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

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Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits The accelerations of IGSO and GEO satellite produced by ocean tides are about 1×10 -10 m/s 2 ; for MEO (GPS) satellite is about 5×10 -10 m/s 2 (Landau, 1988), i.e. after one day orbit arc computation, the maximum errors of IGSO and GEO is less than 0.01 meter, for MEO (GPS) satellite is less than 0.04 meter, therefore for real-time orbit determination the ocean tide terms can be neglected in the satellite dynamic model, but for long period of orbit prediction and batch processing, the ocean tide effects should be included in the satellite dynamic model. 5.4.3 Ocean Tide Loading Ocean tides by attraction of Sun and Moon also cause a periodic deformation of the crust. This phenomenon is called ocean tide loading. The displacements of tracking stations will be produced by the deformation of the crust, which can be described by three components of radial, east-west, north-south. The resulting displacements were computed by Scherneck (1991) using Schwiderski tide model, Green function for an elastic earth and Green function for a visco-elastic structure for stations on continental shelves. The displacement due to ocean loading is about 0.05 meter (Chadwell, 1995) and can be considered as tracking station error. The 0.05 meter of displacements of tracking stations will lead to 0.05 meter of orbit error, which is independent of the satellite type. In precise orbit determination, the effect of ocean loading should be included. 64
Chapter 6 Algorithms of Orbit Determination of IGSO, GEO and MEO Satellites CHAPTER 6 ALGORITHMS OF ORBIT DETERMINATION FOR IGSO, GEO & MEO SATELLITES 6.1 Numerical Integration According to Newton's gravitational law, the satellite movement equation can be written as (Escobal, 1976) ϖ ϖ&r r =−µ (6-1) 3 r where, ϖ&r satellite acceleration vector in inertial coordinate system ϖ r satellite position vector in the same coordinate system µ the earth's gravitational constant Practically, the satellite is affected by various factors such as nonspherical earth gravitation, solar and lunar attractions, solar radiation, etc. Therefore the satellite movement equation can be more accurately expressed as ϖ ϖ&r r ∂R =− µ + (6-2) 3 r ∂t where R is a perturbation function of the sum of various perturbation sources mentioned above. Usually, there are two kinds of methods to solve this equation, analysis solution and numerical integration. The analysis method is complicated and the solution is low accuracy. The numerical integration is widely used and very rigorous, but time consuming for computation, especially for computation of complicated perturbation models. Two common algorithms of numerical integrations are Runge-Kutta and Adams-Cowell (Cappellari et al 1976, Xu 1989 and Engeln-Müllges et al, 1996). 6.1.1 Runge-Kutta Integration The solution of satellite movement equation can be considered as solution of the initial value problem of the following differential equation, i.e. yt &( ) = f( yt ,) � � yt ( 0) = y0 � Please note in Eq.(6-3), y=(y1,y2,y3,y4,y5,y6), which can be expressed as six Kepler orbital parameters. The differential equation (6-3) can be solved by explicit Runge-Kutta algorithm as follows (Cappellari et al 1976, Xu 1989) m � yn+ 1 = yn + � wiki � i= 1 � i− � (6-4) 1 � ki = f( tn + cih, yn + h aijkj) � � j= 1 � where h step length of integration f( ) the right function of satellite movement equation m order of Runge-Kutta method wi weighted coefficients coefficients ci , ki, aij In precise orbit determination, 8-order of Runge-Kutta integration algorithm should be used, which is given by (Cappellari et al 1976, Engeln-Müllges et al, 1996, Xu 1989) 65 (6-3)
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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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Page 22 and 23: Chapter 2 Observations of Orbit Det
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Page 104 and 105: Chapter 8 Geostationary Orbit Deter
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Chapter 9 Software and Simulation R
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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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