UCGE Reports Number 20054

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UCGE Reports Number 20054 Department of Geomatics

in Static GPS Surveying (URL: http://www.geomatics.

1 UCGE Reports Number Department of Geomatics Engineering An Analysis of Some Critical Error Sources in Static GPS Surveying (URL: by Weigen Qiu December 1993

2 THE UNIVERSITY OF CALGARY

3 Some critical error sources ABSTRACT

4 ACKNOWLEGEMENTS I wish to express my sincere appreciation to my supervisor, Professor Gerard Lachapelle,

5 TABLE

6 2.4.6 Receiver Noise... 17

7 Measurements Separation

8 LIST

9 5.7 Comparison

10 Figures LIST OF FIGURES

11 5.1 Approximate Positions of Ottawa GPS Network Stations (a) Comparison of Ionospheric Delay Estimated by The Dual-frequency

12 CHAPTERl INTRODUCTION 1.1 BACKGROUND AND PREVIOUS STUDIES The NAVSTAR GPS ( NAVigation System with Time and Ranging Global Positioning System) is a satellite-based radio navigation system providing precise three-dimensional position, navigation,

13 2 carrier phase relative positioning has yielded accuracy of a few parts per 100 million [Erickson, 1992; Lichten and Bertiger, 1989]. (2) Rapid static surveying.

14 models with an accuracy of ±1%, while the wet component can be modeled by surface weather data 3

15 method" [Counselman and Gourevitch, 1981; Remondi, 1984], and the "Fast Ambiguity Search Filter (FASF)" [Chen, 1993]. Although each 4

16 5 accuracy level of about 30% [McNamara and Wilkinson, 1983]. The model presently offered by the GPS system to single frequency users has been developed by Klobuchar [1987]. It provides a correction for approximately 50% RMS

17 Chapter 6

18 development 7

19 8 CHAPTER 2 POSITIONING WITH GPS In this chapter, the Global Positioning System is introduced. As there are a number

20 users can determine their position, velocity, etc. In addition to sending signals, the satellites can perform several other functions as on-board processing of data, maintenance

21 corresponding wavelengths 10

22 11

23 technology (e.g., squaring, cross-correlation). 12

24 Orbital Errors Orbital errors result from the situation where the satellite is not at the exact position dictated

25 Another possibility to reduce the orbital error is to compute the a posteriori precise ephemerides, based 14

26 Availability (SA). 15

27 Tropospheric Delay The troposphere

28 applications, since 17

29 receiver will 18

30 19 CHAPTERS RAPID STATIC GPS SURVEYS The most accurate relative positioning performed with the Global Positioning System has resulted from carrier phase observations where the initial phase ambiguities

31 20

32 where 21

33 tested 22

34 V 23

35 intervals around 24

36 25

37 26

38 Ambiguity sets with pairs 27

39 the ambiguities to the incorrect integers could be caused by several factors. Insufficient observation time 28

40 searching space grows. 29

41 N 11 30

42 32s ^N 22 -Ni 2 NfJN 12 ) 31

43 of-thumb. However, on occasions post processing reveals that the results of a survey session 32

44 33 Z k =A k X k +e k, e k ~N(0,R k ), (3.29) the optimal estimate of the vector X k and its covariance matrix are given by: (3.30)

45 process noise Q 34

46 Numerical Results To prove

47 36 benefiting from the constraint of this ambiguity. This can be deduced from the marked drop of the formal precision after epoch 240 seconds. The remaining ambiguities are all isolated within 280 seconds. 0.3 SV17-SV23 I ctt SV11-SV23 Q! -o 0.1- SV21-SV23 SV28-SV23 SV26-SV Epoch Time (Seconds) Figure 3.2 Evolution of Formal Phase Ambiguity Precision for 442m Baseline (Ll) The entire data set was then processed using the rapid static ambiguity resolution techniques discussed in this chapter. Fourteen trials, each using 280 seconds of data were tested to determine the site occupation time needed to resolve the ambiguities. Table 3.2 shows the results of the rapid static test. For each

48 processing; These two measures are important since they represent the quality of 37

49 Table 38

50 in rapid static mode. Ten trials each using 250 seconds of observations were tested. 39

51 As it can be seen from Table 3.4, the success rate of trials in which ambiguities are correctly resolved is not high. Further analysis reveals that multipath is one of 40

52 CHAPTER 41

53 Multipath affects both pseudorange and carrier phase measurements. Multipath error 42

54 resolution 43

55 In 44

56 45 = [R 2 (T + T d )-R 2 (T-T d )] + 2CCCOS^F

57 *F m between the direct signal vector Sd(t) and the sum vector S(t) of direct and reflected signals. 46 Let Figure 4.3 Multipath Effect on Carrier Phase

58 where 47

59 MULTIPATH DETECTION AND REDUCTION A major problem in the study of multipath is the isolation of its effects on actual pseudorange

60 To demonstrate the multipath error in pseudorange measurements, the data sets collected with NovAtel GPSCard receivers at Fort Belvoir area [Lachapelle 49

61 NIST 7 VA 7 GPSCaTd, Day343 S o -H W) Jf T

62 N-k-1 i=0 I)* x 2 (i + k) 51 (4.16) A peak (0.711) can be seen in Figure 4.6 at 240 seconds delay. This is the multipath signature since

63 52 The main purpose of using dual frequency carrier phase measurements for geodetic applications is to eliminate the dispersive ionospheric delay. For short baselines, the actual differential ionospheric delay will be very small as the behavior

64 short baseline only a few kilometres in length, the differential ionospheric delay between 53

65 An experiment 54

66 55 clearly indicates that the variations shown in Figures 4.7 and 4.8 are related to repeated satellite geometry, and therefore must be attributed to multipath. The rather regular periodic pattern

67 Multipath Error Reduction Multipath errors affect not only the accuracy of the position, but also the site occupation time to resolve the carrier phase ambiguities. It is hence important to avoid multipath. Possible measures to minimize the effect are: (1) Improve

68 no extended ground plane, (2) use of RF absorbent ground plane, and (3) use of a chokering. The data was collected by one Ashtech P-XII receiver on two consecutive days for each of these cases. The same observation span was used for the two days in order to assess the correlation in pseudorange measurements. The antenna was placed on The University of Calgary's Engineering roof, where large multipath errors have been observed [Lachapelle et al., 1989]. 57

69 58 correlation between * "» -g'sfe"

70 (generally 59

71 By analyzing the power spectrum of the carrier phase multipath errors, the major multipath frequencies 60

72 61 seconds of observation time is really needed to isolate the ambiguities in this case. This conclusion is also true for long baselines to obtain a more accurate baseline determination using a float solution. Table

73 62 The main problem with the power spectrum analysis in estimating the major multipath periods is that we cannot obtain the carrier phase multipath errors in real-time. For single-frequency receivers, the carrier phase multipath error will

74 63 CHAPTERS IONOSPHERIC EFFECT MODELING FOR SINGLE FREQUENCY USERS

75 measurements largely free of multipath errors. The use of divergence measurements yields 64

76 800 65

77 about 66

78 GPS phase measurements are dependent upon the phase refraction index n p. The ionospheric phase delay 5O ion 67

79 68

80 69 J-I W) OJ «- Dunrobin B Burnstown

81 70

82 71 Table 5.3 shows the results of the rapid static tests for the 442 m baseline discussed in Chapter 3 with and without the ionospheric correction. Fourteen trials each using

83 IONOSPHERIC EFFECT MODELING FOR SINGLE-FREQUENCY USERS Ionospheric Effect Modeling Using Code and Phase Measurements If only single-frequency receivers

84 73

85 5.3.2 Separation 74

86 The residual vertical delay dl y is a function of time, user location, satellite elevation 75

87 Results and Analysis Three sets

88 equation (5.21), together with NLI in equation (5.20), were solved simultaneously with 77

89 environment at the station and to relatively constant (in time) ionospheric conditions during the observation period. The differences in the initial delay range from 78

90 79 _5.5- ^ 5* CO CD 45- Q *- D O " = 4" Albert Head, ROGUE SNR8C, SV20, Initial Group Delay: P-O div: 3.3 m P(LI )/P(L2): 4.2m O / Time (GPS sec) Albert Head, ROGUE SNR8C, SV21 Q 5- O '% 4- I 3- >T. JV. Initial Group Delay: P-O div: 2-,,,

91 2. 80

92 81 8- Calgary, 7- Q 0 JC Q. CO O C O 6-5-

93 Calgary, (O H V) H =J O) I c: o

94 9% which means that the Ll code and carrier phase divergence method can remove 90% of the relative ionospheric effect. 3. CVA (Ll) Divergence Versus Broadcast Ionospheric Model A data set collected on December 8, 1992, in Virginia with a NovAtel GPSCard [Lachapelle 83

95 receiver to measure directly the absolute ionospheric delay are however required 84

96 Recovery of the Ionospheric Delay with the Divergence Method for Baseline Determination The performance of the code-carrier phase divergence method to recover the relative effect of the ionosphere for precise baseline determination were investigated. Since double differenced carrier phase observations

97 Figure 86

98 Table 87

99 Table 88

100 ALBH-DRAO 89

101 90 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS In this thesis, ambiguity search strategies for rapid static surveying are discussed and some modifications are explored. Based on the assumption that the impact of the periodic multipath error on code and carrier phase measurements

102 91 Carrier phase multipath will strongly degrade the data quality and thus affect the site occupation time needed to resolve the ambiguities. Multipath errors in pseudorange measurements

103 differential static applications where cycle slip recovery 92

104 architectures 93

105 94 REFERENCES Abidin, H. (1990): "Extra-widelanding for 1 On the Fly' Ambiguity Resolution: Simulation of Multipath Effects." ION GPS-90, Colorado Springs, CO. Abidin, H. Z. and D.E. Wells (1990): "Extra-Widelaning for 'On the Fly' Ambiguity Resolution: Simulation of Ionospheric Effects." Proceedings of the Second International Symposium on Precise Positioning with the Global Positioning System,

106 Beutler, G., 95

107 96 Cohen, C., B. Parkinson (1991): "Mitigating Multipath Error in GPS Based Attitude Determination." Guidance and Control, Vol.74, Advances in the Astronautical Science. Cohen, C., B. Pervan, B. Parkinson (1992): "Estimation of Absolute Ionospheric Delay Exclusively through Single-frequency

108 Frei, E., and G. Beulter (1990): "Rapid Static Positioning Based on the Fast Ambiguity Resolution Approach 97

109 Hatch, R. (199Ia): "Instantaneous Ambiguity Resolution." Proceedings of IAG International Symposium 98

110 99 Lachapelle, G., P. Kielland, and M. Casey (1992b): "GPS for Marine Navigation and Hydrography." International Hydrographic Review, Monaco, Vol. LXIX 7 No.

111 Leick,A. (1990) 100

112 Talbot, 101

113 Symposium 102

Integer Ambiguity Resolution for Precise Point Positioning Patrick Henkel

Integer Ambiguity Resolution for Precise Point Positioning Patrick Henkel Overview Introduction Sequential Best-Integer Equivariant Estimation Multi-frequency code carrier linear combinations Galileo: