Benefiting from multi-constellation Global Navigation Satellite Systems (GNSS), more and more visible satellites can be used to improve user positioning performance. However, due to limited tracking receiver channels and power consumption, and other issues, it may be not possible, or desirable, to use all satellites in view for positioning. The optimal subset is generally selected from all possible satellite combinations to minimize either Geometric Dilution of Precision (GDOP) or weighted GDOP (WGDOP). However, this brute force approach is difficult to implement in real-time applications due to the time- and power-consuming calculation of the DOP values. As an alternative to a brute force satellite selection procedure, the authors propose an end-to-end deep learning network for satellite selection based on the PointNet and VoxelNet networks. The satellite selection is converted to a satellite segmentation problem, with specified input channel for each satellite and two class labels, one for selected satellites and the other for those not selected. The aim of the satellite segmentation is that a fixed number of satellites with the minimum GDOP/WGDOP value can be segmented from any feeding order of input satellites. To validate the proposed satellite segmentation network, training and test data from 220 IGS stations tracking GPS and GLONASS satellites were used. The segmentation performance using different architectures and representations of input channels, including receiver-to-satellite unit vector and elevation and azimuth, were compared. It was found that the input channel with elevation and azimuth can achieve better performance than using the receiver-to-satellite unit vector, and an architecture with stacked feature encoding (FE) layers has better satellite segmentation performance than one without stacked FE layers. In addition, the models with GDOP and WGDOP criteria for selecting 9 and 12 satellites were trained. It was demonstrated that the satellite segmentation network was about 90 times faster than using the brute force approach. Furthermore, all the trained models can effectively select the satellites making the most contribution to the desired GDOP/WGDOP value. Approximately 99% of the tests had GDOP and WGDOP value differences smaller than 0.03 and 0.2, respectively, between the predicted subset and the optimal subset.

Satellite selection with an end-to-end deep learning network

In this paper, a novel method for selecting a navigation satellite subset for a global positioning system (GPS) based on a genetic algorithm is presented. This approach is based on minimizing the factors in the geometric dilution of precision (GDOP) using a modified genetic algorithm (MGA) with an elite conservation strategy, adaptive selection, adaptive mutation, and a hybrid genetic algorithm that can select a subset of the satellites represented by specific numbers in the interval (4 ∼ n) while maintaining position accuracy. A comprehensive simulation demonstrates that the MGA-based satellite selection method effectively selects the correct number of optimal satellite subsets using receiver autonomous integrity monitoring (RAIM) or fault detection and exclusion (FDE). This method is more adaptable and flexible for GPS receivers, particularly for those used in handset equipment and mobile phones.

/pdf/a-novel-method-for-optimum-global-positioning-system-4o27zjeufc.pdf

A Novel Method for Optimum Global Positioning System Satellite Selection Based on a Modified Genetic Algorithm.

This paper is intended to provide an operator's view of the impact of GPS on the air transport industry. The discussion centres on use of GPS for the en-route, oceanic, terminal area and precision approach phases of flight. In summary the author suggests the following: (i) Inefficient use of airspace is costing the airlines a huge amount of money. However, GPS is not a pre-requisite of a move towards more efficient use of that airspace, although it will be required as part of the eventual CNS/ATM package. In the near term, better usage of current equipment such as IRS and DME, together with the introduction of ADS can provide the required level of accuracy for reduced separation in en-route and oceanic airspace. (ii) There is a real need to provide navigation for non-precision approach worldwide, independent of ground-based infrastructure. This is the area in which GPS can provide the most immediate improvement to safety. (iii) There are still a large number of questions hanging over GPS for precision approach. This leads the author to believe that it will not be capable of replacing ILS for the more critical Cat 2 and 3 applications quickly enough to avoid the loss of these capabilities in some critical locations. For this reason, it is postulated that MLS will be required in Europe, at least. Even if MLS is not required, there will still need to be a means of dealing with the transition away from ILS and for this reason the concept of a multi-mode receiver has been developed.

/pdf/the-journal-of-navigation-1r993e7lja.pdf

The Journal of Navigation

GPS receivers convert the measured pseudoranges from the visible GPS satellites into an estimate of the position and clock offset of the receiver. For various reasons receivers might only track and process a subset of the visible satellites. It would be desired, of course, to use the best subset.

In general selecting the best subset is a combinatorics problem; selecting m objects from a choice of n allows for n m potential subsets. And since the GDOP performance criterion is nonlinear and non-separable, finding the best subset is a brute force procedure; hence, a number of authors have described sub-optimal algorithms for choosing satellites.

This paper revisits this problem, especially in the context of multiple GNSS constellations, for the GDOP and PDOP criteria. Included are a discussion of optimum constellations (based upon parallel work of these authors on achievable lower bounds to GDOP and PDOP), musings on how the non-separableness of DOP makes it impossible to rank order the satellites, and a review/discussion of subset selection algorithms. Our long term goal is the development of better selection algorithms for multi-constellation GNSS.

/pdf/multi-constellation-gnss-new-bounds-on-dop-and-a-related-3qo24ltl02.pdf

Multi-Constellation GNSS: New Bounds on DOP and a Related Satellite Selection Process

The number of feature points on the surface of a non-cooperative target satellite used for monocular vision-based relative navigation affects the onboard computational load. A feature point selection method called the quasi-optimal method is proposed to select a subset of feature points with a good geometric distribution. This method, with the assumption that all of the feature points are in a plane and have the same variance, is based on the fact that the scattered feature points can provide higher accuracy than that of them grouped together. The cost is defined as a function of the angle between two unit vectors from the projection center to feature points. The redundancy of a feature point is calculated by summing all costs associated with it. Firstly, the feature point with the most redundant information is removed. Then, redundancies are calculated again with the second feature point removed. The procedures above are repeated until the desired number of feature points is reached. Dilution of precision (DOP) represents the mapping relation between the observation variance and the estimated variance. In this paper, the DOP concept is used in a vision-based navigation system to verify the performance of the quasi-optimal method. Simulation results demonstrate the feasibility of calculating the relative position and attitude by using a subset of feature points with a good geometric distribution. It also shows that the feature points selected by the quasi-optimal method can provide a high accuracy with low computation time.

https://www.mdpi.com/1424-8220/18/3/854/pdf

A Non-Cooperative Satellite Feature Point Selection Method for Vision-Based Navigation System

This paper presents a recursive quasi-optimal satellite
selection algorithm for future GNSS receivers to enhance
positioning accuracy and robustness with limited
resources. For the next decade, new systems, together
with existing systems, will provide as much as 40 visible
satellites with 160 multi-frequency signals. Any receiver
targeting all in-view GNSS signals with fewer channels
will need to choose a subset of satellites to be tracked.
This is essential for low cost commercial receivers where
hardware channels and navigation computer real-time
processing capability are limited (hardware/software
limitations, complexity of certification, etc.). For
example, in order to choose 32 satellites out of 40,
traditional algorithms will need more than 50 billion
Floating point Operations (FLOPs), which is a huge load
for current embedded processors. The algorithm presented
in this paper provides quasi-optimal geometry from any
combination of signal sources, such as GNSS satellites,
space or ground-based augmentation systems, and local
constellations. In contrast with the true optimal algorithm,
the recursive quasi-optimal algorithm requires a
drastically lower computational load. By incorporating
various weighting factors, this algorithm can account for
User Equivalent Range Error (UERE) when optimizing
DOP. Furthermore, when satellites are temporarily
blocked, the algorithm provides a list of next-best
replacement satellites as a by-product. Receiver
Autonomous Integrity Monitoring (RAIM) constraints
can also be applied to this algorithm. All these unique
features will enhance the robustness and overall accuracy
of GNSS receivers. These advantages are unique
compared to other quasi-optimal technique of equivalent
computational burden.

/pdf/a-recursive-quasi-optimal-fast-satellite-selection-method-4w6im4kdmz.pdf

A recursive quasi-optimal fast satellite selection method for GNSS receivers

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A recursive quasi-optimal fast satellite selection method for GNSS receivers