Phase pseudoranges Instantaneous circular frequency f is a derivative of the phase t to time d o By integrating frequency between two time epochs the ignal's phase results g=∫fd Assuming constant frequency, setting the initial phase (t0)to zero, and taking into account the signal travel time tr corresponding to the satellite-receiver distance p, we get =f(-n)=f|t C 2005-3-25 hase pseudoranges PRIt phase of reconstructed carrier with frequency R (t)=f°t-f PRoe and oc are clock errors o.=-f dt and frat ()=q(1)-g2(t) P f+f'dt'-frdtr+(fs-fr Gv Principles of the Global Positioning System 20053-25(126 Principles of the Global Positioning System 2005-3-25 11 Phase pseudoranges ‹ Instantaneous circular frequency f is a derivative of the phase with respect to time ‹ By integrating frequency between two time epochs the signal’s phase results ‹ Assuming constant frequency, setting the initial phase ϕ(t0) to zero, and taking into account the signal travel time tr corresponding to the satellite-receiver distance ρ, we get dt d f ϕ = ∫ = t t f dt 0 ϕ ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − = − c f t t f t tr ρ ϕ Principles of the Global Positioning System 2005-3-25 12 ϕs (t) phase of received carrier with frequency f s ϕR(t) phase of reconstructed carrier with frequency fR f dt f dt f f t c t t t f f dt f dt where t f t c t f t f R s R R s s s R s s R R c R R s s s c s Ro c c R R R c s c s s s ( ) ( ) ( ) ( ) and and are clock errors ( ) ( ) 0 , 0 , , 0 , 0 , 0 , = − = − + − + − = − = − = − = − − ρ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ρ ϕ Phase pseudoranges