GPS Phases: Single Epoch Ambiguity and Slip Resolution

Abstract

An observational equation of the GPS carrier phase contains the pair station — satellite specific and epoch independent bias γ ^s _r = ψ^s(t ₀)−ψ _r (t ₀) +N ^s _r , in which N ^s _r is an integer ambiguity and ψ (t ₀), ψ_r(t ₀) are transmitter and receiver initial phases. Through sequential processing of phases we update in each epoch, among other unknowns, the γ ^s _r estimates, provided specific minimal configurations of satellites, stations and already processed epochs are satisfied. All second differences of the phases, e.g. with respect to a given reference satellite and reference receiver, ∇Δγ ^s _r =∇ΔN ^s _r , should be then integers on each L1 and L2 band. These conditions can be solved for all N ^s _r ’s (thus implying new γ ^s _r -values) about current estimates of the γ ^s _r ’s as soon as the integer values are found by means of a proper search procedure.

Cycle slips come into view as outliers of observations produced by rapid changes of particular γ ^s _r values. In that case a new observation sequence is created, for which new γ-parameters are estimated, and then consequently constrained for ambiguities.