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

Поступила: 29.06.2021. Принята в печать: 12.07.2021.Received: 29.06.2021. Accepted: 12.07.2021.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.Использование фазовых измерений позволяет существенно повысить точность решения различных задач с использованием измерительной информации навигационных приемников. Одна из проблем при использовании фазовых измерений – разрывы (скачки) в измерениях. Существующие алгоритмы поиска и компенсации разрывов в фазовых измерениях одночастотного навигационного приемника либо требует дополнительную информацию (например, допплеровские измерения), либо работают только в дифференциальном режиме, либо могут определять только большие разрывы. Цель исследования – разработка алгоритмов обнаружения малых разрывов в фазовых измерениях одночастотных приемников без использования дополнительной информации. Применяются методы фильтрация медленноменяющегося тренда в фазовых измерениях приемника с использованием полиномиальных или адаптивных базисов, а также модифицированные алгоритмы sparse recovery для оценки разрывов в разности кодовых и фазовых измерений. Алгоритм, применяемый для поиска разрывов в фазовых измерениях, зависит от качества опорного генератора навигационного приемника. Для приемников с опорным генератором с высокой стабильностью (с водородным стандартом частоты) достаточно использование полиномиальной фильтрации медленноменяющегося тренда, что позволяет непосредственно обнаруживать разрывы в фазовых измерениях с вероятностью, близкой к единице. Для навигационных приемников с опорным генератором с низкой стабильностью (приемники на кварцевом стандарте частоты) применение модифицированного алгоритма минимизации полной вариации с фильтрацией тренда к разности кодовых и фазовых одночастотных измерений позволяет обнаружить разрывы в 1 цикл на фоне шумовой составляющей сопоставимой величины с вероятностью 0,8. Результаты могут быть применены при разработке навигационных систем с одночастотными приемниками с низкими требованиями к стабильности опорного генератора, а также при апостериорной обработке измерений для коррекции фазовых измерений на этапе предобработки.The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme No. FSRZ-2020-0011).Работа выполнена в рамках государственного задания Министерства науки и высшего образования Российской Федерации (код научной темы FSRZ-2020-0011)

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. 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.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