Cycle slip detection approach based on time-relative positioning theory

An efficient cycle slip detection method is proposed for high precision positioning and navigation results with global positioning system （GPS）,which is based on the assumption of a high sampling interval, measurement errors are so small that they can be ignored in the temporal single difference observables. And ambiguities are ordinarily equal to zero,but could be the number of cycles that have ＂slipped＂ if loss-of-lock has occurred.Therefore,cycle slips are estimated as parameters of time-relative positioning observation equations.Because the temporal single difference observables are taken at different epochs and different stations with a single GPS receiver,if time-relative positioning observation equations are linearized as that of conventional relative positioning,the design matrix will be rank defective.To obtain a stable linearization scheme,time-relative positioning observation equations are further analyzed,and the concept of virtual measurement is applied.A sample of data collected on a vehicle test shows that a cycle slip detection approach based on time-relative positioning theory can detect slips at the value of one cycle.The results also indicate if two satellites are so near to each other that they have the same equivalent to satellite-receiver geometry,cycle slip detection will be difficult and may get wrong results.Cycle slips of different satellites also affect detection by satellite-receiver geometry.