Cycle slip detection and repair based on Bayesian compressive sensing

Abstract

The presence of cycle slips corrupts the carrier phase measurement which is critical for high precision global navigation satellite system static or kinematic positioning. The process of cycle slips is comprised of detecting the slips, estimating its exact integer and making a repair. In this paper, a novel approach to cycle slip detection and repair based on Bayesian compressive sensing is proposed, in order to reduce the noise effects on the performances of cycle slip detection and repair. Unlike traditional cycle slip detection and repair methods, we exploit the sparse property of the cycle slip signal, aiming to obtain the perception matrix and establish the sparse cycle slip detection model. Then in order to estimate and repair the value of cycle slips, the residuals of carrier phase double difference and the interference noise between multiple satellites, when more than one satellite has cycle slips, are taken into consideration, which is used as prior information to obtain the likelihood expression for cycle slip signal. Finally, we use the prior information about signals based on relevance vector machine principle derived from sparse Bayesian learning to predict cycle slip distribution and then estimate the value of cycle slips. The novel approach is tested with the actual collection of satellite data in the experiment. It is shown that the novel approach proposed in this paper can effectively estimate cycle slips and achieve better performance than orthogonal matching pursuit and l1 norm based algorithm when the redundancy of carrier phase is large enough. In the case of single frequency carrier phase observation, when redundancy is not less than 7, the novel approach can completely detect and repair cycle slips; in the case of dual-frequency carrier phase observation, when cycle slips happen in four of the eight satellites, 97.6% probability of accuracy is accomplished by the new approach.