the feedback compensation mode, the switcher  90  is closed to the pre-processing of inertial measurement unit  50 . The referencing navigation solution from the pre-processing of inertial measurement unit  50 , which is compensated with the feedback optimal estimates of the errors of the referencing navigation solution from the master  86 , is accepted by the subtractor  87  and is passed to the predicted pseudorange and delta range computation  88 , and is output as the full fusion positioning solution. 
     If the pre-processing of inertial measurement unit  50  is implemented in the feedforward compensation mode, the switcher  91  is closed to the subtractor  87 . The referencing navigation solution from the pre-processing of inertial measurement unit  50  and the optimal estimates of the errors of the referencing navigation solution from the master filter  86  are accepted by the subtractor  87  and are used to compensate the errors of the referencing navigation solution with and the optimal estimates of the errors of the referencing navigation solution from the master filter  86 . The compensated referencing navigation solution is passed to the predicted pseudorange and delta range computation  88  and are output as full fusion positioning solution. 
     The satellite ephemeris from each digital signal processing  25  of each tracked satellite channel, the referencing navigation solution from the referencing navigation computation  56  from the substractor  91 , and the optimal estimates of receiver clock offset and offset rate of the global positioning system from the master filter  86  are accepted by the predicted pseudorange and delta range computation  88 . 
     The predicted pseudorange and delta range for each tracked satellite channel is calculated from: the global positioning system satellite position and velocity, the position and velocity of the inertial measurement unit, the Kalman estimated receiver clock offset and offset rate, the deterministic clock correction of the global positioning system receiver, and the computed atmospheric delays. 
     The predicted pseudorange and delta range for each tracked satellite channel is output to the local filter  85  for the corresponding tracked satellite channel, and is transformed to the predicted code delay and carrier Doppler shift, which is output to the digital signal processing  25  of each tracked satellite channel to enclose each signal tracking loop of the global positioning system receiver. 
     3(b)-2. The dynamics of the referencing navigation parameter errors such as 3 position errors, 3 velocity errors 3 attitude errors, and inertial sensor errors accelerometer measurement errors, gyro measurement errors, and receiver clock errors are modeled by each local filter  85  as follows: 
     
       
         X(t)=F(t)X (t)+G (t)W (t) 
       
     
     The measured pseudorange and delta range measurement from the digital signal processing  25 , the predicted pseudorange and delta range measurement from the predicted pseudorange and delta range computation  88  for each tracked satellite channel, and satellite ephemeris and the referencing inertial navigation solution from the predicted pseudorange and delta range computation  88  are output to the local filter  85 , and the following steps are performed in each local filter  85 : 
     Updating the parameters of the system and measurement equations; 
     Computing the parameters for discrete model of the system equation; 
     Computing the parameters for the linear model of the measurement equation; 
     Computing the time propagation of the local state estimation and covariance matrix; 
     Differencing the measured pseudorange and delta range measurement with the predicted pseudorange and delta range measurement for each tracked satellite channel. The difference are compensated with the tracking error of the pseudorange and delta range measurement and are used as the measurement of the local filter  85  of corresponding tracked satellite channel. 
     Computing measurement residuals; 
     Updating the local state estimation and covariance matrix; 
     The updated local state estimation and covariance matrix are output to the master filter  86  and the FDIR  89 . 
     3(b)-3. The local state estimation and covariance matrix from each local filter  85  is input to the master filter  86 , and is used to perform fusion processing to obtain global optimal state estimates. The obtained global optimal state estimates are output to the FDIR  89  and switcher  91 . 
     The global optimal state estimation, which includes optimal estimates of inertial navigation solution errors, the global position system receiver errors, and the inertial sensor errors, and the covariance matrix obtained from the master filter  86  are fed back to each local filter  85  to reset the local filter  85 , and are used to perform information-sharing among the master filter  85  and each local filter  85 . 
     To obtain different system performance, the communication between the master filter  85  and each local filter  85  and estimation method used in the master filter  85  and each local filter may have different approaches. 
     3(b)-4. The local state estimation and covariance matrix from each the local filter  85  and the global optimal state estimation and covariance from the master filter  86  are received by the FDIR  89 , and are used to perform consistency test to detect and isolation possible failure of the input pseudorange and delta range measurements caused by malfunction of the satellite of the global positioning system. If a failure is detected, an indication of the malfunction satellite is output by the FDIR  89  to the master filter  86  to configure the master filter  86  to isolate the malfunction. 
     The performance of the FDIR  89  in the approach 3(b) is better than that of the FDIR  84  in the approach 3(a) to facilitate global positioning system integrity monitoring because the approach 3(b) provides a parallel filtering structure. 
     Integrity means the system&#39;s ability to provide timely warnings to users to shut down operations. The one concern is the possibility that a malfunction of the global may transmit an erroneous navigation signal to the global positioning system receiver. It is required that a malfunction of the global positioning system be detected within 10 s of the time at which the navigation accuracy is outside the defined alarm limits. Unfortunately, the Control Segment of the global positioning system can not react to malfunctions of the global positioning system within this time frame. Typically, it takes the Control Segment from 15 min to 2 hours to determine that there is a problem, identify it, determine a course of corrective action, and implement that action.