Detecting Cycle Slips in Carrier-Phase Measurements of Single Frequency Navigation Receivers with Different Instabilities of Reference Oscillators

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.

Polynomial Filtering Algorithm Applied to Navigation Data Processing under Quadratic Nonlinearities in System and Measurement Equations. Part 1. Description and Comparison with Kalman Type Algorithms

The paper considers the filtering problems solved in navigation data processing under quadratic nonlinearities both in system and measurement equations. A Kalman type recursive algorithm is proposed, where the predicted estimate and gain at each step are calculated based on the assumption on the Gaussian posterior proba-bility density function of the estimated vector at the previous step and minimization of estimation error covariance matrix using a linear procedure with respect to the current measurement. The similarities between this algorithm and other Kalman type algorithms such as extended and secondorder Kalman filters are discussed. The procedure for estimating the performance and comparing the algorithms is presented.