1. 2 Point Positioning with Carrier Phase II. Phase Range Observation Equation 1.3 Point Positioning with Doppler data Φ!(1)=p()+N!+f△6:(t) D(t)=p;(t)+c△6:(t) p/(r)Measured carrier phase expressed in cycles integer unknown D (r)Observed Doppler shift scaled to range rate f Frequency of the satellite signal stantaneous radial velocity between the Observation Equation Ad (t) Time derivative of the combined clock Φ(1)-f6(t)=kp(t)+N/-f△6(t) Unknown 2.1 DGPS with Code Ranges 2. Differential Positioning (DGPS) Station A DGPS calculates pseudorange corrections(PRC)and R4(0)=p4(0)+△8(0)+c6(t0)-c6A(0) nge rate corrections(RRC)(located at A)which are △8(0) Radial orbital er transmitted to the remote receiver(located af B)in near real time The code range correction for satellite j at reference epoch to is PRC(t0)=-R(t0)+8(t0) (t0)-c6(t0)+c6A(0) rom a time series of range corrections, the range rate correction RRC(to) can be evaluated by numerical PRC()=PRC (o)+ PRC (o)(t-t) 2.2 DGPS with Carrier Phases Station B The pseudorange derived from carrier phases at station The code range at station B at epoch t can be modeled R(n)=p()+△6(n)+c6(n)-c6a(1) Ao(o)=P(to)+ApA(to)+NA+c8(to)-c8, (t.) RI(=R()+PRC(0) The phase range correction at reference epoch to is 6g(r)+(△8()-64()-c(6(1)6A(t) PRC()=-(t0)+p(t) Neglecting the difference of the radial orbital errors =-△p(tn)-N-c6/(t0)-c6(t。) R()am=p()-c△6a() Combined error of receiver clocks2 1.2 Point Positioning with Carrier Phase 1. Phase Range Observation Equation ( ) ρ (t) N f δ (t) j i j λ i 1 Φ = + + ∆ j j i j i t (t) j Φi Measured carrier phase expressed in cycles. N j i Phase ambiguity integer number, integer ambiguity, or integer unknown. j f λ Wavelength Frequency of the satellite signal ( ) f δ (t) ρ (t) N f δ (t) i j λ i j 1 Φ − = + − ∆ j j i j j i t Observation Equation: Known Unknown 1.3 Point Positioning with Doppler Data ( ) ρ (t) δ (t) j i D D t = D + c∆ j i j i D (t) j i Observed Doppler shift scaled to range rate ρ (t) j i D Instantaneous radial velocity between the satellite and the receiver δ (t) j i ∆D Time derivative of the combined clock 2. Differential Positioning (DGPS) DGPS calculates pseudorange corrections (PRC) and range rate corrections (RRC) (located at A) which are transmitted to the remote receiver (located at B) in near real time. 2.1 DGPS with Code Ranges ( ) ρ ( ) δ ( ) cδ ( ) - cδ ( ) 0 A 0 j 0 j 0 0 A R t t t t t j A j A = + ∆ + δ ( ) 0 j A ∆ t Radial orbital error The code range correction for satellite j at reference epoch t0 is - δ ( ) - cδ ( ) cδ ( ) PRC ( ) ( ) δ ( ) 0 A 0 j 0 j A 0 j 0 0 A t t t t R t t j A j = ∆ + = − + Station A From a time series of range corrections, the range rate correction RRCj (t0) can be evaluated by numerical differentiation. PRC ( ) PRC ( ) PRC ( )(t - ) 0 0 0 t t t t j j j = + The code range at station B at epoch t can be modeled ( ) ρ ( ) δ ( ) cδ ( ) - cδ ( ) B j j B R t t t t t j B j B = + ∆ + δ ( ) ( δ ( ) - δ ( )) (δ ( ) - δ ( )) ( ) ( ) PRC ( ) B A j A j B B corr t t t c t t R t R t t j j B j B = + ∆ − = + Neglecting the difference of the radial orbital errors ( ) ρ ( ) c δ ( ) AB j corr B R t t t j B = − ∆ Combined error of receiver clocks Station B 2.2 DGPS with Carrier Phases The pseudorange derived from carrier phases at station A at epoch t0 λΦ ( ) ρ (t ) ρ (t ) λN cδ (t ) - cδ (t ) 0 0 j 0 A j 0 0 A j A A j j A t = + ∆ + + The phase range correction at reference epoch t0 is - ρ (t ) λN cδ (t ) - cδ (t ) PRC ( ) λ (t ) ρ (t ) 0 0 j 0 A j A 0 j 0 A j 0 A j A j t = ∆ − − = − Φ +