The above equations are non-linear and require linearization (Taylor series expansion)in order to be solved for the unknown receiver positions and(possibly) for other nuisance unknowns such as receiver clock correction Since we normally have more observations than the unknowns we have a redundancy in the observation system which must consequently be solved by the least squares adjustment econdary(nuisance)parameters, or unknowns in the above equations are satellite and clock errors, troposperic and ionospheric errors, multipath, interchannel biases and integer ambiguities. These are usually removed by differential GPS processing or by a proper empirical model(for example troposphere), and processing of a dual frequency signal Ev Principles of the Global Positioning System 2005-3- 25 Basic GPS observables(simplified form) RI=p+cdt +I/f2+T+ eRI R2=p+cdt+/f22+T+eR2 入①1=p-I/f12+T+1N1+Ea1 n,2=p-1/5+T+nN,+Ea NI, N2-integer ambiguities T-tropospheric effect p-geometric range eri eR2 Egl.Ea2-white noise 入- wavelength Gv Principles of the Global Positioning System 1010 Principles of the Global Positioning System 2005-3-25 19 • The above equations are non-linear and require linearization (Taylor series expansion) in order to be solved for the unknown receiver positions and (possibly) for other nuisance unknowns, such as receiver clock correction • Since we normally have more observations than the unknowns, we have a redundancy in the observation system, which must consequently be solved by the Least Squares Adjustment technique • Secondary (nuisance) parameters, or unknowns in the above equations are satellite and clock errors, troposperic and ionospheric errors, multipath, interchannel biases and integer ambiguities. These are usually removed by differential GPS processing or by a proper empirical model (for example troposphere), and processing of a dual frequency signal (ionosphere). Principles of the Global Positioning System 2005-3-25 20 R1 = ρ + c⋅dt +Ι / f1 2 + T + eR1 R2 = ρ + c⋅dt +Ι / f2 2 + T + eR2 λ1Φ1 = ρ − Ι / f1 2 + T + λ1Ν1 + εΦ1 λ2Φ2 = ρ − Ι / f2 2 + T + λ2Ν2 + εΦ2 Ν1 , Ν2 - integer ambiguities R − pseudorange I / f2 - ionospheric effect Φ − phase T - tropospheric effect ρ − geometric range eR1, eR2, εΦ1, εΦ2 − white noise λ − wavelength Basic GPS observables (simplified form) Basic GPS observables (simplified form)