A Machine Learning Framework for Weighted Least Squares GNSS Positioning based on Activation Functions

Global Navigation Satellite Systems (GNSS) are widely used to provide position, velocity, and timing (PVT) information for various applications, including transportation, location-based communication services, and intelligent agriculture. In urban canyons, high-rise buildings and narrow streets can cause signal obstruction, non-line-of-sight (NLOS) reception, and multipath effects that introduce errors in GNSS pseudorange measurements. Although multi-constellations GNSS effectively increase the number of available satellites, the inclusion of degraded signals can lead to severe positioning errors. This study proposes a machine learning framework for the weighted least squares (WLS) algorithm incorporating activation functions to enhance positioning accuracy. Several signal quality indicators are employed as training features for ensemble learning algorithms to identify poor quality signals by providing quality scores. Then, activation functions are employed to transform the machine learning predicted scores to appropriate weights for WLS positioning. To evaluate the performance of our approach, experiments are conducted using real-world datasets from Hong Kong and Tokyo urban areas. Comparative analysis of activation functions reveals that sigmoid functions consistently yield the greatest improvements with different machine learning algorithms and GNSS constellation configurations. The proposed algorithm demonstrates substantial reductions in positioning errors for both single- and multiconstellation scenarios. Furthermore, our results indicate that the proposed algorithm exhibits strong geographical transferability. The proposed algorithm maintains comparable level of performance when trained on data from other regions with similar levels of urbanization.

An Introduction to Complex Random Tensors

This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning, and Control systems, the concepts of linear algebra combined with random variables have been indispensable tools. With the evolution of these subjects to multi-domain communication systems, multi-way signal processing, high dimensional data analysis, and multi-linear systems theory, there is a need to bring in multi-linear algebra equipped with the notion of random tensors. Also, since several such application areas deal with complex-valued entities, it is imperative to study this subject from a complex random tensor perspective, which is the focus of this paper. Using tools from multi-linear algebra, we characterize statistical properties of complex random tensors, both proper and improper, study various correlation structures, and fundamentals of tensor valued random processes. Furthermore, the asymptotic distribution of various tensor eigenvalue and singular value definitions is also considered, which is used for the study of spiked real tensor models that deals with recovery of low rank tensor signals perturbed by noise. This paper aims to provide an overview of the state of the art in random tensor theory of both complex and real valued tensors, for the purpose of enabling its application in engineering and applied science.