WO1998049577A2

WO1998049577A2 - Methods for gyro bias estimation using gps

Info

Publication number: WO1998049577A2
Application number: PCT/US1998/006568
Authority: WO
Inventors: George Jeffrey Geier
Original assignee: Motorola Inc.
Priority date: 1997-04-07
Filing date: 1998-04-02
Publication date: 1998-11-05
Also published as: EP0934506A2; EP0934506A4; WO1998049577A3

Abstract

Augmenting the GPS receiver (30) with some form of Dead Recknoning (DR), such as a gyros (35), fills in the gaps occurring as a result of loss of GPS coverage. The present invention permits reliable and automatic estimation and calibration of the gyro zero rate bias. In particular, three specific methods (FIGs. 2-4) are disclosed whereby one method (FIG. 2) makes use of a 'GPS gyro' for detecting vehicle heading change, another (FIG. 3) makes use of a 'GPS accelerometer' for detecting stationary periods, and another (FIG. 4) makes use of a Kalman filter model for open loop heading error and is used to extract the contribution of and so estimate the gyro bias.

Description

METHODS FOR GYRO BIAS ESTIMATION USING GPS

Background of the Invention

Use of global positioning satellite (GPS) receivers in automotive navigation, emergency messaging, and tracking systems is now widespread. However, systems based solely on GPS generally do not work well in dense city environments, where signal blockage and reflection by tall buildings, in addition to radio frequency interference, often occurs. A cost effective solution to this problem is to augment the GPS receiver with some form of Dead Reckoning (DR), to fill in the gaps occurring as a result of loss of GPS coverage and improve the accuracy of the GPS trajectory.

A DR system often takes the form of an interface to the transmission odometer of the vehicle to provide an indication of speed, in combination with a low cost gyro to track the vehicle's heading. The accuracy of the DR system is critically dependent upon the accuracy to which the vehicle's heading is determined whereby each degree of heading error, in the absence of GPS, produces a cross-track position error which grows approximately as 1.7% of distance traveled. The error associated with low cost rate gyros is generally dominated by their zero rate bias, which can be several degrees per second at turn on, and drift significantly with both time and temperature variations. This rate bias, if not removed, produces a heading error which grows linearly, proportional to the bias, in the absence of GPS heading information. This heading error growth produces a quadratic growth in cross track position error, in the absence of GPS position information. Calibration of this zero rate bias is therefore essential in using the low cost gyro, even for relatively short duration lapses in GPS coverage.

Traditional methods of gyro bias calibration make use of knowledge of stationary periods of the host vehicle, since the vehicle is usually not turning unless it is moving. Such methods, such as the one described in Ribbens, W.B., "Understanding Automotive Electronics", Howard W. Sams & Co., Fourth Edition, 1992, generally rely upon the vehicle's odometer to determine the stationary periods, and so work best with Hall-effect sensing.

U.S. Patent number 5,416,712 discloses a method, whereby a low pass filter is used to update the gyro's zero rate bias from measurements which are made during stationary periods. Similarly, in an article entitled "Design and Analysis of a Low Cost GPS Aided Navigation System", James F. McLelland, M.S. Thesis, Department of Surveying, University of Calgary, Calgary, CA, January 1992, a similar approach is used, with zero rate bias measurements input to a Kalman filter which estimates the bias. However, these methods are unreliable or ineffective if Hall effect sensors are not installed in the host vehicle whereby variable reluctance sensors are typically used, which do not reliably sense low vehicle speeds. Therefore, with variable reluctance sensors, the vehicle may be moving (and so turning) when the sensor indicates that the vehicle is stationary. Further, speeds up to several miles per hour may not be sensed. Accordingly, traditional methods of gyro bias calibration, when used with variable reluctance sensors, can undesirably interpret vehicle turns as gyro zero rate bias, which can lead to excessive errors in the navigation system.

This invention permits reliable and automatic estimation and calibration of the gyro zero rate bias without requiring the installation of Hall effect sensors. Three methods, which can be used individually or in combination, are disclosed whereby two of the methods are based upon innovative GPS detection schemes, referred to as a "GPS gyro", used for detecting vehicle heading change, and a "GPS accelerometer", used for detecting stationary periods. Note that neither of these methods requires information from the vehicle's odometer. Note however that the effectiveness of each method can be improved by using vehicle speed data. The third method operates at periodic intervals, without requiring knowledge of stationary or straight driving, and makes use of a Kalman filter model for open loop heading error to extract the contribution of and so estimate the gyro bias.

Brief Description of the Drawings FIG. 1 is a block diagram illustrating the components of a GPS receiver integrated with a gyro and transmission odometer-based DR system installed in a movable vehicle;

FIG. 2 is a flowchart which indicates the use of a GPS gyro-based approach in gyro bias calibration in accordance with a preferred embodiment of the present invention;

FIG. 3 is a flowchart which indicates the use of a GPS accelerometer-based approach in gyro bias calibration in accordance with a preferred embodiment of the present invention; and

FIG. 4 is a flowchart which indicates the use of an open loop heading propagation in conjunction with a Kalman filter for gyro bias calibration in accordance with a preferred embodiment of the present invention.

Detailed Description of the Drawings

FIG. 1 illustrates the components of the vehicle navigation system which could make use of the present invention, comprised of a GPS receiver 30, with a serial port input message added for input of DR sensor information to the receiver (i.e., the gyro sensed heading change, and odometer derived distance travelled) and software added to the receiver's microprocessor to implement the gyro bias calibration. The gyro can be placed anywhere in the vehicle: its sensitive axis, however, must be oriented toward the local vertical to sense heading rate.

Referring to FIG. 1, a block diagram illustrating components of a GPS and DR system installed in a movable vehicle 10 is shown. FIG. 1 includes DR processor 40 and GPS receiver 30 that is coupled to a GPS antenna 20, all of which are suitable for installation in movable vehicle 10. Also shown in FIG. 1 are a plurality of GPS satellites 5 for generating GPS signals that are received by the GPS receiver 30 for enabling GPS receiver 30 to determine the position of movable vehicle 10 in a well known manner. Generally, four satellites are required for enabling GPS receiver 30 to obtain a three-dimensional position fix for vehicle 10. DR processor 40, which may be embedded in the GPS receiver, receives GPS data 32, such as Doppler or heading measurements, from GPS receiver 30, and accepts angular rate data 45 from a gyro 35, and speed data 46 from odometer interface 47 which may be coupled to the transmission of the vehicle. The DR processor 40 also outputs the integrated position data 50 to an application specific device 60. For vehicle navigation applications, application specific device 60 may be a separate processor which implements a map matching algorithm to locate the vehicle on the correct street and to generate a display visible to the driver. For vehicle navigation applications, application specific device 60 may be a separate processor which implements a map matching algorithm to locate the vehicle on the correct street and to generate a display visible to the driver. For emergency messaging and vehicle tracking applications, application specific device 60 may provide the necessary interface to a cellular phone or radio for establishing a communication link to proper third parties thereby informing such third parties of the location of movable vehicle 10.

The "GPS gyro" based approach for gyro bias calibration is illustrated in FIG. 2. GPS Doppler residuals are collected from the GPS receiver 300 and used in a unique way to determine when the vehicle's heading is essentially constant. This enables an accurate measurement of the gyro bias when the vehicle is moving. Each Doppler residual is found by removing the contribution of the (known) satellite velocity from the measured Doppler shift to that satellite, which is derived by the receiver's tracking loop. Successive pairs of Doppler differences are differenced to form a Doppler double difference δΔDopp_res in 310, which is used to determine the heading change 320 using Eqn. (1) below:

ΔHGPS¹³ = (δΔDopp_res - Δv Δvf_actor) / (v ΔHf_actor) (1)

where: δΔDopp_res = (Dopp_j-eg¹ - Dopp_resJ)k - opp^¹ -

Dopp_resJ)k-l' the Doppler double difference; i and j are the two satellite indices; k is a time index;

Dopp_res i_s the Doppler measurement residual;

Δvf_act_or = cosEj cosdAzj - cosEj cosdAzj;

ΔHf_act_or = cosEj sindAzj - cosEj sindAzj;

Δv is the sensed speed change over the current second; v is the speed at the previous second;

Ei, Ej are the two satellite elevation angles; dAz = H - Az;

Azj, Azj are the two satellite azimuth angles; and

H is the heading at the previous second.

Note that Eqn. (1) utilizes only two Doppler measurements. Also note that v and Δv in Eqn. (1) are determined as a function of DR sensor availability. However, if vehicle speed data is supplied (i.e., an interface to the vehicle's transmission or wheel sensors exists), then this can be used to estimate both speed and speed change in Eqn. (1). On the other hand, if such an interface does not exist, speed and acceleration information are derived from GPS.

If more than two satellites are tracked by the GPS receiver (which is generally the case), each pair-wise difference can be used to construct a Doppler double difference and solve for a heading change. Each of these heading changes ΔHGPS^1J is optimally combined using Weighted Least Squares (WLS) 330, where the heading change solution from each Doppler pair is weighted inversely proportional to its error variance. The error variance for the heading change solution from each Doppler pair is given by Eqn. (2) below:

σ²ΔH = I² (^PRR¹ + σ²PRRJ) + σ²QSF ^{Δv2 Δ} factor² +

ΔsinE² (Δv² OM² + v² _σΔM ² )} / v² ΔH_factor ² (2) where: °"²PRR ⁼ ith satellite Doppler measurement noise variance; σ²oSF ⁼ odometer scale factor error variance; ΔsinE = sinEi - sinEj;

OM² = variance associated with road slope; and ^σΔM^{2 =} variance associated with road slope change.

Note that the error variances associated with the road slope and its rate of change are preassigned values representative of general road conditions.

Following computation of the WLS solution for heading change 330 from the solutions derived for each Doppler pair, an integrity test statistic is computed in 340. This statistic is the normalized root-sum-square of the solution residuals (i.e., the difference between the WLS solution and the heading change solution found from each Doppler double difference). A solution residual magnitude which is excessively large relative to the assumed heading change solution measurement variance σ ^H will invalidate the WLS solution, and the integrity test 350 will fail. Failure of the integrity test will cause the gyro bias estimator to be bypassed. On the other hand, if the solution residuals are consistently small, the integrity test 350 will pass, and the magnitude of the WLS heading change will be examined in 360.

If the WLS solution for heading change is sufficiently small such that nearly straight travel can be assumed, the measurement of the gyro bias is formed 370 as given by Eqn. (3) below.

b^m = ΔHgyro - ΔHGPSgyro (3)

where: b = gyro bias measurement;

ΔHGPSgyro is the WLS solution for heading change, found by inversely weighting (according to O"²ΔH ) the solutions from each GPS Doppler pair AHQPS^; and ΔHgyro is the gyro sensed heading change.

Note that Eqn. (3) could alternatively be formed by excluding the subtraction of AHGPSgyro whereby the significance of its inclusion is determined from the magnitude of the threshold used for detection of straight travel in 360. For sufficiently small thresholds, the contribution of ΔHGPSgyro in Eqn. (3) is only representative of the WLS solution error. On the other hand, use of a larger threshold in 360 will likely include periods of slow vehicle heading change, when subtraction of ΔHGPSgyro n Eqn. (3) is important. Eqn. (3) represents a measurement, contaminated by gyro "noise", (reduced by high rate sampling of the gyro signal), other gyro error effects (e.g., scale factor error, reduced by restricting the use of Eq. (3) to relatively small heading changes), and errors in the GPS gyro determined heading change. It is therefore applied to a low pass filter (to attenuate high frequency error effects), or a Kalman filter, which would model the gyro error dynamics associated with the gyro bias before the gyro bias estimate is updated 380, as indicated by Eqn.(4) below.

b^est = b^est + k (b^m - b^est) (4)

where b is the bias estimate used to compensate the gyro output, initialized to zero; and k is the filter gain.

In summary, this first approach for estimating the zero gyro bias includes making use of GPS heading information in a unique way to achieve a gyro bias estimate. The GPS headings are used with odometer derived speed, when available, to form an angular rate estimate ΔHGPSgyro- This rate estimate is highly accurate, since it makes use of Doppler double differencing, which removes the dominant error source in each GPS heading (i.e., the contribution of SA). The rate estimate can be used to determine when the vehicle is travelling nearly straight, when the gyro bias can be reliably measured. Note that ΔHGPSgyro can alternatively be found by simply differencing successive headings derived directly from GPS. However, although use of the Doppler double differencing is preferred, this simpler approach may be adequate in many embodiments of the invention, and replaces the sequence of operations indicated in steps 300-350 of FIG. 2 by a simple differencing of the GPS headings.

Referring now to FIG. 3, the "GPS accelerometer" based approach is illustrated. GPS Doppler information is also used in a unique way to determine when the vehicle is not accelerating whereby this information can be accurately estimated from GPS information, since the acceleration associated with Selective Availability (SA), the dominant source of GPS Doppler error, is below the level of any vehicle acceleration. When knowledge of zero acceleration is coupled with speed information derived from either GPS (i.e., without the odometer interface), and/or from the (non Hall- effect sensing) odometer, and the sensed speed is below some threshold, it can be reliably determined that the vehicle is stationary.

The "GPS accelerometer" approach begins by collecting the available Doppler residuals from the receiver 400, as was done with the GPS gyro approach. The Doppler double differences are then formed 410, as previously detailed below Eqn. (1). Each Doppler double difference can then be used to estimate the change in vehicle velocity 420, as given by Eqn. (5) below.

ΔvGPS^1] = [δΔDoppresij + ΔH (ΔHfactor)] / Δvfactor (5)

where ΔH is the heading change sensed by the gyro.

As was the case for the GPS gyro determined heading change, Eqn. (5) is based on information from only a pair of satellites. Generally, more satellites are available, and the acceleration determined from each pair will be combined optimally using WLS 430, where each velocity change solution will be weighted inversely proportional to its error variance. Eqn. (6) provides an expression for the error variance associated with each pair-wise solution. σ² _Δv = {2 (σ² _PRRi + σ²PRRJ) + v² ΔH² ΔHf_actor ² (σ²GSF + ^σ2OSF)

ΔsinE² v² σ^M² 1 / Δvf_actor ² (⁶)

Following formation of the WLS solution, an integrity test statistic is formed 440 before computing the acceleration estimate. This statistic is this normalized root- sum-square of the solution residuals (i.e., the difference between the WLS solution and the velocity change solution found from each Doppler double difference). A solution residual magnitude which is excessively large relative to the assumed velocity change solution measurement variance σ² _Δv will invalidate the WLS solution, and the integrity test 450 will fail. Failure of the integrity test 450 will cause the gyro bias estimator to be bypassed. On the other hand, if the solution residuals are consistent, the integrity test 450 will pass, and the magnitude of the WLS velocity change solution is tested 460. If the computed velocity change is sufficiently small, it is concluded that the host vehicle is not accelerating, and a test 470 for a stationary condition may be performed. If the velocity change magnitude test 460 fails, on the other hand, the bias estimation is bypassed for this cycle.

Given that the GPS accelerometer, in combination with the odometer and /or GPS determined speed has determined that the vehicle is stationary, the gyro sensed heading change is a direct measurement of the gyro bias 480, as indicated in Eqn. (7), and can (again) be applied to a low pass or Kalman filter to update 490 the estimate of the gyro bias, as described previously by Eqn. (4).

b^m = ΔHgyro (7)

Note that the acceleration estimate Δv can alternatively be found by simply differencing succesive GPS speeds, which can replace steps 400 through 460 in FIG. 3. Although use of the Doppler double differencing is preferred, this simpler approach may be adequate in many embodiments of the invention. In summary, this second approach for estimating the zero gyro bias includes making use of GPS acceleration information to achieve a gyro bias estimate. In forming the acceleration estimate, Doppler double differencing is used, which removes the dominant error source in each GPS determined speed (i.e., the contribution of SA). The acceleration estimate can be used to determine when the vehicle is nearly stationary, when the gyro bias can be reliably measured.

Referring now to FIG. 4, the gyro bias estimation method based on Kalman filter extraction from an "open loop" propagation of the DR system heading is illustrated. The open loop propagation is initiated periodically from a reliable GPS heading 500. In addition, error variances, denoted σ²HOL ^anc* ^σ2Hδb_> which represent the uncertainty associated with the open loop propagation of heading, and the uncertainty attributable to the uncompensated gyro bias, are initialized, as indicated in the equations below.

^HOL = ^HGPSstart (8)

where HQL is the open loop heading; and

HGPSstart i^s the GPS heading used to initialize the open loop propagation.

σ²HOL = 0 (9) σ² _Hδb = 0 (10)

Propagations of the open loop heading HQL 510 and the error variances associated with the open loop heading σ²HOL ^an<^ the uncompensated gyro bias σ²Hδb 520 are then initiated, as given by the equations below:

HQL = HQL + ΔHgyro (11) where ΔHgy_ro is the gyro sensed heading change, compensated with the current gyro bias estimate.

σ²HOL = σ²HOL + σ²HGSF + σ²Hδb (¹²)

where ^σ2HGSF ^s the heading error variance associated with the gyro scale factor error.

σ²Hδb = σ²Hδb + ²σδHδb (13)

where ^σδHδb i^s the correlation between the heading error and the uncompensated gyro bias.

σδHδb = σgHδb + ^δb (14)

where o δb is the error variance associated with the uncompensated gyro bias.

These propagations 510 and 520, as mechanized by Eqns. (11)-(14) above, continue until sufficient heading error has accumulated due to the gyro bias, as evidenced by the magnitude of σ²Hδb- A test 530 is performed whereby if the threshold is not exceeded by σ²j-[δb ^ test 530, the gyro bias estimation is bypassed for this cycle. On the other hand, if the bias error variance σ^gj-, exceeds a predetermined threshold (e.g., representing 5 degrees of error accumulation, one sigma), a bias measurement 540 will be constructed, which may lead to an update of the estimated bias 580 (if test 560 passes). The equation used to form the bias measurement 540 is given below.

b^m = (HQL - HGPSstop) / Δtbias (15) where HGPSstop is the GPS heading at the time at which the open loop propagation is stopped;

Δtbias the time interval over which the gyro bias is propagated; and

HGPS is the GPS derived heading.

The bias must be extracted from the measurement expressed by Eqn. (15) using a Kalman filter which models the error contributors to H_0L-

Following formation of the bias measurement 540, the measurement noise and residual variances are computed in 550, as given by the equations below.

σ² _n = σ²HGPSstart + σ²HGPSstop + °²ngyro (¹⁶)

where °²HGPSstart i^s the error variance assigned to the GPS heading used to initialize the open loop propagation in Eqn. (8); ^σ2HGPSstop i^s the heading error variance assigned to the GPS heading at the end of the propagation interval, used in Eqn. (15) to construct the bias measurement; and θ" ngyro is the error variance associated with the noise in the gyro reading itself, including quantization error.

σ²res = °²n + σ²HOL (17)

If the residual variance test 560 fails, the bias update 580 is bypassed. On the other hand, if the residual variance test 560 passes, the Kalman gain is computed using Eqn. (18):

kgain = ^σ2Hδb / σ²res (18) Once the gain is computed, the bias estimate, its error variance, and its correlation with the DR system heading error can be updated 580, as given by the equations below.

b^est = b^est + k_gain (b^m - b^est) (19)

σ²δb = (1 - k_gain) σ²g (20)

^σδHδb = (1 " kgain) σδHδb (²1)

Following update of the bias estimate in 580, a new open loop propagation is initiated 590 by resetting the error variances and the open loop heading propagation, using equations identical to those used for initialization 500 (i.e., Eqns. (8) through (10) above). Following this reset of the propagation, 590, the open loop propagation in 510 and 520 will be continued on the next cycle.

Returning to condition 560 of FIG. 4, a failure counter is incremented 600 each time that a residual test 560 failure occurs. If the failure counter has not reached a maximum allowable value (e.g., representing five to ten successive residual test failures) in test 610, the bias estimation is bypassed. On the other hand, if the maximum allowable failure count is reached in test 610, the bias estimate and its error variance are reset to the measured values 620, and the error variances associated with the open loop heading propagation are similarly reset 630, as given by the equations below.

best ₌ m (22)

σ²δb = σ²n (23) HθL = HGPSstart (²⁴) σ²HOL = 0 (25) σ² _Hδb = 0 (26)

Following this reset of the open loop propagation 630, processing control is returned to point E in the flowchart of FIG.4, and the gyro bias estimation continues.

The present invention discusses three different methods which are used to form the bias measurement, as indicated for the GPS gyro based approach in Eqn. (3), the GPS accelerometer based approach in Eqn. (7), and the open-loop heading propagation approach in Eqn. (15). Although each of these equations is quite different, they are measuring the same (zero-rate) bias. The differences in the equations arise from the fundamentally different ways in which the bias measurements are constructed. In particular, for the GPS gyro approach, the vehicle may be turning slowly, so it is necessary to subtract ΔHGPSgyro in forming the bias measurement. On the other hand, when using the GPS accelerometer to sense a stationary condition, a pure bias measurement can be made from the gyro reading. Finally, in the open loop propagation based approach, the vehicle is neither travelling straight nor stationary, necessarily, so the bias must be extracted from the measured difference between the open loop heading propagation and GPS determined heading.

While a preferred embodiment of the present invention is described, it is contemplated that various modifications may be made thereto without departing from the spirit and scope of the present invention. Accordingly, it is intended that the embodiments described be considered only as illustrative of the invention and that the scope of the invention be determined by the claims hereinafter provided.

Claims

What is claimed is:

1. A method for calibrating a zero rate bias of a gyro associated with a terrestrial navigation system installed in a movable vehicle, said system including a GPS receiver integrated with said gyro and being coupled to an odometer of said movable vehicle, said method comprising the steps of: receiving GPS data from said GPS receiver; receiving velocity data from said odometer; determining whether said movable vehicle is stationary by using said GPS data and said velocity data to measure an acceleration of said movable vehicle; forming a zero rate bias from an output of said gyro when said movable vehicle is determined to be stationary; and filtering said zero rate bias measurement to produce a zero rate bias estimate.

2. The method of claim 1 wherein said filtering is performed using a low pass filter.

3. The method of claim 1 wherein said filtering is performed using a Kalman filter.

4. A method for calibrating the zero rate bias of a gyro associated with a terrestrial navigation system installed in a movable vehicle, said system including a GPS receiver integrated with said gyro and being coupled to an odometer of said movable vehicle, said method comprising the steps of: receiving GPS data from said GPS receiver; receiving velocity data from said odometer; determining whether said movable vehicle is moving in a straight direction by using GPS data and said velocity data to measure a heading rate of said movable vehicle; forming a zero rate bias from an output of said gyro when said movable vehicle is determined to be moving in a straight direction; and filtering said zero rate bias measurement to produce a zero rate bias estimate.

5. The method of claim 4 wherein said filtering is performed using a low pass filter.

6. The method of claim 4 wherein said filtering is performed using a Kalman filter.

7. A method for calibrating the zero rate bias of a gyro associated with a terrestrial navigation system installed in a movable vehicle, said system including a GPS receiver integrated with said gyro and being coupled to an odometer of said movable vehicle, said method comprising the steps of: periodically determining a first heading of said movable vehicle by using heading information from said GPS receiver and said gyro; determining a second heading of said movable vehicle by using heading information from only said GPS receiver; determining a heading error between said first and second headings; forming a measurement of said zero rate gyro bias from the said heading error; and extracting an estimate of said zero rate bias from said zero rate bias measurement

8. The method of claim 7 wherein said step of extracting includes using a Kalman filter which models the effect of said zero rate bias upon said error of said heading propagation.