Cycle slip detection and repair with a circular on-line change-point detector

•The aim of this article is the processing of angular data, with application to GNSS signals phase and frequency estimation.•We propose a circular particle filter for the processing of angles in case of non-linear state/observation equations.•We propose a circular change point detector for the processing of abrupt changes in angular data.•We propose a phase open loop and a frequency semi-open loop for the tracking of GNSS signals.•The proposed methods are assessed on synthetic data for phase and frequency estimation and on real data for positioning application.

In this article, we propose a circular change-point detector for on-line processing of the phase and the frequency of a GPS-L1 signal. The aims of this processing are to get an accurate estimation of the phase and to use it to get centimeter precise position estimates every millisecond. We propose to track the phase of the GPS signal in an open loop and the frequency in a semi-open loop. In an open loop, the phase delay evolves as a circular random variable. Furthermore, the phase is subject to cycle slips. These abrupt changes must be detected and repaired. We propose a circular generalized likelihood test for the on-line detection of changes in the phase measurements. With the estimation and detection being non-linear, we propose a particle filter defined according to the circular von Mises distribution for the estimation of the phase and frequency. The proposed architecture is assessed using synthetic and real data.