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

More documents

Recommendations

Info

Chapter 6 Algorithms of Orbit Determination of IGSO, GEO and MEO Satellites 2 + ∂ U , ∂∂ yz 2 ∂ U ∂z �� sm sm , 2 + �� 2( yi−y) 3( yi−y) − 3 2 2 2 ( x − ) + ( − ) + ( − ) �� i x yi y zi z � � � ( xi − x) + ( yi − y) + ( zi −z) xz = 3 − r , � � µ i � � �� ( xi − x) zi−z + ( yi − y) + ( zi −z) � 5 2 2 2 i= s m z 1 =−( 1−3 ) − 2 3 r r 2 � i= s, m � � µ i � �� z − z i 76 2 2 2 − �� 2 2 2 i − + i − + i − ( x x) ( y y) ( z z) 3 � � � 5 2 i i � � � � �� ( y −y) ( z −z) 2 2 2 i − + i − + i − ( x x) ( y y) ( z z) 2( zi−z) 3( zi−z) − 3 2 2 2 ( x − ) + ( − ) + ( − ) �� i x yi y zi z � � � ( xi − x) + ( yi − y) + ( zi −z) 3 2 2 2 � � � 3 � � � 5 � � � � �� 5 � � � � �� (6-68) (6-69) (6-70) 3) No Perturbations If in the state transit matrix the perturbation influence on the satellite dynamic model is not considered, the derivative components in Eq.(6-47) may be written as 2 2 ∂ U x 1 =−( 1−3 ) 2 2 3 ∂x r r (6-71) 2 ∂ U xy = 3 5 ∂∂ xy r (6-72) 2 ∂ U xz = 3 5 ∂∂ xz r (6-73) 2 ∂ U y 1 =−( 1−3 ) 2 2 3 ∂y r r (6-74) 2 ∂ U yz = 3 (6-75) 5 ∂∂ yz r 2 2 ∂ U z 1 =−( 1−3 ) (6-76) 2 2 3 ∂z r r Now Kalman filter algorithm for dynamic orbit determination can be summarized as follows ϖ ϖ x& k′ = f( xk′ , t) ϖ ϖ ϖ yk = Hkxk′ + Gkzk P′= Φ P T Φ + Γ Q Γ k k, k−1 k−1 k, k−1 kk , −1 k−1 T kk , −1 T k xk k k T T −1 −1 T −1 −1 { k x k k[ k k( k k k) k k ] } K = P′ H H P′ H + R I −G G R G G R ~ ϖ xk ϖ ϖ = xk′ + Kk( yk − Hkxk′ ) −1 Px = ( I− K H ) P′ k k k xk ~ ϖ −1 −1 −1 z =−( G R G ) G R ( H K ϖ ϖ −I)( y − H x′ ) k k T k k k = ( −1 −1 ) + −1 ( − ) ′ −1 ( −1 −1 ) T k k k k k k z k T k k k T k k k k x k T k k k T k k k k −1 [ ] P G R G I G R H I K H P H R G G R G Eq.(6-77) is also called Extended Kalman Filter (EKF). � � � � � � � � � � � � � � � �� (6-77)
Chapter 6 Algorithms of Orbit Determination of IGSO, GEO and MEO Satellites 6.2.3 Kinematic Orbit Determination The kinematic method, which is traditionally used for ground navigation and positioning, can also be used for orbit determination. Kinematic orbit determination is independent of the satellite dynamic force model and is a geometrical method, which does not consider the dynamic property of moving objects. In other words the kinematic method does not consider the attractions from various sources on satellites. This property is especially beneficial for orbit determination during satellite maneuver, because the exact satellite maneuver force model is difficult to be constructed. The accuracy of the kinematic orbit determination is strongly dependent on the accuracy of observations. This is big difference from dynamic method. The accuracy of the dynamic orbit determination method is not only dependent on the observation, but also dependent on the satellite force models. The disadvantage of kinematic orbit determination is that the observation sample rate should be higher than that of dynamic orbit method, which results in huge observation volume. Another disadvantage is that it is not able to use the kinematic method to predict satellite orbit. This may be a serious problem for users of real-time navigation and positioning applications. Specifically, the kinematic orbit determination is used in such situations where the satellite dynamical forces are difficult to be precisely described by mathematical models, for example, during satellite maneuver. In addition, kinematic orbit determination can also be used to determine some dynamic parameters. Another interesting aspect of kinematic orbit determination is onboard satellite autonavigation. In this mode, high accuracy of orbit determination can be achieved. The satellite orbit integrity is enhanced by comparing the orbit results determined onboard with the results by the ground-based method. It should be noted that kinematic orbit determination described here is different from other kinematic orbit applications (Byun et al 1998 and Balbach et al 1998). Byun et al used onboard GPS receivers to determine satellite orbit just like ground kinematic navigation and positioning. In our method, onboard GPS receivers are not necessary and the kinematic orbit determination is still based on ground-based tracking network. For GEO satellite, the state vector may be written as � x � � y � � � � z � � � x& � � � y& � � � � z& � ϖ x = � x&� � � � y& � � z&� � � � p1 � � � �p 2 � � Μ� � � �� pn �� where x x component of satellite position in the Earth-fixed system y y component of satellite position in the Earth-fixed system z z component of satellite position in the Earth-fixed system &x x component of satellite velocity in the Earth-fixed system &y y component of satellite velocity in the Earth-fixed system &z z component of satellite velocity in the Earth-fixed system &x x component of satellite acceleration in the Earth-fixed system &y y component of satellite acceleration in the Earth-fixed system &z z component of satellite acceleration in the Earth-fixed system pi other parameters such as clock error, tropospheric correction etc. 77 (6-78) Kinematic orbit determination can be used in the Earth-fixed coordinate system. This is different from dynamic orbit determination which is only used in an inertial coordinate system. For state vector Eq.(6-78), state transition matrix is given by
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 12 and 13:
Chapter 2 Observations of Orbit Det
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Chapter 3 Orbit Tracking System and
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35: 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
Page 74 and 75: Chapter 6 Algorithms of Orbit Deter
Page 94 and 95: Chapter 7 Orbit Determination Using
Page 104 and 105: Chapter 8 Geostationary Orbit Deter
Page 122 and 123: Chapter 9 Software and Simulation R
Page 134 and 135:
Chapter 9 Software and Simulation R
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Conclusion 144
Page 154 and 155:
References Carpino M. (1995): SAEG
Page 156 and 157:
References Klobuchar, J. A.(1996):
Page 158 and 159:
References Traquilla, J. M. and J.
Page 160 and 161:
Acknowledgments 152
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?