Efficiency research of signal recovery algorithms with long gaps and rare arrival of measurements

Abstract

Subject of Research. Efficiency study of cameral signal recovery algorithms is carried out in the presence of single long gaps and rare arrival of measurements. Quantitative comparison of the algorithms is performed by modeling and cameral processing of satellite navigation receiver real solutions. The standard error is an algorithm measure of efficiency. Method. The algorithm is considered based on a quadratic model taking into account constraints on the signal size and its derivative. The algorithm is known from the literature, however, it is used for the first time in satellite navigation problems. Moreover, comparison is made with the other two algorithms: quadratic approximation without regard to constraints and linear interpolation. Main Results. After analyzing the results, the following recommendations have been developed on the use of recovery algorithms in order to achieve the minimum mean square error of recovery. It is established that the quadratic approximation with constraints is the best of the considered algorithms in terms of accuracy; however, when recovering the signal during the long-term measurement absence at the beginning and at the end of the gap, it is better to use linear interpolation. In order to achieve the minimum standard error in the central part of the gap, it is recommended to use the algorithm with constraints and break down a fragment of the processed measurement implementation so that no more than one polynomial interval junction of the restored signal is located on the measurement absence section. For short measurement intervals to the left and to the right of the gap, the best option is to split the implementation fragment into 2 intervals. In case of the signal restoration under conditions of rarely received measurements, it is advisable to choose the interval duration of the polynomial representation less than the period of measurement discreteness. Practical Relevance. The application of the developed algorithms can improve the positioning accuracy for the users of global-positioning satellite systems, however, their application area may be more extensive and include post-processing of field measurements in geodesy and mapping tasks.