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Chapter 6 Algorithms of Orbit Determination of IGSO, GEO and MEO Satellites x = rcosϕcos λ� � y = rcosϕsin λ � z = rsinϕ � � we can obtain, 2 ∂ U 2 ∂x e 2 2 74 (6-49) ∂ Ue ∂r 2 ∂Ue ∂ r = ( ) + (6-50) 2 2 ∂r ∂x ∂r ∂x e 2 Ue 2 ∂ Ue ∂r ∂r ∂Ue xy e 2 ∂r ∂x ∂y ∂r 2 Ue 2 ∂ Ue ∂r ∂r ∂Ue xz e 2 ∂r ∂x ∂z ∂r 2 Ue 2 y e 2 ∂ Ue = 2 ∂r ∂r ∂y 2 ∂Ue + ∂r 2 Ue 2 ∂ Ue ∂r ∂r ∂Ue yz e 2 ∂r ∂y ∂z ∂r 2 Ue 2 z e 2 ∂ Ue = 2 ∂r ∂r ∂z 2 ∂Ue + ∂r ∂ ∂∂ ∂ ∂∂ ∂ ∂ ∂ ∂∂ ∂ ∂ 2 ∂ r = + (6-51) ∂∂ xy 2 ∂ r = + (6-52) ∂∂ xz 2 ∂ r ( ) (6-53) 2 ∂y 2 ∂ r = + (6-54) ∂∂ yz 2 ∂ r ( ) (6-55) 2 ∂z where, the symbol | e means the derivatives in the earth-fixed coordinate system. These derivatives will be converted to the inertial coordinate system. If only the J2 term in geopontential Eq.(6-48) is considered, the Eq.(6-50) to Eq.(6-55) become, 2 e 2 3 3 2 e ∂ U ∂x 2 ∂ Ue ∂∂ xy 2 ∂ Ue ∂∂ xz ∂ U ∂y � GM GM ae 2 2 � 2 2 GM ae 2 2 2 = 2 −6 J 3 ϕ −1 ϕ λ 6 J ϕ λ 3 2 2 � � ( ) ( sin ) r r r � � cos cos − ( ) sin cos r r � GM 3 GM ae 2 2 � 2 + − + − � � J 3 3 2 ( ) ( 5sin ϕ 1) r 2 r r � � sin λ � GM GM ae 2 3 7 2 � 2 2 + − + − + � � 3 J 3 3 2 ( ) ( sin ϕ) r r r 2 2 � � sin ϕ cos λ (6-56) e �GM GM ae 2 2 � 2 GM ae 2 = −3 J ϕ ϕ λ ϕ ϕ λ 3 3 2 3 −1 2 3 J 3 2 2 2 2 � � ( ) ( sin ) r r r � � cos sin − ( ) sin sin sin r r � GM 3 GM ae 2 2 � − − + − � � J 3 3 2 ( ) ( 5sin ϕ 1) r 2 r r � � sin λcos λ � GM GM ae 2 3 7 2 � 2 + − + − + � � 3 J 3 3 2 ( ) ( sin ϕ) r r r 2 2 � � sin ϕsinλcosλ (6-57) e �GM GM ae 2 2 � GM ae 2 2 2 = −3 J ϕ ϕ λ ϕ ϕ ϕ λ 3 3 2 3 −1 2 6 J 3 2 2 � � ( ) ( sin ) r r r � � sin cos + ( ) sin (cos −sin ) cos r r � GM GM ae 2 3 7 2 � − − + − + � � 3 J 3 3 2 ( ) ( sin ϕ) r r r 2 2 � � sinϕcosϕcosλ (6-58) 2 e 2 3 3 2 e � GM GM ae 2 2 � 2 2 GM ae 2 2 2 = 2 −6 J 3 ϕ −1 ϕ λ 6 J ϕ λ 3 2 2 � � ( ) ( sin ) r r r � � cos sin − ( ) sin sin r r � GM 3 GM ae 2 2 � 2 + − + − � � J 3 3 2 ( ) ( 5sin ϕ 1) r 2 r r � � cos λ
Chapter 6 Algorithms of Orbit Determination of IGSO, GEO and MEO Satellites 2 ∂ Ue ∂∂ yz ∂ U ∂z � GM GM ae 2 3 7 2 � 2 2 + − + − + � � 3 J 3 3 2 ( ) ( sin ϕ) r r r 2 2 � � sin ϕsin λ (6-59) e �GM GM ae 2 2 � GM ae 2 2 2 = −3 J ϕ ϕ λ ϕ ϕ ϕ λ 3 3 2 3 −1 2 6 J 3 2 2 � � ( ) ( sin ) r r r � � sin sin + ( ) sin (cos −sin ) sin r r � GM GM ae 2 3 7 2 � − − + − + � � 3 J 3 3 2 ( ) ( sin ϕ) r r r 2 2 � � sin ϕcosϕsin λ (6-60) 2 e 2 3 3 2 e � GM GM ae 2 2 � 2 GM ae 2 2 = 2 −6 J 3 ϕ −1 ϕ 6 J ϕ 3 2 2 � � ( ) ( sin ) r r r � � sin − ( ) sin (6-61) r r 2)Solar and lunar Attractions The solar and lunar attractions Eq.(5-23) may be rewritten in the following forms: � x x&=− µ + � � µ i r � i= s, m � x − x x � − � r � � i i 3 2 2 2 ( xi − x) + ( yi − y) + ( zi −z) 3 i y � y& =− µ + � � µ i r � i= s, m � y − y y � − � r � � i i 3 2 2 2 ( xi − x) + ( yi − y) + ( zi −z) 3 i � z z&=− µ + � � µ i r � i= s, m � z − z z � − � r � � i i 3 2 2 2 ( xi − x) + ( yi − y) + ( zi −z) 3 i From Eq.(6-62) to Eq.(6-64), we can get 2 ∂ U ∂x 2 s, m 2 + ∂ U , ∂∂ xy 2 �� sm ∂ U , ∂∂ xz 2 ∂ U ∂y sm sm , 2 x 1 = −( 1− 3 ) − 2 3 � r r = 2 i s, m � � µ � i �� x − x i 2 2 2 ( x − ) + ( − ) + ( − ) � i x yi y zi z � � 2( xi−x) 3( xi−x) − 3 2 2 2 ( x − ) + ( − ) + ( − ) �� i x yi y zi z � � � ( xi − x) + ( yi − y) + ( zi −z) xy = 3 − r xz = 3 − r , � � µ i � � �� ( xi − x) yi−y + ( yi − y) + ( zi −z) � 5 2 2 2 i= s m , � � µ i � � �� ( xi − x) zi−z + ( yi − y) + ( zi −z) � 5 2 2 2 i= s m y 1 =−( 1−3 ) − 2 3 r r 2 � i= s, m � � µ i � �� y − y i 75 2 2 2 − − �� 2 2 2 i − + i − + i − ( x x) ( y y) ( z z) 3 3 � � � 5 2 i i � � � � �� ( x −x) ( y −y) 2 2 2 i − + i − + i − ( x x) ( y y) ( z z) 2 i i ( x −x) ( z −z) 2 2 2 i − + i − + i − ( x x) ( y y) ( z z) � � � 3 � � � � � � 5 5 � � � � �� (6-62) (6-63) (6-64) (6-65) (6-66) (6-67)
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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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Page 32 and 33: 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
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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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