Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations

Abstract

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning

“…In most studies, unit weight variances are considered for different types of equations. To define realistic (co)variance components for each system, the Least-Squares Variance Component Estimation (LS-VCE) method can be used [ 20 , 60 , 61 ]. If one considers the covariance matrix as a linear combination of q (co)variance components, then: where is the known part of the variance matrix, is an unknown (co)variance components, and is known symmetric and positive definite cofactor matrices.…”

“…Using the estimated (co)variance matrix in the least-squares adjustment allows one to obtain a realistic precision of the unknowns. Due to the large size of the A matrix, as in [ 61 ], the multivariate linear model was used to reduce the computational load and memory usage for VCE. In other words, the model is suggested for a number of successive epochs in each group.…”

GNSS/IMU Sensor Fusion Performance Comparison of a Car Localization in Urban Environment Using Extended Kalman Filter

“…With this rapid development of GNSS, multi-GNSS and multi-frequency Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) technologies have IOP Publishing doi:10.1088/1755-1315/1127/1/012006 2 been extensively researched to enable high-precision positioning [2,3]. Positioning accuracy in RTK mode can also be improved to centimeter levels, for example by using dual antennas with baseline constraint vector [4], utlilize multi-station RTK and rate of TEC correction [5], or enhance strategy to determine stochastic model of observation [6]. Besides that, there has been a solution to reduce the cost of GNSS observation through the increasing availability of low-cost GNSS in recent years.…”

Analysis of Different Weighting Functions of Observations for GPS and Galileo Precise Point Positioning Performance

“…There are different variations of the VCE method: minimum norm quadratic unbiased estimator (MINQUE), the best invariant quadratic unbiased estimator (BIQUE), the least-squares variance component estimator (LS-VCE), the restricted maximum likelihood estimator (REML) or the Bayesian approach to VCE [23]. One of the more commonly used in GNSS measurement analysis is the LS-VCE methods [24][25][26][27].…”