Precise Orbit Determination of Global Navigation Satellite System of ...

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Chapter 7 Orbit Determination Using Carrier Phase Observation λλ ∃ 1 3 ρ ( III) = ( Φ1 −Φ 3 − N13) (7-34) λ − λ 3 1 ∃ ρ ∃ ( III) N1 = Φ1 − λ 1 ∃ ρ ∃ ( III) N2 = Φ2 − λ 2 ∃ ρ ∃ ( III) N3 = Φ3 − λ 3 (7-35) N : [ N N N N N ∃ = ] : = [ ] : = [ ] (7-36) 1 1 2 2 3 3 The first step is very important for the successful solution of the initial integer ambiguities for TCAR algorithm. If under strong multipath environment, the error of ∃ ρ ( I ) is larger than ±10 meter, it is impossible for N12 to get integer solution. Thus from the second step to the last step, a big bias will be introduced into all integer ambiguity solutions, which lead to ambiguity resolution failure. The multipath effects may be reduced using linear combinations, which will be discussed in the next section. L3 is an ionospheric-free linear combination that is little affected by multipath effects as well (see Table 7-7). In order to eliminate the influence of multipath effects and ionospheric errors on TCAR algorithm, the ionosphere- free or multipath-free linear combination of E1/E3 code measurements should be formed as the first step for ρ ( I ) , i.e. improved TCAR steps may be written as follows, Step1: Ionospheric-free linear combinations of E1 and E3 code pseudoranges should be produced by 2 2 f ∃ E1 fE3 ρ( I) = ρE−ρ 2 2 1 2 E f − f f − f E1E3 2 3 (7-37) E1E3 From Table 7-7, it is guaranteed that ∃ ρ ( I ) has much little influence from ionospheric errors and multipath effects. Thus the float ambiguity ∃ N 12 is solved by using widelane linear combinations of E1 and E2 phase observations and ∃ ρ ( I) ∃ 1 1 12: = Φ1−Φ2−( − )∃ ρ ( ) (7-38) λ λ N I 1 2 Because the wave length of linear combination of Φ1 − Φ2 is about 10 meter and the accuracy of ∃ ρ ( I ) is much better than 10 meter, integer ambiguity N12 can easily be obtained by rounding ∃ N12 to the nearest integer, i.e. N : [ N∃ = ] (7-39) 12 12 where N12 integer ambiguity ∃N 12 float ambiguity N∃ : = N − N 12 1 2 Step 1 is a big difference from the original TCAR algorithm Eq.(7-28) and will significantly reduce the ionospheric errors and multipath effects. In Step 2 there is no influence from multipath effects, hence Step 2 does not need to be changed. Step 3 also remains without changes. From the discussion above it is clear that TCAR still can not guarantee 100% success in the integer ambiguity resolution of original carrier phase observations. The key step is the last step. For example, if L1 is strongly affected by ionospheric and/or multipath errors, the last step will not be successful. In other words, the accuracy of ∃ ρ ( III ) in Eq.(7-34) and Eq.(7-35) should be better than 0.10 meter, otherwise, the last step may be a failure. 94
Chapter 8 Geostationary Orbit Determination And Prediction During Satellite Maneuvers CHAPTER 8 GEOSTATIONARY ORBIT DETERMINATION AND PREDICTION DURING SATELLITE MANEUVERS Geostationary satellites (GEO) are important candidates for the GNSS-2 system. Theoretically, a geostationary orbit is one where the orbit has the same period as the earth's rotation period, and remains at a “fixed” point on the sky at all times and stationary over a single point on the Earth's surface. The orbit is a circle and the orbit must lie in the earth's equatorial plane. Because of various perturbations such as nonspheric earth gravitation, solar and lunar attractions, once a satellite is placed in the proper position of geostationary orbit, it doesn't stay there, it tends to drift. Geostationary satellite drifts can be divided into two parts, one is the in-plane drift and the other is the out-ofplane drift. The in-plane drift is caused by changes of the orbital parameter longitude of the ascending node, Ω . The out-of-plane drift is produced by variation of the orbital parameter inclination of orbit, i. When geostationary satellite drifts away from its “fixed” position, satellite maneuver or station keeping operation will be started. The operation frequency is dependent on the deadbands, normally 0.1 degree or larger. Regular weekly or two weekly longitude maneuvers may be preferred for simplicity, inclination maneuvers will be less frequent, larger and will normally have an in-plane component that will need to be corrected rapidly (Dow, 1999). For almost weekly maneuvers, geostationary satellite is very difficult to be used for navigation application purpose. MEO and IGSO satellites also meet the maneuver problems, but it is not so serious as GEO satellites, because the frequencies of maneuver operation for MEO and IGSO are much lower than for GEO satellites. Therefore in this chapter, the emphasis is on GEO satellite maneuvers. The kinematic orbit determination method discussed in Chapter 6 will be used to solve this problem during GEO satellite maneuvers. 8.1 Perturbations of Geostationary Satellite For geostationary satellite maneuvers or stationkeeping, the changes of orbital parameters longitude of the ascending node Ω and inclination of orbit i under influence of the perturbations are very important. The changes of these two parameters are analyzed as follows. The orbital elements and time are related to perturbation functions by the following system of differential equations, also called Lagrange equations: da R = dt na M de e R e R = dt na e M na e d i R e R dt na e i i na e e di R i R dt na e i na e i d R dt na e i i dM e R R n dt na e e na a − − − − =− + − − = + − − = − = − − 2 ∂ � ∂ � � 2 2 1 ∂ 1 ∂ � 2 2 � ∂ ∂ω � 2 � ω cos ∂ 1 ∂ � 2 2 2 1 sin ∂ ∂ � � � 1 ∂ cos ∂ � 2 2 2 2 � 1 sin ∂Ω 1 sin ∂ω � Ω 1 ∂ � � 2 2 1 sin ∂ � 2 � 1 ∂ 2 ∂ − � 2 ∂ ∂ �� 95 (8-1)
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PRECISE ORBIT DETERMINATION OF GLOB
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Summary GNSS-2 (Global Navigation S
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3.2.2.1 Principle..................
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9.3.3 The Effect of Distribution of
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Chapter 1 Introduction 1.2 Developm
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Chapter 2 Observations of Orbit Det
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Chapter 3 Orbit Tracking System and
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Chapter 4 Major Error Sources of Sa
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Page 52 and 53: Chapter 5 Perturbation Models of IG
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Conclusion 144
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References Carpino M. (1995): SAEG
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References Klobuchar, J. A.(1996):
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References Traquilla, J. M. and J.
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Acknowledgments 152
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