accuracy and price, so those best suited to the application must be chosen (Bullock ... equipment ,except for the laptops which used the car's 12. V power ou tlet.
Development of a GNSS-Based Multi-Sensor Vehicle Navigation System J. Stephen and G. Lachapelle Department of Geomatics Engineering The University of Calgary
BIOGRAPHIES Mr. Jim Stephen has spent the last two years with the Positioning and Navigation group at the University of Calgary pursuing an M.Sc. in Geomatics Engineering. He received his B.Sc. in Geomatics Engineering from the same department in 1997. Dr. Gérard Lachapelle is a Professor and Head of the Department of Geomatics Engineering where he is responsible for teaching and research related to positioning, navigation, and hydrography. He has been involved with GPS developments and applications since 1980. ABSTRACT An integrated multi-sensor vehicle navigation system is presented which uses a low cost rate gyro and differential odometry to supplement GNSS availability under signal masking. The purpose of the system is to provide various applications with 10 m accuracy nearly 100% of the time. The equipment used is discussed in detail, and the method of filtering the data is explained. Results from two tests with simulated GPS signal masking for 100 and 200 s intervals are presented. Tests demonstrate that the use of differential odometry augmentation does not reach the 10 m specifications, but with the use of a gyro and odometry they are nearly met. After further tuning of the filters and data processing techniques, these specifications will likely be met. INTRODUCTION The navigation system presented in this paper attempts to improve the inadequacies of GPS vehicle navigation through augmentation with dead-reckoning sensors and GNSS. GPS suffers from signal masking and multipath errors in areas such as urban canyons, densely treed streets, tunnels, and parkades. Services that add value to position information, such as those listed in Table 1,
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
require continuous position availability to operate effectively. Positional accuracy requirements vary by application, but most require knowledge of the exact street and block. Many require better still in order to function to their potential. Table 1. Services Which Add Value to Position Data Application Desired Accuracy (m) Commercial Fleet Mgmt. 100 Ambulance / Fire / Police calls 10 Location of services, e.g. restaurants 10 Route Finding 25 Retrieval of lost / stolen vehicles 10 A variety of sensors are available for augmenting GPS, some of which are listed in Table 2. They vary greatly in accuracy and price, so those best suited to the application must be chosen (Bullock 1995). For vehicle location and navigation, sensors must be chosen to add minimal cost to the production or modification of a vehicle, while delivering continuous position availability with an accuracy better than 10 m under most circumstances. Table 2. Several Aiding Sensors Heading Sensors Accuracy Vibrating rate gyro 0.1°/s Mechanical rate gyro 0.03°/s Fiber-optic gyro 0.001°/s Fluxgate compass 2-4° Gyro compass 2-4° Distance Sensors Reluctance odometer 0.5% Hall effect odometer 0.5% Doppler radar 1% Other Aiding Barometer-height 5m Inclinometer-attitude 2°
Comments Temp. Sensitive Short life Expensive Sensitive to iron Large / expensive High cut-off speed Road irregularities Local variations Acceleration error
1
A low cost piezoelectric vibrating gyro and differential odometer, provided by the ABS already installed on my vehicle, were chosen for this system. An inclinometer was also used to correct the gyro output. Extended Kalman filtering was used to process the navigation data, while independent filters were employed to calibrate the aiding sensors.
The equipment used in the system was • 1998 Honda Civic, with installed ABS • Murata Gyrostar rate gyro • 2 NovAtel Millenium receivers (DGPS) • 2 Laptop computers • 16 Bit National Instruments A/D converter
Differential Odometry The voltage of the rear wheel speed inputs to the Halleffect type ABS system were sampled at 2000 Hz. Hall effect (active) odometer systems allow sensing of lower wheel speeds than passive sensors. The sinusoidal signal is tracked by a phase and frequency feedback digital PLL (Kaplan 1996 and Thomas 1991). This was done for the ease of sampling all of the analog output sensors near simultaneously with a single operation on the A/D converter. It also allowed for simple synchronization of the analog data and GPS data without the use of computer clock time. Other, including a brake strength indicator, reverse indicator, and park brake indicator were available for monitoring. These could be useful in interpreting the data, e.g. when to calibrate and whether the measured speed was in the forward or reverse direction. The PLL was implemented as follows: Pr eSize
QP =
∑ sin( f * t + θ )
Eq. 1
∑ cos( f * t + θ )
Eq. 2
t =1 Pr eSize t =1 −1
δθ = tan
(Q P
IP )
K1 = 4 BLT
K 2 = K 212
where
Test Vehicle A front wheel drive 1998 Honda Civic with installed ABS system was used as the test vehicle. The external sensors were fixed to an aluminum plate, which was tied to a rack on the roof of the vehicle. The laptop computers, A/D converter, and GPS receiver were located on the back seat of the vehicle. The ABS system was located under the dashboard on the passenger side of the vehicle. An independent 12 V battery was used to power the equipment ,except for the laptops which used the car’s 12 V power ou tlet.
Eq. 3
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
Eq. 4
j =1
r r +1 r
θ n +1 = θ n + ∆θ n +1 f n +1 = f n + ∆θ n +1 T
EQUIPMENT
IP =
n
∆θ n +1 = K 1δθ n + K 2 ∑ δθ j
Eq. 5 Eq. 6 Eq. 7 Eq. 8
f is the signal frequency θ is the signal phase T is the integration period BL is the loop parameter bandwidth K1, K2 are loop filter constants r is the damping factor IP,QP are the in-phase and quadrature sums
The integration time was chosen as 0.05 s (100 samples). The noise bandwidth was set at 6 Hz, and the damping factor at 4 (critically damped). The integration values QP and IP must exceed a threshold value before the loop is considered locked. The frequency is initialized to 120 rad/s when the vehicle is stationary and remains constant until the tracking threshold is exceeded. The frequency was also forced to the positive domain, as several times the mathematically equivalent negative frequency was tracked. If one of the wheel’s PLLs loses lock, the frequency from the other wheel is used to reacquire it quickly. If both wheels lose lock, a DFFT is performed to re-acquire the frequencies (Press et. al. 1992), however this has not been observed. It is the frequency measured on each wheel that is input to the navigation system. There are approximately 30 pulses generated per rotation of 1.5 m circumference, giving a maximum signal frequency of about 800 Hz at 40 m/s. The wheel scale factors were determined by estimatig an average scale factor between the GPS velocity and the frequency of each wheel. This is because both wheels have slightly different sizes and slippages due to tread wear. Slippage can be considered almost constant on clean paved roads and amounts to less than 1% of the distance traveled. Tire size varies with temperature, the weight load to each tire, and speed. Also, when a vehicle turns, the differential allows the inside tire to travel a shorter distance and the outside tire a longer distance without greatly increased slippage. Although the speed of each wheel varies from the speed of the vehicle (i.e. the GPS velocity) while it is turning, the use of a small gain factor on the calibration filter will cancel out this effect; the amount of turning in each direction should eventually even out. Distance traveled over ground by the vehicle is computed through averaging the two wheel speeds, as in Eq. 9, where the subscripts indicate left and right distance measurements.
2
∆d =
∆d L + ∆d R 2
Eq. 9
It is by using the difference between the speeds of the two tires that heading change can be determined. A method has been suggested (Harris, 1989) which is illustrated in Figure 1, and the formula presented in Eq. 10.
∆az =
∆d L − ∆d R Track Width
Eq. 10
Left wheel path Centre line Right wheel path ∆az ∆dL RR
∆dR
∆az Track Width
RL
Figure 1. Differential Odometer Geometry The track width is the effective turning width of the car (approximately the distance between tire centers). This formula holds for fixed wheels, which do not turn with the steering wheel. This generally applies to the rear wheels of a vehicle, although a few vehicles employ 4wheel steering. A second consideration is the greater amount of slippage on powered wheels. Powered wheels slip much more frequently than non-powered wheels, often with the insidious slippage of one wheel. When only one wheel slips, a false heading change is registered. Data monitoring could catch some of these errors, but certainly not all. Etak has developed an algorithm for using the front wheels of a vehicle to estimate distance traveled and heading change (Zavoli et. al. 1988). The time derivatives of the preceding formulae are employed in the system to determine ABS heading. The speed should be interpreted as an average speed over the interval, as estimated by the PLLs. The heading changes are based on the average heading rate over the interval; they are summed and output to the filter, i.e. they correspond to the heading at the end of the interval. To simplify matters, both measurements are assumed to be taken at the end of the integration interval. This gives the speed estimates a lag time of 0.025 s, which is of little consequence given vehicle dynamics and the loop tracking noise.
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
Rate Gyro The Murata Gyrostar piezoelectric vibrating gyro was used for this system. The specifications of the automotive version of the sensor (ENV-05D series) are found in Table 3. Table 3. Selected Murata Gyrostar Specifications Characteristic Min Std Max Units Supply Voltage 4.5 5.0 5.5 VDC Current @ 5 VDC 17 mA Max Angular Rate (ω) -80 +80 °/s Output at ω = 0 2.2 2.5 2.8 VDC Scale Factor 19.3 22.2 25.1 mV/°/s Asymmetry 3 °/s Temperature Scale ±10 %FS Temperature Drift 9 °/s Operating Temperature -30 80 °C Noise Level (7 kHz) 20 mV Dimensions 18 ×30×41 mm The gyro was selected for its low cost (approximately $15 in large quantities), small size, and good performance relative to the others in its class. The voltage output from the gyro is proportional to rotation rate, which is sampled at 2000 Hz by the A/D converter. The samples are integrated at 10 Hz to give a heading change over the interval, added to the previous summed output, and passed to the filter. The gyro has instability in both the zero-rotation output voltage and the scale factor, as a result of temperature and power variations. The variations require regular calibration of these values. The gyro has also demonstrated limited endurance to shock and some susceptibility to vibration (Geir 1998). Vibration in vehicles varies greatly, both in magnitude and frequency, depending on engine speed, temperature, and numerous other factors. Accelerations reach 0.7 g’s at spectral frequencies up to 10 Hz (Skaloud 1995). Figure 2 shows a sample of the gyro output while the vehicle is stationary. Since all the equipment in the system is powered by an independent and stable power source, there should not be significant power fluctuations. There is still, however, a definite oscillation at about 65 Hz visible in the zerorotation output. Difficulties also arise in trying to calibrate both the zero-rotation offset and scale factor simultaneously. The gyro also suffers from the limitation of remaining on a fixed plane with the vehicle, not remaining on plane orthogonal to the gravity vector. It is therefore not sensing the entire rotation in heading, but also sensing rotations in pitch and roll. This situation is presented graphically in Figure 3. The formulae which describe the relationship between the measured quantity and the desired heading change are presented in Eq. 11-14 (St. Lawrence 1993).
3
2.442 2.441 2.44
Output (V)
2.439 2.438
sin 2 θ + sin 2 ϕ + cos 2 ξ = 1
Eq. 12
θ β = tan −1 ϕ
Eq. 13
and using the small angle approximation sin(x) = x:
2.437
ωΨ =
2.436 2.435
2.433
0
0.02
0.04
0.06 0.08 Time (s)
0.1
0.12
0.14
Figure 2. Gyro Zero-Rotation Output Variation ZLL= -g ωψ
ZFOG
Horizontal Plane
ωFOG
Gyro Plane
ξ Direction of Travel ωφ
YLL β
ωθ
XFOG XLL
YFOG
Figure 3. Geometry of a Tilted Gyro ω FOG = ωΨ cosξ + ωϕ cos β sin ξ + ωθ sin β sin ξ Eq. 11
where
ωFOG is the measured rotation rate ωΨ is the desired azimuth rotation rate ωθ is the pitch rotation rate ωϕ is the roll rotation rate ϕ is the roll angle θ is the pitch angle
Since we have no way of measuring the pitch and roll rotation rates, their effects will be ignored. These effects are proportional to the tilt of the vehicle and the rotation rates on their respective axes. The pitch and roll generally remain small and tend to cancel out over the long term. Localized errors will be induced into the heading through roll, which occurs when the vehicle corners, and when vertical gradients are changing. The resulting heading errors when integrated should result in random walk behaviour (Harvey 1998). The remaining term can be derived from the direction cosines of the gyro axes on to the local level axes as follows:
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
Eq. 14
1−θ 2 − ϕ 2
The resulting formula relies on the observation of vehicle pitch and roll, i.e. data from an inclinometer. Vehicle tilt has the effect of decreasing the sensed rate of rotation during a turn by a small amount. A short numerical example will illustrate error that would be induced by this approximation. For a measured rotation rate of 20°/s, which is seldom exceeded, with a vehicle tilt of 20°, the heading rate should be 21.3°/s. This would result in a heading error of 1.3° for each second the turn lasted, i.e. up to 6° error for a 90° turn. This correction could be ignored if it was assumed that GPS outages seldom occur under high tilt conditions since a tilt of 10° only causes an error of about 1.3° on the 90° turn. It is difficult to equate heading errors to positional errors since they vary greatly depending on vehicle dynamics, but it can be easily seen that small heading errors can quickly lead to large position errors. The scale factor would be increased slightly to compensate for some sort of RMS tilt value. An inclinometer would be necessary if positions were required inside covered or underground parkades. A sample distribution of the tilts experienced in various residential and freeway driving environments is found in Figure 4. It can be seen in this figure that vehicle tilt seldom exceeds 10° under normal driving conditions, at which there is a 1.5% heading change error induced by ignoring tilt. 200 100 Number of Occurrences
2.434
ω FOG
0
-20
-15
-10
-5
0
5 Pitch (°)
10
15
20
25
400 200 0
-40
-30
-20
-10
0 Roll (°)
10
20
30
5
10
15
20 Tilt (°)
25
30
35
300 200 100 0
0
Figure 4. Sample Vehicle Tilts From Varied Driving
4
Inclinometers for land applications must have a range of about 30° to handle normal operating conditions. Inclinometers designed specifically for low cost environments such as automotive applications would probably cost around $10. A liquid-bubble type inclinometer was used in this application, being a module of the Precision Navigation TCM-2 digital magnetic compass. A typical 2-axis bubble type inclinometer similar to the one used in this project would be the Applied Geomechanics Model 900 Biaxial Clinometer, available at $90 in large quantities. The operation of the inclinometer will be described below, as the principles of other inclinometers are similar. The liquid-bubble inclinometer uses a vial, partially filled with a conductive liquid to determine the tilt of the vehicle in one or more axes. Electrodes around the vial estimate the liquid height or height difference between sensors. These measurements are converted to pitch or roll measurements. A diagram of a typical sensor is found in Figure 5.
Liquid Surface
η av
Sensing Electrode
η
an = g + av
g
Figure 5. Bubble Inclinometer Bubble inclinometers (and other inclinometer types, as well) suffer from an acceleration related error, since an acceleration will make the liquid rise up one side of the vial. Also, there will be some sort of damped oscillation in the fluid even after the acceleration has finished. The error due to acceleration can be described by:
η = av g
Eq. 15
Inclinometer data was generated at a rate of 5 Hz from by the TCM-2. The compass provides RS232, proprietary or NMEA format output, which was collected with a passthrough log on the NovAtel receiver. This method kept the timing simple by avoiding the use of computer clock time; the data was given a GPS time stamp accurate to better than 1 ms. No corrections were made to compensate for acceleration errors, however it would be possible to make corrections to the inclinometer output using the gyro and differential odometer to derive the
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
accelerations. GPS code measurements can not provide an accurate enough measurement of acceleration to use for this correction (Harvey, 1998). GNSS The system employs NovAtel MiLLenium receivers for the reference station and remote GNSS data. The remote receiver was used in a wide correlator mode to somewhat simulate low-cost GPS sensor performance. This type of equipment would no doubt be used in a mass produced automotive navigation system. The system makes use of position and velocity estimates only; the raw data is not used by the data integration system. Heading was derived from the velocity estimates and a function was designed to provide heading variance based on speed. The covariance law derivation of this relationship seemed pessimistic, so an exponential function with a cut-off of 2 m/s was used. In a real-time implementation, differential corrections would be likely be obtained from a satellite system, e.g. WAAS or Racal LandStar, or a local area provider, such as the 300 kHz marine navigation services or an FM subcarrier system. Although the system could have used the NMEA output of a differentially corrected receiver, the GPS solutions were post-processed using the University’s C3NAVG2 GPS/GLONASS single-difference carriersmoothed code processing software. The reason for this is to eventually look at the increased availability, reliability, and accuracy of augmentation of the GPS solution with GLONASS, clock offset modeling, and barometric height aiding (Ryan et. al. 1999). Poor geometry and increased multipath in urban canyons can lead to gross errors in GPS computed positions (Lachapelle et. al., 1997). These errors can be greatly reduced through the use of augmentations. Maximum Horizontal Error (MHE), defined as the largest error which could be caused by an undetected blunder, of GPS only solutions in urban canyons can be reduced dramatically through these augmentations. Blunders can be more easily detected and removed before they corrupt the position solution. Work is presently underway to add clock coasting and barometric height aiding to C3NAVG2. Both receivers employed Vectron 10 MHz OCXOs as external clock references to allow for clock coasting in times of reduced satellite visibility. This clock heas excellent stability for periods up to several minutes (Petovello and Lachapelle, 2000). If the reference system used a precise oscillator (such as an OCXO or atomic reference), or without the presence of Selective Availability (SA), the user receiver could effectively use a model to estimate the clock bias and remove one unknown from the GPS solution (Zhang, 1997). This would allow position solutions with as few as two
5
satellites, if the heights were also constrained. Removing the clock offset from a weakly determined GPS solution is also advantageous since measurement errors will not be absorbed into the clock offset. Height determination is dramatically improved through the use of clock aiding since there is a high correlation (which is always positive) between height and clock-offset estimates, usually exceeding 0.8. Although the correlation between horizontal position and clock offset estimates takes on both positive and negative values depending on geometry, the correlation coefficients can reach near ± 1 with DOPs as low as 1.5. The arguments for the use of barometric aiding are similar to those for clock aiding. The redundancy of the solution and the number of available solutions increases dramatically with the use of barometric height aiding. Height fixing to the last known height can add to the availability of position estimates, but often by the time a receiver switches to a 2-D mode its height estimate is already severely degraded. This error in the fixed height will translate into errors in the other parameters, i.e. horizontal position and clock offset. Height information can also serve a purpose in locations with no GPS coverage such as finding a car in a parkade. GLONASS or other satellite system augmentation can also be effective at increasing availability, reliability, and accuracy of the satellite solution. With the other two sources of aiding in place, it is possible to compute a position using two satellites from any system, as long as the difference in system times has been determined by the clock offset model. With the prospect of a European GPS counterpart (Galileo), GLONASS, and geo-stationary satellite augmentation, availability of position solutions could increase substantially. A/D Converter The analog data acquisition was carried out using the National Instruments DAQ-Pad MIO 16XE-50. Some specifications of the device are presented in Table 4. Table 4. Selected DAQ Pad MIO 16XE-50 Specifications Characteristic Specification Analog Input Channels 16 single or 8 differential Signal Input Ranges 0.1 to 10 V uni- or bipolar Resolution 16 bit Maximum Sampling Rate 20kS/s Relative Accuracy ± 1 LSB max Settling Time 50 µs max to ± 1 LSB Analog Outputs 2, 12 bit Counter/Timers 2 up/down, 24 bit Digital I/O 8 TTL/CMOS input/output Power Supply 9-42VDC, 325 mA at 12V Differential input was used to minimize interference with the ABS’ normal operation. All leads and wires were
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
formed into twisted pairs where possible, shielded with foil and grounded at the A/D converter. All of the analog devices were low-impedance, so 100 kΩ resistors were used to ground both ends of each differential input. Only the rate gyro was powered from the A/D converter 5 V supply. All other equipment was powered directly from the independent 12 V battery. The data acquisition was performed by a “C” program, functions of which called the pre-loaded data acquisition drivers. The program called for individual samples at 16 kHz, with a scan of the 4 used channels at 2 kHz. The acquisition was driven by the internal 20 MHz oscillator, which was also used to trigger a pulse generator at 1 s intervals. This pulse was routed to the mark input pin on the NovAtel receiver. Since the two functions were driven by the same oscillator, and started by the same trigger, the pulse time-tags generated by the GPS receiver were coincident with each 2000th sample. FILTER DESIGN The navigation filter employs an Extended Kalman Filter. The filter equations are given by (Gelb, 1974): Given a system model with no deterministic input x = f ( x, t ) + u (t ) Eq. 16
∂f dx −1 Φ k = L−1 [sI − F ]
F=
{
Eq. 17
}
Eq. 18
t = ∆t
and linear measurement model
z k = H k xk + vk
Eq. 19
and supplied with initial conditions P0 and X0, the prediction equations can be given by
xk−+1 = Φk xk+ − k +1
P
Eq. 20 + k
T k
= Φ k P Φ + Qk tk +1
∫ Φ (ξ )ww
Eq. 21
Φ (ξ ) d ξ T
Eq. 22
x k+ = x k− + K k [ z k − H k x k− ]
Eq. 23
Qk =
k
T
tk
and the update equations by
Pk+ = Pk− − K k H k Pk− − k
T k
− k
Eq. 24 T k
−1
K k = P H [ H k P H + Rk ] where
Eq. 25
x is the vector of unknows P is the covariance of the unknowns Q is the dynamics noise matrix K is the Kalman gain matrix R is the covariance matrix of the observations Z is the vector of observations w is the vector of spectral densities Φ is the state transition matrix
6
Several methods of filtering the data were attempted before a final form was chosen. An initially designed Federated filter was unstable and showed poor performance. One of the problems was the linearized dynamics model. Frequently, the Qk matrix had off diagonal elements an order of magnitude greater than the diagonal elements. The matrices that were formed through the filter operations became ill-conditioned. Similar results were seen until the controllability of the system was improved. Process noise was not added to the position states in the early implementation, but it proved to be necessary to keep the covariance matrix of the unknowns positive definite. This matrix is also forced back to symmetry occasionally to keep truncation errors in check. There are 8 states in the filter at present, but the two Gauss-Markov states will likely be removed from the final implementation. The states are as follows: • Latitude (m) • Longitude (m) • Speed (m/s) • Heading (rad) • ABS Heading random walk • ABS Heading Gauss-Markov error • Gyro Heading random walk • Gyro Heading Gauss-Markov error The vehicle dynamics model itself is very simple in form. Given a heading expressed with 0° due East and counterclockwise positive, the equations describing the vehicle dynamics are:
∆N = S sin α ∆E = S cos α
Eq. 26 Eq. 27
Latitude and longitude are kept in metres to simplify the formulation. The partials will not be derived in detail, as they are easily computed. Residual checking is performed on the innovation sequences to detect measurement blunders and erroneous bias estimates. The statistical testing uses the following:
rk = zk − H k xk
Eq. 28
Prk = H k Pk− H kT + Rk
Eq. 29
The threshold used in most cases is (Krakiwsky, 1987)
rk >4 Prk
Eq. 30
The treatment of detected blunders varies for the observation type, number of consecutive rejections, and several other criteria.
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
The other components to the system are the calibration filters for the wheel scale factors, and the gyro zero-offset and scale factor. The present implementation for determining the gyro zero-offset voltage uses high gain on a filter of the output voltage when the vehicle is stationary, and very low gain on the output voltage when the vehicle is in motion. This method assumes that left and right turning will eventually cancel out. It is necessary to calibrate this value more often than just when stationary for the system to be effective on freeways and highways where there are long periods without stopping. The scale factor is determined using a low gain on a filter of the ratio between GPS heading changes and gyro heading changes over short intervals. The filter only operates when the speed is above a threshold of 5 m/s so the GPS heading would be sufficiently accurate. The calibration technique for tire sizes was previously discussed, however it must be ensured that the calibration of the wheels does not induce significant drifts in heading, This is monitored in the same fashion as the gyro’s scale is calibrated. SYSTEM TESTING Two sample data sets were collected on the afternoon of January 10th, 2000, in the residential areas of Coach Hill and Strathcona in Calgary, Alberta, Canada. The areas both have vertical elevation changes of over 200 m and are located about 5 km from the University of Calgary, where the reference receiver was operated. At the time, it was about –5° C and the roads were partially covered with snow and ice. Gravel is used extensively on Calgary roads to improve traction. Speeds during the tests reached approximately 60 km/h and both tests lasted about 20 minutes. There were few stops during the tests. GPS positions were available throughout the test periods, although on a few occasions only 4 satellites were in view. GPS outages were therefore simulated by removing the GPS data, alternating every 100 s. A second test with alternating 100 s availability and 200 s outages was then analyzed. Two modes of operation were tested: ABS only and ABS derived speed (ABSS) with gyro heading (no ABS heading). The tests were designed to observe the performance of the system under a worst case scenario: total masking for an extended period of time on slippery roads with large vertical variation; the ability of the gyro and differential odometry would be challenged. TEST RESULTS The GPS heading is shown with the integrated gyro output (shifted by an approximate initial heading) for the first test in Figure 6. The gyro heading error is shown in Figure 7. No statistics are given for the error since it would be followed by a random walk process; the difference between the random walk and the graph would
7
be the system error. If there were a significant error in the gyro zero-rotation offset, a slope would be seen in the data. The errors can be correlated with particular turns, but none of the experimentation with different offsets and scales could remove these. Some errors may be due to a difference between the gyro and inclinometer planes. Results processed without inclinometer observations were substantially worse; measured rotations on steep hills were clearly degraded. It should be noted that the scale factor and offset for each of the two tests were slightly different (2 LSB offset, 0.8% scale), but the calibration filters did not change the values during the short test periods. The short tests performed thus far have not allowed for optimal tuning of the calibration gains.
indicating that the scale factors are accurate. The velocity of each wheel is shown in Figure 10, with errors in Figure 11 and statistics in Table 5. Note that much of this error is due to the GPS speed error, and the errors caused by wheel speed variations during turns. Table 5. ABS Speed Error Statistics (m/s) Left Wheel Right Wheel Max 0.77 0.90 Min -0.53 -0.47 Mean 0.00 0.00 Std. Dev. 0.13 0.13
Figure 8. Test #1: GPS and Integrated ABS Heading 5 0
Heading Error (°)
Figure 6. Test #1: GPS and Integrated Gyro Heading 10 8
Heading Error (°)
6
-5 -10 -15 -20
4 2
-25
0
-30 156400 12:27
-2 -4
156700 157000 157300 12:32 12:37 12:42 GPS Time (s) Local Time (HH:MM)
157600 12:47
Figure 9. Test #1: Integrated GPS Heading Error
-6 -8 -10 156400 12:27
156700 157000 157300 12:32 12:37 12:42 GPS Time (s) Local Time (HH:MM)
157600 12:47
Figure 7. Test #1: Integrated Gyro Heading Error The ABS integrated heading is presented in the same manner in Figure 8, with the resulting heading error in Figure 9. Again, there is no significant drift in the error
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
8
Speed (m/s)
20
Left Wheel During GPS Outage Reference Trajectory
15
100m
10
Scale
5 0
Speed (m/s)
20
Right Wheel ABS GPS
15 10 5
0 156490 12:28
156790 157090 157390 12:33 12:38 12:43 GPS Time (s) Local Time (HH:MM)
Figure 10. Test #1: ABS Speed Estimates Figure 12. Test #1: ABS Only With 100 s Outages 1
Left Wheel Right Wheel
0.8
Speed Error (m/s)
0.6 0.4 0.2 0 -0.2 -0.4 -0.6 156490 12:28
156790 157090 157390 12:33 12:38 12:43 GPS Time (s) Local Time (HH:MM)
Figure 11. Test #1: ABS Speed Errors
During GPS Outage Reference Trajectory
The position domain results are found in Figures 12-19. Only a limited number of tests could be shown, but all of the results are summarized in the statistics found in Table 6. The reference trajectory was computed using the complete data set. The gyro with ABS greatly outperforms ABS only aiding. This could be predicted from comparing Figure 7 with Figure 9. If the filter is tracking the random walk and loses its input, it will stay at a nearly constant value. As the ABS heading error drifts more quickly than that of the gyro, larger heading errors will result.
Scale
Table 6. Position Error Statistics (m) ABS Only Outage (s) Max RMS Test #1 100 94 19 200 116 26 Test #2 100 154 21 200 170 29
100m
Figure 13. Test #2: ABS Only With 100 s Outages
During GPS Outage Reference Trajectory 100m Scale
ABSS/Gyro Max RMS 14 9 61 13 7 6 20 7 Figure 14. Test #1: ABS Only With 200 s Outages
J. Stephen and G. Lachapelle, ION NTM 2000, Anaheim, CA, January 25-28, 2000
9
During GPS Outage Reference Trajectory 100m Scale
Figure 15: Test #2: ABS Only With 200 s GPS Outages
Figure 18. Test #1: Gyro ABSS with 200 s Outages
During GPS Outage Reference Trajectory 100m Scale
During GPS Outage Reference Trajectory 100m Scale
Figure 16. Test #1: Gyro/ABSS With 100 s Outages
Figure 19. Test #2: Gyro/ABSS With 200 s Outages CONCLUSIONS The ABS system on a vehicle can provide accurate estimates of speed and moderately accurate estimates of heading changes. The heading suffers from wheel slippage and integration approximation in the present system design, but some of this error could be removed by accumulating the phase over the integration interval instead of estimating the frequency of the signal. Pulse count could also be used if there were more pulses generated for each rotation (some systems use
