Incrementally Learned Mixture Models for GNSS Localization GNSS localization is an important part of todayu0027s autonomous systems, although it suffers from nonGaussian errors caused by nonlineofsight effects. Recent methods are able to mitigate these effects by including the corresponding distributions in the sensor fusion algorithm. However, these approaches require prior knowledge about the sensoru0027s distribution, which is often not available. We introduce a novel sensor fusion algorithm based on variational Bayesian inference, that is able to approximate the true distribution with a Gaussian mixture model and to learn its parametrization online. The proposed Incremental Variational Mixture algorithm automatically adapts the number of mixture components to the complexity of the measurementu0027s error distribution. We compare the proposed algorithm against current stateoftheart approaches using a collection of open access real world datasets and demonstrate its superior localization accuracy.

Helmert Variance Component Estimation for MultiGNSS Relative Positioning The Multiconstellation Global Navigation Satellite System (MultiGNSS) has become the standard implementation of high accuracy positioning and navigation applications. It is well known that the noise of code and phase measurements depend on GNSS constellation. Then, Helmert variance component estimation (HVCE) is usually used to adjust the contributions of different GNSS constellations by determining their individual variances of unit weight. However, HVCE requires a heavy computation load. In this study, the HVCE posterior weighting was employed to carry out a kinematic relative MultiGNSS positioning experiment with six shortbaselines from day of year (DoY) 171 to 200 in 2019. As a result, the HVCE posterior weighting strategy improved MultiGNSS positioning accuracy by 20.5%, 15.7% and 13.2% in eastnorthup (ENU) components, compared to an elevationdependent (ED) priori weighting strategy. We observed that the weight proportion of both code and phase observations for each GNSS constellation were consistent during the entire 30 days, which indicates that the weight proportions of both code and phase observations are stable over a long period of time. It was also found that the quality of a phase observation is almost equivalent in each baseline and GNSS constellation, whereas that of a code observation is different. In order to reduce the time consumption of the HVCE method without sacrificing positioning accuracy, the stable variances of unit weights of both phase and code observations obtained over 30 days were averaged and then frozen as a priori information in the positioning experiment. The result demonstrated similar ENU improvements of 20.0%, 14.1% and 11.1% with respect to the ED method but saving 88% of the computation time of the HCVE strategy. Our study concludes with the observations that the frozen variances of unit weight (FVUW) could be applied to the positioning experiment for the next 30 days, that is, from DoY 201 to 230 in 2019, improving the positioning ENU accuracy of the ED method by 18.1%, 13.2% and 10.6%, indicating the effectiveness of the FVUW.