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

A Geometric Layout Method for Synchronous Pseudolite Positioning Systems Based on a New Weighted HDOP

The positioning accuracy of a ground-based system in an indoor environment is closely related to the geometric configuration of pseudolites. This paper presents a simple closed-form equation for computing the weighted horizontal dilution of precision (WHDOP) with four eigenvalues, which can reduce the amount of calculation. By comparing the result of WHDOP with traditional matrix inversion operation, the effectiveness of WHDOP of the proposed simple calculation method is analyzed. The proposed WHDOP has a linear relationship with the actual static positioning result error in an indoor environment proved by the Pearson analysis method. Twenty positioning points are randomly selected, and the positioning variance and WHDOP of each positioning point have been calculated. The correlation coefficient of WHDOP and the positioning variance is calculated to be 0.82. A pseudolite system layout method based on a simulated annealing algorithm is proposed by using WHDOP, instead of Geometric dilution of precision (GDOP). In this paper, the constraints of time synchronization are discussed. In wireless connection system, the distance between master station and slave station should be kept within a certain range. Specifically, for a given indoor scene, many positioning target points are randomly generated in this area by using the Monte Carlo method. The mean WHDOP value of all positioning points corresponding to the synchronous pseudolite layout is used as the objective function. The results of brute force search are compared with the method, which proves the accuracy of the new algorithm.

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.

On-line Optimal Ranging Sensor Deployment for Robotic Exploration

<div>Navigation in an unknown environment without any preexisting positioning infrastructure has always been hard for mobile robots. This paper presents a self-deployable ultra wideband UWB infrastructure by mobile agents, that permits a dynamic placement and runtime extension of UWB anchors infrastructure while the robot explores the new environment. We provide a detailed analysis of the uncertainty of the positioning system while the UWB infrastructure grows. Moreover, we developed a genetic algorithm that minimizes the deployment of new anchors, saving energy and resources on the mobile robot and maximizing the time of the mission. Although the presented approach is general for any class of mobile system, we run simulations and experiments with indoor drones. Results demonstrate that maximum positioning uncertainty is always controlled under the user's threshold, using the Geometric Dilution of Precision (GDoP).</div>

On-line Optimal Ranging Sensor Deployment for Robotic Exploration

<div>Navigation in an unknown environment without any preexisting positioning infrastructure has always been hard for mobile robots. This paper presents a self-deployable ultra wideband UWB infrastructure by mobile agents, that permits a dynamic placement and runtime extension of UWB anchors infrastructure while the robot explores the new environment. We provide a detailed analysis of the uncertainty of the positioning system while the UWB infrastructure grows. Moreover, we developed a genetic algorithm that minimizes the deployment of new anchors, saving energy and resources on the mobile robot and maximizing the time of the mission. Although the presented approach is general for any class of mobile system, we run simulations and experiments with indoor drones. Results demonstrate that maximum positioning uncertainty is always controlled under the user's threshold, using the Geometric Dilution of Precision (GDoP).</div>

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.

TDMA Datalink Cooperative Navigation Algorithm Based on INS/JTIDS/BA

Position information is very important tactical information in large-scale joint military operations. Positioning with datalink time of arrival (TOA) measurements is a primary choice when a global navigation satellite system (GNSS) is not available, datalink members are randomly distributed, only estimates with measurements between navigation sources and positioning users may lead to a unsatisfactory accuracy, and positioning geometry of altitude is poor. A time division multiple address (TDMA) datalink cooperative navigation algorithm based on INS/JTIDS/BA is presented in this paper. The proposed algorithm is used to revise the errors of the inertial navigation system (INS), clock bias is calibrated via round-trip timing (RTT), and altitude is located with height filter. The TDMA datalink cooperative navigation algorithm estimate errors are stated with general navigation measurements, cooperative navigation measurements, and predicted states. Weighted horizontal geometric dilution of precision (WHDOP) of the proposed algorithm and the effect of the cooperative measurements on positioning accuracy is analyzed in theory. We simulate a joint tactical information distribution system (JTIDS) network with multiple members to evaluate the performance of the proposed algorithm. The simulation results show that compared to an extended Kalman filter (EKF) that processes TOA measurements sequentially and a TDMA datalink navigation algorithm without cooperative measurements, the TDMA datalink cooperative navigation algorithm performs better.

Comparing Localization Performance of IEEE 802.11p and LTE-V V2I Communications

The future of transportation systems is going towards autonomous and assisted driving, aiming to reach full automation. There is huge focus on communication technologies expected to offer vehicular application services, of which most are location-based services. This paper provides a study on localization accuracy limits using vehicle-to-infrastructure communication channels provided by IEEE 802.11p and LTE-V, considering two different vehicular network designs. Real data measurements obtained on our highway testbed are used to model and simulate propagation channels, the position of base stations, and the route followed by the vehicle. Cramer–Rao lower bound, geometric dilution of precision, and least square error for time difference of arrival localization technique are investigated. Based on our analyses and findings, LTE-V outperforms IEEE 802.11p. However, it is apparent that providing larger signal bandwidth dedicated to localization, with network sites positioned at both sides of the highway, and considering the geometry between vehicle and network sites, improve vehicle localization accuracy.

Statistical models to provide meaningful information to GNSS users in the presence of ionospheric scintillation

Ionospheric scintillation is one of the most challenging problems in Global Navigation Satellite Systems (GNSS) positioning and navigation. Scintillation occurrence can not only lead to an increase in the probability of losing the GNSS signal lock but also reduce the precision of the pseudorange and carrier phase measurements, thus leading to positioning accuracy degradation. Statistical models developed to estimate the probability of loss of lock and Geometric Dilution of Precision normalized 3D positioning errors as a function of scintillation levels are presented. The models were developed following the statistical approach of nonlinear regression on data recorded by Ionospheric Scintillation Monitoring Receivers operational at high and low latitudes. The validation of the probability of loss of lock models indicated average correlation coefficient values above 0.7 and average Root Mean Squared Error (RMSE) values below 0.35. The validation of the positioning error models indicated average RMSE values below 10 cm. The good performance of the developed models indicates that these can provide GNSS users with information on the satellite loss of lock probability and the error in the 3D position under scintillation.