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

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Chapter 2 Observations of Orbit Determination S ( t2 ) the geocenter vector of ground tracking station at t 2 From Figure 2-1, 1 1 2 1 2 T 1 2 1 2 S = || r ( t ) − S ( t ) || = {[ r ( t ) − S ( t )] [ r ( t ) − S ( t )]} (2-2) 2 1 S = [ r( t ) − S ( t )] [ r( t ) − S ( t )] = [ r ( t ) r( t ) − r ( t ) S ( t ) − S ( t ) r( t ) + S ( t ) S ( t ) = r T 1 ( t ) r ( t ) + S 1 1 2 T T ( t ) S ( t ) − 2r ( t ) S ( t ) 2 1 2 2 T 1 T 1 2 1 T 1 Eq.(2-1) can be written as L = c t − t ) = || r( t ) − S ( t ) || (2-4) ( 2 1 1 2 By linearizing Eq. (2-4), Eq.(2-1) becomes 0 0 0 ∂L ∂L L = L + δ L = || r ( t1) − S ( t2) || + δr ( t1) + δS ( t2) (2-5) ∂r ( t1) ∂S ( t2) where the partial derivatives are T T ∂L [ r( t1) − S ( t2 )] [ r ( t1) − S ( t 2 )] = = (2-6) ∂r ( t1) || r( t1) − S ( t2 ) || L T T ∂L [ r ( t1) − S ( t2)] [ r ( t1) − S ( t2)] = − = − (2-7) ∂S ( t ) || r ( t ) − S ( t ) || L 2 1 2 ∂r( t1) ∂r ( t1) ∂p( t1) δ r( t1) = δr( t0) + δp( t0) (2-8) ∂r( t0) ∂p( t1) ∂p( t0) where p dynamical model parameters of satellite orbit Inserting Eq.(2-6) - Eq.(2-8) into Eq.(2-5), the final linear observation equation can be written as T T [ r( t1) − S ( t 2 )] ∂r( t1) ∂r ( t1) ∂p( t1) [ r ( t1) − S ( t 2 )] δL = [ δr( t0 ) + δp( t0 )] − δS ( t 2 ) (2-9) 0 r( t ) p( t ) p( t ) 0 L ∂ ∂ ∂ L where t 0 initial epoch 0 1 0 2.1.1.2 Error Budgets The accuracy of range observations is dependent on the chip rate or frequency. Discussion in detail about influence on range measurements from various error sources such as tropospheric, ionospheric errors and multipath effect are given in Chapter 4. In this section the major error sources of range measurement related to the receiver are discussed and the error budget based on experiences of current satellite navigation systems is presented. Range measurements are implemented inside the receiver in two ways: 1) tone range; 2) pseudocode ranging like GPS C/A code measurements. The major error sources related to receivers are the following two types. i) Tone Range Error The accuracy of ranging is set by the highest major carrier frequency and the signal-to-noise ratio: c 1 σ r = 2 2πf s where K S / N (2-10) σ r distance error c speed of light fs major tone frequency S/N signal-to-noise ratio K receiver-related parameter ii) Pseudonoise(PN)-Code Ranging Error with Delay Lock Loop (DLL) For a Delay Lock Loop, the accuracy of range measurement can be expressed by 4 2 T 2 1 T 2 2 (2-3)
Chapter 2 Observations of Orbit Determination ( / ) N C BL σ r = D (2-11) 2 0 where BL loop bandwidth D chip-length of single PN-code chip C/N0 carrier-to-noise ratio in 1 Hz bandwidth Using GPS as an example, the total error budget for one-way range measurement is listed in Table 2-1. Table 2-1 Error Budget of One-Way GPS Ranging (NATO GPS Interface Document, 1988) Segment Error P-Code Error C/A-Code Error Source Source 1 σ [m] 1 σ [m] Clock & Nav. Sub-System Stability 3.0 3.0 Space Predictability of Satellite Perturbations 1.0 1.0 Other 0.5 0.5 Control Ephemeris Prediction Model Implementation 4.2 4.2 Other 0.9 0.9 Ionospheric Delay Compensation Tropospheric Delay 2.3 5.0-10.0 Compensation 2.0 2.0 User RCVR Noise & Resolution 1.5 7.5 Multipath 1.2 1.2 1 σ System UERE [m] Other 0.5 0.5 Total 5 6.6 10.8-13.9
Page 1: PRECISE ORBIT DETERMINATION OF GLOB
Page 4 and 5: Summary GNSS-2 (Global Navigation S
Page 6 and 7: 3.2.2.1 Principle..................
Page 8 and 9: 9.3.3 The Effect of Distribution of
Page 10 and 11: Chapter 1 Introduction 1.2 Developm
Page 14 and 15: Chapter 2 Observations of Orbit Det
Page 26 and 27: Chapter 3 Orbit Tracking System and
Page 40 and 41: Chapter 4 Major Error Sources of Sa
Page 52 and 53: Chapter 5 Perturbation Models of IG
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Chapter 5 Perturbation Models of IG
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Chapter 6 Algorithms of Orbit Deter
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Chapter 7 Orbit Determination Using
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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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