SATELLITE SELECTION ALGORITHMS FOR POSITIONING, NAVIGATION AND TIMING USERS

Проведен обзор методов и алгоритмов формирования рабочего созвездия навигационных космических аппаратов при решении задач определения местоположения потребителя ГНСС. Появление новых орбитальных группировок и развитие прошлых поколений глобальных навигационных спутниковых систем (ГНСС) способствует увеличению как количества навигационных аппаратов, так и навигационных радиосигналов, излучаемых каждым спутником, в связи с чем решение проблемы выбора навигационных аппаратов является важной составляющей навигационной задачи. Рассмотрены исследования, посвященные типовым алгоритмам формирования рабочего созвездия, а также современным алгоритмам, построенным с привлечением элементов теории машинного обучения. Представлена связь ошибок определения координат потребителя, погрешностей определения псевдодальностей и пространственного расположения навигационных аппаратов и потребителя. Среди рассмотренных алгоритмов выделены три направления исследований: 1) нацеленных на поиск оптимального рабочего созвездия, обеспечивающего минимальную оценку выбранного геометрического фактора снижения точности; 2) нацеленных на поиск квазиоптимальных рабочих созвездий с целью уменьшения вычислительной сложности алгоритма ввиду большого количества видимых спутников; 3) позволяющих одновременно работать в совмещенном режиме по нескольким ГНСС. Приводятся особенности реализаций алгоритмов, их преимущества и недостатки. В заключении приведены рекомендации по изменению подхода к оценке эффективности алгоритмов, а также делается вывод о необходимости учета как геометрического расположения космических аппаратов, так и погрешности определения псевдодальности при выборе космического аппарата в рабочее созвездие The article provides an overview of methods and algorithms for forming a satellite constellation as a part of the navigation problem for the positioning, navigation and timing service. The emergence of new orbital constellations and the development of past GNSS generations increase both the number of navigation satellites and radio signals emitted by every satellite, and therefore the proper solution of satellite selection problem is an important component of the positioning, navigation and timing service. We considered the works devoted to typical algorithms of working constellation formation, as well as to modern algorithms built with the use of machine-learning theory elements. We present the relationship between user coordinates errors, pseudorange errors and the influence of spatial location of satellites and the user. Three directions of researche among reviewed algorithms are outlined: 1) finding the best satellite constellation that provides the minimum geometric dilution of precision; 2) finding quasi-optimal satellite constellation in order to reduce the computational complexity of the algorithm due to the large number of visible satellites; 3) possibility to work in a combined mode using radio signals of multiple GNSS simultaneously. The article presents the features of the algorithms' implementations, their advantages and disadvantages. The conclusion presents the recommendations to change the approach to assessing the performance of the algorithms, and concludes that it is necessary to take into account both the satellite geometric configuration, and pseudorange errors when satellite constellation is being formed

Fast satellite selection algorithm for GNSS multisystems based on the Sherman-Morrison formula

The usage efficiency of GNSS multisystem observation data can be greatly improved by applying rational satellite selection algorithms. Such algorithms can also improve the real-time reliability and accuracy of navigation. By combining the Sherman-Morrison formula and singular value decomposition (SVD), a smaller geometric dilution of precision (GDOP) value method with increasing number of visible satellites is proposed. Moreover, by combining this smaller GDOP value method with the maximum volume of tetrahedron method, a new rapid satellite selection algorithm based on the Sherman-Morrison formula for GNSS multisystems is proposed. The basic idea of the algorithm is as follows: first, the maximum volume of tetrahedron method is used to obtain four initial reference satellites; then, the visible satellites are co-selected by using the smaller GDOP value method to reduce the GDOP value and improve the accuracy of the overall algorithm. By setting a reasonable precise threshold, the satellite selection algorithm can be autonomously run without intervention. The experimental results based on measured data indicate that (1) the GDOP values in most epochs over the whole period obtained with the satellite selection algorithm based on the Sherman-Morrison formula are less than 2. Furthermore, compared with the optimal estimation results of the GDOP for all visible satellites, the results of this algorithm can meet the requirements of high-precision navigation and positioning when the corresponding number of selected satellites reaches 13. Moreover, as the number of selected satellites continues to increase, the calculation time increases, but the decrease in the GDOP value is not obvious. (2) The algorithm includes an adaptive function based on the end indicator of the satellite selection calculation and the reasonable threshold. When the reasonable precise threshold is set to 0.01, the selected number of satellites in most epochs is less than 13. Furthermore, when the number of selected satellites reaches 13, the GDOP value is less than 2, and the corresponding probability is 93.54%. These findings verify that the proposed satellite selection algorithm based on the Sherman-Morrison formula provides autonomous functionality and high-accuracy results.

A satellite selection algorithm based on adaptive simulated annealing particle swarm optimization for the BeiDou Navigation Satellite System/Global Positioning System receiver

In this article, we propose a new particle swarm optimization–based satellite selection algorithm for BeiDou Navigation Satellite System/Global Positioning System receiver, which aims to reduce the computational complexity of receivers under the multi-constellation Global Navigation Satellite System. The influences of the key parameters of the algorithm—such as the inertia weighting factor, acceleration coefficient, and population size—on the performance of the particle swarm optimization satellite selection algorithm are discussed herein. In addition, the algorithm is improved using the adaptive simulated annealing particle swarm optimization (ASAPSO) approach to prevent converging to a local minimum. The new approach takes advantage of the adaptive adjustment of the evolutionary parameters and particle velocity; thus, it improves the ability of the approach to escape local extrema. The theoretical derivations are discussed. The experiments are validated using 3-h real Global Navigation Satellite System observation data. The results show that in terms of the accuracy of the geometric dilution of precision error of the algorithm, the ASAPSO satellite selection algorithm is about 86% smaller than the greedy satellite selection algorithm, and about 80% is less than the geometric dilution of precision error of the particle swarm optimization satellite selection algorithm. In addition, the speed of selecting the minimum geometric dilution of precision value of satellites based on the ASAPSO algorithm is better than that of the traditional traversal algorithm and particle swarm optimization algorithm. Therefore, the proposed ASAPSO algorithm reduces the satellite selection time and improves the geometric dilution of precision using the selected satellite algorithm.

Research on Task Satellite Selection Method for Space Object Detection LEO Constellation Based on Observation Window Projection Analysis

Aiming at the task planning and scheduling problem of space object detection LEO constellation (SODLC) for detecting space objects in deep space background, a method of SODLC task satellite selection based on observation window projection analysis is proposed. This method projects the spatial relative relationships of the SODLC observation blind zone, observation range, and the initial spatial position of the objects onto the surface of the earth for detectable analysis of satellites and targets and binds the dynamic observation conditions to the satellite trajectory after projection calculation of the visible relationship between target changes. On this basis, combined with the features of SODLC with high orbital symmetry, the task satellite selection is divided into two steps: orbit plane selection and task satellite selection. The orbit planes are selected based on the longitude range of the ascending node with the geographic location of the targets, and the task satellites are selected according to the relative motion relationship between the satellites and the targets together with the constraints of observable conditions. The selection method simplifies the calculation process of scheduling and selecting task satellites. Simulation analysis prove the method has better task satellite selection efficiency. The method has high practical value for task planning and scheduling for event-driven SODLC.

Research on Satellite Selection Strategy for Receiver Autonomous Integrity Monitoring Applications

Satellite selection is an effective way to overcome the challenges for the processing capability and channel limitation of the receivers due to superabundant satellites in view. The satellite selection strategies have been widely investigated to construct the subset with high accuracy but deserve further studies when applied to safety-critical applications such as the receiver autonomous integrity monitoring (RAIM) technique. In this study, the impacts of subset size on the accuracy and integrity of the subset and computation load are analyzed at first to confirm the importance of the satellite selection strategy for the RAIM process. Then the integrated performance impact of a single satellite on the current subset is evaluated according to the performance requirement of the flight phase. Subsequently, a performance-requirement-driven fast satellite selection algorithm is proposed based on the impact evaluation to construct a relatively small subset that satisfies the accuracy and integrity requirements. Comparison simulations show that the proposed algorithm can keep similar accuracy and better integrity performances than the geometric algorithm and the downdate algorithm when the subset size is fixed to 12, and can achieve an average 1.0 to 2.0 satellites smaller subset in the Lateral Navigation (LNAV) and approach procedures with vertical guidance (APV-I) horizontal requirement trial. Thus, it is suitable for real-time RAIM applications and low-cost navigation devices.