4. 4 Linearization Model for Relative Positioning restricted to carrier phases, since it should be obvious how to change from the more expanded model of phases to a code 4a)「4,()吨)吗)40·0 6)-e)-a) M]4()呢))A0 The model for the double-difference u)-副)-e8") )吨()吗 A(r)=P1()+入Nk 2)吨(a)鸣(2)0A4 Where: PA(0=Pi(o)-pi(0-P(+pl(o 或)砖()哦)00x equation reflects the fact of four measurement Each of the four terms must be linearized Lineaized Equation YB+a2△B+)NA -o+x(Am△xn+y(=y△v Whe:l()=λ(1)-p2s()+p2()+p()-pl(n) a及 △XA+ ak=? Observation Equation E Ax 2(Q-2A△zA 5.1 Single baseline Solution Problem: 1. The adjustment principle requires observations are uncorrelated 5. Network Adjustment differences and triple-differences are correlated 3. The implementation of the double-difference correlation can be easily accomplished. Alternatively, decorrelated algorithm using a Gram-Schmidt orthogonalization. 4. The implementation of the correlation of the triple. differences is questionable since the noise of the triple-differences will always prevent to obtain a refined solution.3 4.4 Linearization Model for Relative Positioning For the case of relative positioning, the investigation is restricted to carrier phases, since it should be obvious how to change from the more expanded model of phases to a code model. The model for the double-difference jk AB jk λΦ (t) = p (t) + λN jk AB AB p (t) p (t) p (t) p (t) p (t) j A k A j B k B jk Where: AB = − − + Above equation reflects the fact of four measurement quantities for a double-difference. Each of the four terms must be linearized. Lineaized Equation: l = Ax jk X B Y B Z B AB X A Y A Z A jk AB a X a Y a Z λN δ (t) a X a Y a Z B B B A A A + ∆ + ∆ + ∆ + = ∆ + ∆ + ∆ jk jk jk jk jk jk ( ) λΦ ( ) ( ) ( ) ( ) ( ) 0 0 0 0 jk AB l t t p t p t p t p t j A k A j B k AB B jk = − + + − a ? a ? a ? a ? a ? a ? B B B A A A X Y Z X Y Z = = = = = = jk jk jk jk jk jk Where: Observation Equation: 5. Network Adjustment 5.1 Single Baseline Solution 1. The adjustment principle requires observations are uncorrelated. 2. The single-differences are uncorrelated, whereas double￾differences and triple-differences are correlated. 3. The implementation of the double-difference correlation can be easily accomplished. Alternatively, decorrelated algorithm using a Gram-Schmidt orthogonalization. 4. The implementation of the correlation of the triple￾differences is more difficult. Furthermore, it is questionable since the noise of the triple-differences will always prevent to obtain a refined solution. Problem: