Basic GPS Observables(cont P,n, P2-pseudoranges measured between station i and satellite k on LI and L d., a-phase ranges measured between station i and satellite k on LI and L2 Po, P. -initial fractional phases at the transmitter and the receiver, respectively 4: -ambiguities associated with L, and L2, respectively M,=19 cm and n2= 24 cm are wavelengths of L, and L, phases p.geometric distance between the satellite k and receiver i, ionospheric refraction on LI and L2, respecti T-the tropospheric refraction term ey Principles of the Global Positioning System 2005-3- Basic GPS Observables(cont d -the i-th receiver clock error dr- the k-th transmitter(satellite)clock error fr, f,- carrier fre c- the vacuum speed of light e e,2 E E,- measurement noise for pseudoranges and phases on LI and L2 M, ,M,2,m, , m 2 -multipath on phases and ranges bil, bz, b3-interchannel bias terms for receiver i that represent the sible time non-synchronization of the four measurements b,- interchannel bias betweenΦandΦ , 2, 6, -biases between q. and Pl, dpi and P 2 Gv Principles of the Global Positioning System 18)9 Principles of the Global Positioning System 2005-3-25 17 P P i k i k , , ,1 2 − pseudoranges measured between station i and satellite k on L1 and L2 Φ Φ i k i k , , , 1 2 −phase ranges measured between station i and satellite k on L1 and L2 ϕ 0 ϕ 0 k i , −initial fractional phases at the transmitter and the receiver, respectively N N i k i k , , , 1 2 −ambiguities associated with L and L , respectively 1 2 λ1 ≈ 19 cm and λ2 ≈ 24 cm are wavelengths of L1 and L2 phases ρ i k - geometric distance between the satellite k and receiver i, I f I f i k i k 1 2 2 2 , - ionospheric refraction on L1 and L2, respectively Ti k - the tropospheric refraction term Basic GPS Observables (cont.) Basic GPS Observables (cont.) Principles of the Global Positioning System 2005-3-25 18 dti - the i-th receiver clock error dtk - the k-th transmitter (satellite) clock error f1, f2 - carrier frequencies c - the vacuum speed of light e e i k i k i k i k ,, , , 12 1 2 , , , - measurement noise for pseudoranges and phases on L1 and L2 ε ε bi,1, bi,2 , bi,3 - interchannel bias terms for receiver i that represent the possible time non-synchronization of the four measurements bi i k i k , ,, 1 12 - interchannel bias between and Φ Φ bb P P ii i k i k i k i k ,, , , , , , 23 1 1 1 2 − biases between and , and Φ Φ M M mm i k i k i k i k , , ,, , ,, 1 212 − multipath on phases and ranges Basic GPS Observables (cont.) Basic GPS Observables (cont.)