Augmentation of GPS with a Barometer and a Heading Rate Gyroscope for Urban Vehicular Navigation

Transcription

1 UCGE Reports Number 298 Department of Geomatics Engineering Augmentation of GPS with a Barometer and a Heading Rate Gyroscope for Urban Vehicular Navigation (URL: by Nobuyuki Hayashi December 1996

2 THE UNIVERSITY OF CALGARY Augmentation of GPS with a Barometer and a Heading Rate Gyroscope for Urban Vehicular Navigation by Nobuyuki Hayashi SUBMITTED A THESIS

3 This PREFACE

4 ABSTRACT

5 ACKNOWLEDGEMENTS I would like to thank my supervisor, Dr. Gerard Lachapelle, for his unlimited support and encouragement. He gave me a tremendous opportunity to pursue the project, showed

6 DEDICATION

7 TABLE OF CONTENTS APPROVAL PAGE...ii ABSTRACT...in ACKNOWLEDGEMENTS...^ DEDICATION...^ TABLE

8 3.3.4 Cross-Track Position Error Model...

9 7.2.3 Test Results Unaided

10 LIST

11 7.12 Position Estimate Difference Between Reference Trajectory

12 7.22 GPS Range Error Detection Thresholds, Downtown Calgary, August 17, (Height and Heading Constraint Least Squares) GPS Range Error Detection Thresholds, Downtown Calgary, August 17, (Height

13 LIST OF FIGURES 1.1 Trimble Placer GPS/DR System from (Geier et al. 1993) Architectural Design of the AVLIN 2 Prototype System from (Harris 1989) PortaNav Map-Aided GPS Navigation System from (Bullock 1995) Weak Satellite Geometry. Three GPS Satellites are Aligned As Shown By

14 3.1 The US Standard Atmosphere Pressure-To-Height Conversion Chart from (Lutgens & Tarbuck 1982) Viatran Model

15 7.6 DOPs, Springbank, June 29, (3 Cross-Track Cutoff Angle, Unaided Least Squares) D Position, Springbank, June 29, (3 Cross-Track Cutoff Angle, Unaided Least Squares)...

16 7.18 2D Position, Springbank, June 29, (3 Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)

17 7.31 2D Position, Springbank, June 29, (45 Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares)

18 7.43

19 7.57

20 Symbols: NOTATION

21 P k P smoothed range measurement at t k

22 w(/) random forcing function w cdt

23 5 least squares adjustments to parameters d(t) Dirac delta function 8/i height position error dh height rate error d'k longitude position error 6A, longitude rate error 6(j) latitude position error 6(j> bd AZ, A<j) latitude rate error mean distance traveled over a data interval path length difference phase difference b (*k+\) barometric height error at time t k+l e fc i b s cr (*/fc+i) e,('*+i) e g e g barometric height offset (residual) error linear barometric height drift rate cross-track position error at t k+l gyro error at t k+} gyro heading rate offset (residual) error gyro drift error 6 GP5 GPS cross-track position estimate error e p receiver noise

24 K P ratio of circumference of circle to its diameter geometric range latitude position o o k 1 a a o o a o o a 2 b P 2 2 Sdt 2 Siono 2 Strop 2 8p 2 a o ( C a

25 a xb cross product

26 P code PC PCMCIA PDOP Precision code (1.23 MHz) Personal Computer Personal Computer Memory Card International Association Positional Dilution

27 CHAPTER ONE INTRODUCTION The field of land vehicle navigation is growing rapidly with the maturation of the Global Positioning System (GPS) and the advancement of positioning-related technologies in recent years. GPS is a satellite based radionavigation system developed by the U.S. Department

28 2

29 less than 3

30 m/ phase 4

31 Kao (1991) examined

32 NU-METRICS Odometers

33 Magnetic mount GPS antenna Active matrix colour LCD Etak digital road map stored

34 such a vehicle still requires the installation of an odometer output reader. Since most testing 8

35 Table 1.1. Single Point GPS Error Budgets from (Lachapelle 1995, Braasch 1996, Bullock 1995) Error source Tropospheric delay Ionospheric delay Satellite orbit errors Satellite clock errors Selective availability (SA) Measurement noise Multipath Typical

36 input from sensors 1

37 11 27 Figure 1.4. Weak Satellite Geometry. Three GPS Satellites are Aligned As Shown By The Solid Line

38 moved from vehicle to vehicle, a DR system could not be implemented. A new concept had 12

39 to the Kalman filter approach. Finally, conclusions and recommendations are presented in Chapter Eight. 13

40 CHAPTER 14

41 15 to maintain flexibility. It operates with GPS alone, GPS and barometer, GPS and gyro or all three sensors. The system utilizes

42 2.2 Hardware Components 16

43 used at the monitor station to generate differential GPS corrections. 17

44 data with 18

45 acquisition board 19

46 Figure 2.3. Typical Hardware Installation. (Top) Laptop Computer and Barometer in 2

47 21 with NovAtel GPSCards in ideal conditions (Cannon & Lachapelle 1992). For this project, this program

48 CHAPTER THREE 22 SENSOR DATA ACQUISITION PROCEDURE A sensor is a device for receiving an external information such as heat, light, or pressure and transmitting it to a user. For most low cost land navigation applications, certain types

49 23 sensors. Specific discussions of the barometric pressure transducer and the heading rate gyro employed in the current system are presented. Finally, the error models of barometric height, gyro heading rate, sensor heading

50 24 North a. i+1 e\ pa^ \ett^e ^ ceove V\ne ^1-T \gw^ee r i.i+1,i * Figure 3.2. Differential Odometer Geometry from (Harris 1989) (M L -M R ) (3.1) where (3.2) and d 1^ df distance measured at time /. by left wheel odometer, distance measured at time t i by right wheel odometer, d t L +] distance measured at time t i+l by left wheel odometer,

51 df +l distance measured 25

52 compasses 26

53 by gyros which have become available 27

54 28 CAPAOnVB PLATES / ELECTRONICS BOARD SPRING DISK MOTOR Figure 3.4. Spinning Rate Gyro from (Phillips 1993) to the motor and chassis. These positional changes are detected by measurement of capacitance between the disk and the plates on the circuit board (Phillips 1993). As the technology matures, cost and reliability continue to be of concern. Currently,

55 exceptionally 29

56 which yields 3

57 A = d ',- 1=-^- [m] (3.6) 31 where c the speed of light in a vacuum [m/s], 7i

58 (3.9) 32 Alternatively,

59 33 atmosphere and a corresponding pressure versus altitude curve. In reality, the real atmosphere varies widely from the theoretical standard and is quite dynamic. These variations must

60 34 deflect a spring, whose deflection can be measured; it may change the tension in a string and hence its vibrating frequency; or it may move a capacitor plate closer to one fixed plate

61 In some instruments 35

62 36

63 Pressure expressed in inches of Hg may be converted to Pascal using 37 Pascal

64 25"Hg = 635mmHg = Pa and 38 32" Hg = mm Hg= Pa (3.15) where g = [m/s 2 ] p = 136 [kg m 3 ] gravity force, density of Hg. A linear relation between pressure in Pascal/? and output voltage v is given from equations (3.13) and (3.15) as

65 U.S. Standard Atmosphere (Lutgens 39

66 4 Decelerations v^o-u GPS Time [sec] Figure Viatran Model 246 Electric Barometer Measurement Error in

67 41 selected for this project. This gyro is a single axis, digital output, interferometric fiber optic rate gyro.

68 TM Figure Andrew AUTOGYRO 1 * 1 from (Alien 42

69 43 3dB Directional Coupler 3dB Directional Coupler Sine Wave Generator PZT Phase Modulator Rotation Rate

70 44.1 T 3

71 (3.17) 45 where

72 respect 46

73 1 47

74 48 The effect of appropriate scale factor determination is obvious from figures 3.17 and Forward and reverse runs are shown in each figure. Improper scale factor may cause severe position estimate displacement

75 removed 49

76 factors which 5 Modeling the long-term behavior of e fc is extremely difficult since there are many

77 51 Powell, 1995) and the effect of the earth rotation (Da & Dedes, 1995) are ignored in this thesis since they

78 3.3.3 Sensor Heading Error Model 52 heading must Since the fibre optic gyro only senses the change in vehicle heading, the initial

79 where 53 8 cr (*k+\) cross-track position error at t k+l [m], 'GPS

80 CHAPTER FOUR 54 SENSOR CONSTRAINT POSITIONING THEORY This chapter discusses the sensor constraint positioning algorithm. In sensor constraint positioning, position estimates are constrained by the sensor measurements when

81 p = r - R geometric range [m], 55

82 where 56 heading defined clockwise from zero dk

83 measurements C /3 the a priori position estimate vector x and the misclosure vector w, 57

84 58, o, o (4.9) where distance between dk

85 barometric height error variance [m 2 ], * sensor heading error variance [rad 2 ]. 59

86 6 The variance of smoothed range measurements may be expressed as a function of the range and carrier phase errors. The smoothed range measurement variance may be given as

87 61 {AC;V(/Ocsc( )} b 2 rl 47CV 7 v {csc( )}.5 where N(h) linear integral AC / AK

88 The smoothed range measurement variance should decrease proportional 62

89 where 63 b (t k ) barometric height error at t k from equation (3.17), sensor heading error at t k from equation (3.19). Note that the variances computed by equations (4.16) and (4.17) increase with time, reflecting the cumulative sensor measurement errors. Equations (4.15) to (4.17) allow a navigation algorithm

90 CHAPTER FIVE 64 KALMAN FILTERS This chapter describes

91 65 and measurement of the process is assumed to occur at discrete points in time according

92 66 The standard Kalman filter equations are derived as follows (Brown & Hwang 1992). The blending factor called Kalman filter gain is given by (5.6) where P^

93 where the optimal gain has been substituted in. Since w 67

94 68 vehicle is not moving). Also, it is preferable to keep the size of matrices used in the filter as small as possible since a matrix inversion is required to calculate the Kalman gain. Another concern

95 , G(t) matrices arising in the formulation. 69 appropriate Several researchers suggest that the integrated Gauss-Markov process may be

96 Although analytical evaluation 7

97 71 Substituting equations (5.3), (5.13), (5.14), (5.16) and (5.17) into equation (5.15) yields =nr -\T =r =r Jo 1 -l-e- K = J (5.18) The integration of each element gives the final form Q _ i^2 2,2 (5.19) where a. = f (5.2) + tf, +

98 72 (52i) Af zpy (5.22) 2 3 '~ and (5.23) an element Note that there is an important distinction to be made between q and Q. The # is

99 73 q =2pa 2. (5.24) The above discussion facilitates the development of the sensor filters. All sensor filters

100 74 8c6 5d) " 1-8co (5.28) Finally,

101 75

102 76 where X " p* p, p, 1 -p* - time time time 1 -Px - correlation correlation correlation 1 P, constant constant constant 1 -pj X ~4~ " 1%(~ v>»x(') i»i( **(') W *C) w cdl (t) J--«J

103 77 1 ±(l-e-w e * ) 1 1, (1 e~ ' PV e~^. ) 1 J-(l- e -p^ c ) 1 /i

104 ca CO " ca CN ca oo co en r- co OO CO ca << ca CO. ca <^ ca CN CO O) ca ^ <N ^ <N -s: ca O) d

105 79 687=278, (5-48) and, ( v ' ') where q^, q^ q^, q^ spectral density of latitude position and rate errors, spectral density

106 8 heading is determined by previous position estimates. Thus, it may introduce a significant initial heading bias into the Kalman position estimator and cause a filter to breakdown. An adaptive process noise covariance matrix routine

107 CHAPTER SIX 81 SOFTWARE

108 corresponding sensor data 82

109 83

110 84 Kalman Measurement Filters Get Filtered Barometer Height and Gyro Heading Rate Standard Least Squares Estimator (No Constraint) Good Position Estimate? Kalman Barometer Error Corrector Update 8/24 Apply Barometer

111 85 Kalman Measurement Filters Get Filtered Barometer Height and Gyro Heading Rate Standard Kalman Position Estimator (No Constraint) Good Position Estimate? Kalman Barometer Error Corrector Update Apply Barometer

112 86 where 8 Pars*

113 87

114 88

115 Real-Time Implementation A real-time operation

116 Figure 9

117 91 Latitude Longitude Optimal Heading error standard deviation (deg) current Heading error standard deviation (deg) Figure 6.5. Position Error of Optimal Estimator with Good Initial Heading

118 CHAPTER SEVEN 92 SYSTEM TESTING AND RESULTS The sensor constraint portable GPS vehicle navigation system has been developed in previous chapters. The purpose of this chapter is to evaluate its performance. Generally, estimates from

119 93

120 Table 7.1. Satellite Coverage 94

121 Table 7.2. Position Estimate Difference between SEMIKEV 95

122 Table 7.3. Parameters Used 96

123 Table 7.5. Parameters Used in Kalman Barometer Measurement and Correction Filters Description Time correlation p Spectral density q Measurement error r 1/s m 2 /s 3 m Barometer measurement 1/ Barometer correction 1/ Table 7.6. Parameters Used in Kalman Gyro Measurement, Correction and Heading Filters Description Time correlation

124 98 East Figure 7.3. Virtual Wall Concept Given a cross-track cutoff angle a

125 99 Assuming d CT is a constant, the height of the walls may be computed as h = ten(cn CT )'d CT. (7.2) Given a vehicle's heading at /,,,., and the azimuth of a satellite &

126 is 1

127 11 Cutoff Angle = 3, Azimuth = Cutoff Angle = 3, Azimuth - 9 Cutoff Angle

128 12 predetermined threshold value, the barometric height and / or heading constraint are used

129

130 S Easting [m] 8 1 Figure D Position, Springbank, June 29,1996. (3 Cross-Track Cutoff Angle, Unaided Least Squares) 2 4

131 Table 7.8. Position Estimate Difference Between Reference Trajectory and Unaided Least Squares Solutions, Springbank, June 29,1996. (3 Cross-Track Cutoff Angle) 15 Mean

132 16 Figure 7.9 shows the differences between the reference trajectory and the unaided least squares solutions with 2a error envelopes. 2a estimated error envelopes

133 Height constraint least squares solutions are then examined. Although four or more satellites were observed 17

134 18 Table 7.9. Position Estimate Difference Between Reference Trajectory and Height Constraint Least Squares Solutions, Springbank, June 29,1996. (3 Cross-Track Cutoff Angle) Mean [m] Standard Deviation [m] Max. Difference [m] Min. Difference [m] Position Availability Latitude Longitude Height % 7356 epochs weak

135

136 3 cr5* c Height Difference Longitude, Difference [m] ^4 h-i w W 'w cf5* ^^2^ n

137 Ill Both height and heading constraints are used next. The observations, sensor measurements and constraint positioning periods of least squares are identical to those of the Kalman filter. As a consequence, the DOPs are also identical. Figure 7.14 shows the DOP plot with height and heading constraint positioning. One notices that the GDOP is further reduced

138 112 3 T c:.o.<2 O O c: o Q GPS Time [s] Figure DOPs, Springbank, June 29,1996. (3 Cross-Track Cutoff Angle, Height

139 113 advantage of Kalman filters. As shown in Table 7.11, the accuracy and standard deviation

140 Easting

141 Height Difference M n.8 2 s a "- 5 ' n

142 Easting [m] 8 1 Figure 7.18.

143 TO =3 O w 2 TO*

144 Cross-Track Cutoff Angle 118

145 Satellite PRN Number -» -» ro ro co O Dilution of Precision Ol o 1 o 1 o U-l o n a 3 <g W» «f» as 9Q e ss cn 2. a- as 8 8 oro. 3* «(TO ^ O" Cl as f* re 3 ' e -t S" 3' s?w > g [1 5" v2, 6H S CD C ON as n VO ON 8 o -» to Ol O) -«J < > -» O Number

146 g- -6 "*^d O> S -8 i Easting

147 oro e d Difference o cn] o 1 o Longitude, Difference -g 3 S ws -t O l 3? -t 9 >?* TO 3' CD ~h ^i Jl

148 Next, height constraint least squares 122

149 r c: 1.o o c, 1 -: Q

150 I i

151 OTQ S, s VO =

152 126 Heading constraint is then applied in addition to height constraint. Both the least squares and Kalman filter solutions are examined. Figure 7.3 shows the effectiveness of adding the heading constraint. The NDOP and GDOP are now reduced to approximately 1. Comparing Figure 7.3 with Figure 7.26, the heading constraint improves the NDOP

153 127 1 T c: 1.o.w s^ 1 O c:.q 1 -: GPS Time [s] Figure 7.3. DOPs, Springbank, June 29,1996. (45 Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares and Kalman Filter) Figures 7.34

154 ^ vs discussed in Chapter Six. It appears that the Kalman filter produces solutions even with extremely poor measurements. The range residual checking algorithm did not warn of contaminated range measurements. More stringent error detection routines may be required. Position availability for height and heading constraint Kalman filter positioning is 1%.

155 129-2 QBQEU EDOOOQOQJ3C HftP-fflflBO -4 g i Easting [m] 8 1 Figure 7.31.

156 orq c He/gfA)f Difference n W 2. TO* *"tas sr a - ~ e a- =2 iff

157

158 TO 3 M QTQ p+ as a O QTQ - O f a? n" cw S H s

159 Cross-Track Cutoff Angle of 6 Degrees 133 Many satellites

160 Table Position Estimate Difference Between Reference Trajectory 134

161 Easting [m] 8 1 Figure 7.39.

162 U) C7N TO C Height Difference Longitude, Difference [m] Latitude Difference [m] ± o ensj] o I,, en o o. o. ^ i o *+ C/3 n-g o ^ o O I g > " S 5 g 9 TO a 1 S f vo ON

163 137 Height constraint least squares positioning is evaluated next. Figure 7.42 is the DOP plot for height constraint least squares. Since the visible satellites in Section A are identical to those for a 45 cross-track cutoff angle, we see the DOPs growing rapidly as seen

164 138 1 c:.o 55O 1. o c.o

165 * Easting [m] 8 1 Figure 7.43.

166 era ON O c/5 2. <w* n 2. n t a o o oro s s r 5' Cj «^- n c t- 1 s «B VO w..^

167 Section 141 Height and heading constraint positioning could not provide position estimates in

168 This 142

169 143 numimm.a IBL JHUHIII IHFIEI Easting [m] 8 1 Figure 7.48.

170 TO e p 2 W TO* c* as ^ s ON (7)^ & -a PM n ** ft i. ^9 a- s» TO

171 Table Position Estimate Difference Between Reference Trajectory 145

172 146 u 1 I 1-6- c son

173 orci e Height Difference Longitude, Difference [m] en o Qj o en o en Latitude Difference, InnliiiJfeMilMiilMMliinl 2. cf3* 3- O 2. S <g, 5* 3 3 ^

174 Table 7.2. Position Estimate Difference Between Reference Trajectory 148

175 7.2 Downtown Calgary Field Test Objectives and Strategies

176 operation, etc. 15

177 151 Figure Test Route, Downtown Calgary, August 17,1996 well. The buildings there use mirrored windows to reflect sunlight. These windows also reflect GPS signals quite efficiently. 4th and 8th avenues are in the downtown core where satellite visibility

178 152 3 T 8 CD -Q 25-W V* CD e 75 "CD 5 4 ;g io 1 CD co -

179 153 sufficient for urban land navigation applications. Solutions are obtained only on the edge of downtown. This result agrees with the satellite visibility plot, Figure 7.55, in which there are two long GPS signal outage periods. The first outage period starts near 9th avenue

180 154-3 Figure D Position, Downtown Calgary, August 17,1996. (Unaided Least Squares) Height and Heading Constraint GPS Results

181 1 -F. 1 c. I 3 1 -:

182 156 solution. If it is smaller, the algorithm will keep activating sensor constraints without adequate initializations and calibrations. For the best performance, both extremes should

183 157 Figure 7.59 shows the effect of height and heading constraint. We have a good number of positioning solutions throughout the session. It is expected that we would not obtain continuous solutions because

184 158 Table GPS Range Error Detection Thresholds, Downtown Calgary, August 17,1996. (Height and Heading Constraint Kalman Filter) Target Horizontal Acceleration Vertical Acceleration Range Residual Threshold 4m/s 2 1.5m/s 2 3.m -3 Figure D Position, Downtown Calgary, August 17, (Height and Heading Constraint Kalman Filter)

185 Figure 7.6 shows 159

186 Figure 7.61 gives 16

187 CHAPTER EIGHT 161 CONCLUSIONS

188 more likely 162

189 time with height 163

190 164 accelerometer. The distance sensor can be incorporated into the constraint algorithm as a distance constraint or used to complete DR positioning with a gyro. Another possibility is to use an on-board precise clock. If the clock is stable enough, the receiver clock offset may

191 This system has been developed using NovAtel GPSCard receivers but the algorithm itself is totally independent of the GPS receiver used. Although the data logging program is tightly integrated with NovAtel commands, adaptation to any other receiver would not be difficult. The navigation program is designed to accept any C 165

192 REFERENCES 166 Abbott,

193 Brown, 167

194 Gao, 168

195 169

196 17 Martin, E. H. (198). "GPS User Equipment Error Models," Special Issue of Navigation on the Global Positioning System^ Volume 1, The Institute of Navigation, Alexandria, VA. Martinelli, V. and R. Ikeda (1995). "Next Generation Fiber Optic Gyroscopes for Use with GPS in Vehicle Navigation and Location Systems," Proceedings of ION GPS-95 (Palm Springs, California, September 12-15, 1995), The Institute of Navigation, Alexandria,

197 171 Sushko, M. S. K. (1993). "Dead Reckoning Navigation (DRN) Assistance for GPS Based Tang, AVL Systems," Proceedings of the 1993 National Technical Meeting of The Institute of Navigation, January, 1993, pp