Analysis of a Combined Glonass/Compass-I Navigation Algorithm

Analysis of a Combined GLONASS/ Compass-I Navigation Algorithm

Item Type text; Proceedings

Authors Peng, Song; Xiao-yu, Chen; Jian-zhong, Qi

Publisher International Foundation for Telemetering

Journal International Telemetering Conference Proceedings

Download date 30/09/2021 05:49:18

Link to Item http://hdl.handle.net/10150/595792 ANALYSIS OF A COMBINED GLONASS/COMPASS-I NAVIGATION ALGORITHM

SONG Peng CHEN Xiao-yu QI Jian-zhong (College of Information Engineering, North China University of Technology, Beijing 100144, China)

Abstract: Compass-I system is China has built satellite navigation system. It’s a kind of regional position system according to the double-star position principle. Commonly, Compass-I system need adopt active position，in the paper several passive position methods are put forward. A combination navigation mode based on GLONASS and Compass-I passive navigation is proposed in this paper. The differences of coordinates and time systems between those two navigation systems are analyzed. User position is calculated by least squares method. Combination Navigation Algorithm can improve visible satellite constellation structure and positioning precision so as to ensure the reliability and continuity of positioning result.

Key words: Combination Positioning Algorithm; Compass-I system/GLONASS system; least squares method;

Ⅰ. INTRODUCTION

Compass-I system is a system with independent intellectual property in China. It is an active answering satellite navigation system. The system is a double-star position system, dominated by two satellites and supplemented with one satellite. The three satellites of the system are on the equator. So the positioning accuracy of the low-latitude users is not good. GLONASS satellite navigation system is developed by the former Soviet Union keeping up with GPS satellite navigation system of the United States. The satellites are distinguished by frequency division multiple access. Due to the limited size of the satellite constellation, there are still some certain problems in independent application. A combination navigation mode based on GLONASS and Compass-I passive navigation is proposed in this paper. We can make full use of the respective advantages of the navigation systems to improve the reliability and continuity of positioning result.

Ⅱ. COMPASS-I SYSTEM

A. Active position principle

The navigation system is made up of two synchronous satellites, as shown in Figure 1.

Figure 1. Navigation system

Central station gets two measurements by launching signals to users and receiving signals from users. The central station gets two time difference, because there are two synchronous satellites forwarding signals. CTΔ=2( R + S ) 111 (1) CTΔ=2121() R + R ++ S S2 222 Ry11=+−+−(x-x)()(yz 1z 1 ) (2) 222 R22=+−+−(x-x)(yy 2 )( zz2 ) Where: C - The light speed;

ΔT1 , ΔT2 - The measurements of the central station;

S1 , S2 - The distance between synchronous satellites and the central station;

R1 , R2 - The distance between synchronous satellites and the receiver; (,x yz ,) - The coordinates of the receiver;

( xiii,,yz) - The coordinates of the satellites. If you can get the height of the user by the user's own altimeter, it can get the user's coordinates according to the following formula.

CTΔ=1112( R + S )

CTΔ=211() R + S (3)

22 2 2 Hfxyz=−(1 ) ( ++− ) Re Where: f - Earth's eccentricity;

Re - Radius of the earth.

B. Passive position principle

Compass-I passive positioning mode and GPS positioning mode are basically the same. Passive positioning scheme have the following choices. Table 1. Passive positioning scheme

2 The number Composition of system Numbers of Information of the solution equations

1 Two satellites and altimeter 3 Three dimensional coordinates

2 Three satellites 3 Three dimensional coordinates 3 Three satellites and altimeter 4 Three dimensional coordinates and clock offset 4 Two satellites and one pseudolite 3 Three dimensional coordinates 5 Two satellites and one pseudolite 4 Three dimensional and altimeter coordinates and clock offset 6 Three satellites and one pseudolite 4 Three dimensional coordinates and clock offset

The first, the second and the fourth scheme can not get clock offset, and the fifth scheme needs of pseudolite technology. The pseudolite signals have interference on Compass-I satellite signals. So we choose the third scheme. Three synchronous satellites on the Equator receive the navigation messages launched by the central station and forward them to the users. Receivers capture and track satellite signals and get pseudorange measurements. The pseudorange measurements include the uplink distance from central station to navigation satellite and the downlink distance from navigation satellites to the user. We can get the pseudorange on basis of satellites, deducting the uplink distance. Then, we can get information of the satellite by despreading and demodulating navigation messages. Pseudorange measurements can be expressed as 222 ρii=−+−+−+•Δ()()()x xyyzzc iitu

22 2 2 HfxyzR=−(1 )( ++− ) e (4) (1,2,3)i = Where: c - The light speed;

Δtu - Receiver’s clock offset relative to Compass-I system clock; f - Earth's eccentricity;

Re - Radius of the earth;

(,xiiiyz ,) - The coordinates of the synchronous satellite in the BJ-54 Coordinate System; According to the Taylor series expansion, the equation is as follows:

3 ⎡⎤⎡∂∂∂∂∂∂∂Δρρ11///1x ρ 1yz ρ 1 ⎤⎡x⎤ ⎢⎥⎢∂∂∂∂∂∂∂Δρρ///1x ρyz ρ ⎥⎢y⎥ ⎢⎥⎢22=• 2 2⎥⎢⎥ ⎢⎥⎢∂∂∂∂∂∂∂Δρρ33///1x ρ 3yz ρ 3⎥⎢z⎥ ⎢⎥⎢ ⎥⎢⎥ ⎣⎦⎣∂∂∂∂∂∂∂ΔHHxHyHz///0⎦⎣h⎦ (5) ⎡⎤eee11 12 13 1 ⎡⎤Δx ⎢⎥eee1 ⎢Δy⎥ =•⎢⎥21 22 23 ⎢ ⎥ ⎢⎥eee31 32 33 1 ⎢Δz⎥ ⎢⎥⎢ ⎥ ⎣⎦eee41 42 43 0 ⎣⎦Δh

Where hc=•Δ tu ,

xx000−−−iii yy zz eeii12===;; e i 3 ρρρ000iii 22 ()11−−fx00() fy z eee==;;=0 41 42 43 HH00H0

222 ρ00ii=−+−+−()()()xx yy 0 ii zz 0

222 2 HfxyzR00=−()()1 +0 +−0

(,x000yz ,) - The estimates of initial position of the receiver;

⎡⎤ΔΔρ1 ⎡⎤eee11 12 13 1 ⎡x⎤ ⎢⎥ΔΔρ ⎢⎥eee1 ⎢y⎥ Δ=CE⎢⎥2 =⎢⎥21 22 23 Δ=X⎢⎥ (6) ⎢⎥ΔΔρ3 ⎢⎥eee31 32 33 1 ⎢z⎥ ⎢⎥ ⎢⎥⎢⎥ ⎣⎦ΔΔHh⎣⎦eee41 42 43 0 ⎣⎦

Where Δ=ρiiρρ −0i, Δ=HHHii −0 . The coordinates and clock offset of the receiver can be calculated by least squares method. The formula is as follows:

T−1 T Δ=X ⎡⎤⎣⎦EEEΔC (7)

Ⅲ. GLONASS SATELLITE NAVIGATION SYSTEM

GLONASS positioning mode and GPS positioning mode are basically the same. But the time and coordinate systems of GLONASS satellite navigation system and GPS satellite navigation system are different. The time and coordinate systems of GLONASS satellite navigation system are GLONASS system time and PZ-90 coordinate system. The satellite orbit information is the speed[,x yz,], acceleration[,xyz, ] and accelerations[,x yz, ] due to solar and lunar tttbbb tttbbb tttbbb gravitational perturbations. Their reference time is tb . According to the satellite orbit information at the reference time, we generally use the method of binomial extrapolation and the method of numerical integration of differential equations of the motion of the satellite. But the

4 method of numerical integration can provide a higher precision and longer time-span. Numerical integration generally use four-order Runge-Kutta formula. The time of calculating the coordinate of the satellite is as follows:

t(GLONASS=+ttttτ c +τγ nb) − nb()( −t b) (8) Where: t - Time of transmission of navigation signal in onboard time scale; tb - The reference time of navigation messages;

τ c - GLONASS time scale correction to UTC(SU) time; th τ nb()t - Correction to the n satellite time tn relative to GLONASS time tc , which is equal to phase shift of PR ranging code of navigation signal transmitted by nth satellite relative to the system reference signal at instant tb .

γ nb()t - Relative deviation of predicted carrier frequency value of n-satellite from nominal value at the instant tb . Although GLONASS positioning mode and GPS positioning mode are basically the same, the clock offset is different. The clock offset of GLONASS position mode is relative to GLONASS navigation system clock.

Ⅳ. COMPASS-I NAVIGATION SYSTEM/GLONASS NAVIGATION SYSTEM

We need to consider the differences of coordinates and system time between Compass-I system and GLONASS system, if Compass-I navigation system combines with GLONASS navigation system. The system clock of Compass-I navigation system is BD system clock and the coordinate system is BJ-54. The system clock of GLONASS navigation system is GLONASS system clock and the coordinates system is PZ-90. In order to facilitate system expansion, we transform coordinate into the WGS-84 coordinate of GPS navigation system. As to the time system, both systems use their own system. According to the large amounts of data that P. N. Misra and others get in the MIT Lincoln Laboratory of United States, the transformation formula[4] between PZ-90 coordinate and WGS-84 coordinate is as follows: ⎡⎤xe ⎡ 11.960−− ⎤⎡⎤x ⎡ 0 ⎤ ⎢⎥ ⎢ ⎥⎢⎥ ⎢ ⎥ ⎢⎥ye=− ⎢1.9 6 1 0⎥⎢⎥ y+ ⎢2.5 ⎥ (9) ⎢⎥zz ⎢ 001⎥⎢⎥ ⎢0 ⎥ ⎣⎦WGS −−84 ⎣ ⎦⎣⎦PZ 90 ⎣ ⎦ The transformation formula[2,4] between BJ-54 coordinate and WGS-84 coordinate is as follows: ⎡⎤xx ⎡⎤ ⎡−12.333 ⎤ ⎢⎥ ⎢⎥ ⎢ ⎥ ⎢⎥yy=− ⎢⎥ ⎢149.054 ⎥ (10) ⎢⎥zz ⎢⎥ ⎢81.280 ⎥ ⎣⎦WGS −−84 ⎣⎦BJ 54 ⎣ ⎦ The method of calculating the coordinate and the clock offset in combined navigation system is the same as the method of GPS navigation system. But a new variable is added. It is the clock offset relative to Compass-I system clock. Pseudorange measurements can be expressed as 222 ρii=−+−+−+•Δ()()()x xyyzzc iit (11) Where:

5 (,x yz ,) - The coordinates of the receiver in the WGS-84 Coordinate System;

(,xiiiyz ,) - The coordinates of the satellite in the WGS-84 Coordinate System;

Δ=Δttgl - Clock offset relative to GLONASS system clock, if the satellite is one of satellites of GLONASS system;

Δ=ΔttBD - Clock offset relative to Compass-I system clock, if the satellite is one of satellites of Compass-I navigation system. We suppose that there are n satellites of GLONASS system and m satellites of Compass-I system involved in positioning. (11) is written in matrix form: 111 ⎡⎤aaaxyz10 ⎢⎥ ⎢⎥##### ⎢⎥nnn aaaxyz10 A = ⎢nnn+++111 ⎥ (12) ⎢⎥aaaxyz01 ⎢⎥##### ⎢⎥ nm+++ nm nm ⎣⎦⎢⎥aaaxyz01 Where: i a xyz - Direction cosine. T ⎡⎤ (13) X=Δ⎣ x Δ y Δ z −•Δ ctgj −•Δ ctBD ⎦ T Δ=Δρρ[ 11"" Δ ρNN Δ ρ+ Δ ρ NM+] (14) Δ=ρ AX (15) When the satellites tracked are more than five, we generally use least-squares method to process data. T −1 −1 XA=⎣⎦⎡⎤ AAΔρ (16)

Ⅴ. CONCLUSION

This paper analyses the principle of active positioning and passive positioning of Compass-I navigation system and details the methods of calculating the coordinates and clock offset of the receiver. According to the results of simulation, the precision of active positioning is higher than the precision of passive positioning. But the capacity of the users is limited and real-time is not good if active positioning mode is used. Passive positioning mode has not these disadvantages. It also describes GLONASS navigation system. In the end, the paper details combination navigation algorithm. The precision of combination navigation algorithm is higher than the precision of a single system.

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