LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.

Testing of Software for the Planning of a Linear Object GNSS Measurement Campaign under Simulated Conditions

The precision of a linear object measurement using satellite techniques is determined by the number and the relative position of the visible satellites by the receiver. The status of the visible constellation is described by the Dilution Of Precision (DOP). The obtained geometric coefficient values are dependent on many variables. When determining these values, field obstacles at the receiver location and satellite positions changing with time must be taken into account. Carrying out a series of surveys as part of a linear object Global Navigation Satellite System (GNSS) measurement campaign requires the optimisation problem to be solved. The manner of the inspection vehicle’s movement should be determined in such a way that the surveys are taken only within the pre-defined time frames and that the geometric coefficient values obtained at subsequent points of the route are as low as possible. The purpose of this article is to develop a software for the planning of a linear object GNSS measurement campaign to implemented in motion and taking into account the terrain model and its coverage. Additionally, it was determined how much the developed program improves DOP values on the planned route under simulated conditions. This software has no equivalent elsewhere in the world, as the current solutions for the planning of a GNSS measurement campaign, e.g., Trimble GNSS Planning, GNSS Mission Planning, or GPS Navigation Toolbox, allow the satellite constellation geometry to be analysed exclusively for specific coordinates and at a specific time. Analysis of the obtained simulation test results indicates that the campaign implementation in accordance with the pre-determined schedule significantly improves the quality of the recorded GNSS data. This is particularly noticeable when determining the position using the Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS) satellite constellations at the same time. During the tests conducted on the road along a three-kilometre-long route (tram loop) in Gdańsk Brzeźno, the average value of the obtained Position Dilution Of Precision (PDOP) decreased by 22.17% thanks to using the software to plan a linear object GNSS measurement campaign. The largest drop in the geometric coefficient values was noted for an area characterised by a very large number of field obstacles (trees with crowns and high buildings). Under these conditions, the PDOP value decreased by approx. 25%. In areas characterised by a small number of field obstacles (single trees in the vicinity of the track, clusters of trees and buildings located along the track), the changes in the PDOP were slightly smaller and amounted to several percent.

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.

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.

A Cost Function for the Uncertainty of Matching Point Distribution on Image Registration

Computing the homography matrix using the known matching points is a key step in computer vision for image registration. In practice, the number, accuracy, and distribution of the known matching points can affect the uncertainty of the homography matrix. This study mainly focuses on the effect of matching point distribution on image registration. First, horizontal dilution of precision (HDOP) is derived to measure the influence of the distribution of known points on fixed point position accuracy on the image. The quantization function, which is the average of the center points’ HDOP* of the overlapping region, is then constructed to measure the uncertainty of matching distribution. Finally, the experiments in the field of image registration are performed to verify the proposed function. We test the consistency of the relationship between the proposed function and the average of symmetric transfer errors. Consequently, the proposed function is appropriate for measuring the uncertainty of matching point distribution on image registration.