### Detecting cycle slips in carrier-phase measurements of single frequency navigation receivers with different instabilities of reference oscillators

#### Аннотация

The use of carrier-phase measurements significantly increases the accuracy of solutions when using the measurements of navigation receivers. One of the problems in carrier-phase measurements is discontinuities (cycle slips) in the measurements. The existing algorithms of detection and compensation of cycle slips in carrier-phase measurements of a singlefrequency navigation receiver either require additional information (for example, Doppler measurements), or operate only in differential mode, or can only detect large cycle slips. The purpose of the research is the development of algorithms for detecting small cycle slips in carrier-phase measurements of single-frequency receivers without using additional information. We use methods of filtering of the trend in the carrier-phase measurements using polynomial or adaptive bases, as well as modified sparse recovery algorithms to estimate cycle slips in the difference between code and carrier-phase measurements. The algorithm which is used to search cycle slips in carrier-phase measurements depends on the quality of the reference oscillator of the navigation receiver. For receivers with high-stability reference oscillators (e.g. active hydrogen maser), one can use polynomial filtering of the trend, the filtering result directly detects discontinuities in carrier-phase measurements with a probability close to unity. For navigation receivers with low-stability reference oscillators (quartz reference oscillators), a modified algorithm for minimization of the total variation with filtering of the trend applied to the difference between the code and carrier-phase single-frequency measurements detects discontinuities in 1 cycle slip against the background of the noise component of comparable magnitude with a probability of 0.8. The results may be applied in navigation systems with single-frequency receivers with low stability reference oscillators, as well as in a posteriori processing of receivers’ measurements to correct carrier-phase measurements on the preprocessing stage.

Pustoshilov A. S., Tsarev S. P. Detecting cycle slips in carrier-phase measurements of single frequency navigation receivers with different instabilities of reference oscillators. Ural Radio Engineering Journal. 2021;5(2):144–161. DOI: 10.15826/urej.2021.5.2.004.

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