Best Integer Equivariant Estimation Based on Unsupervised Machine Learning for GNSS Precise Positioning and Navigation in Complex Environments

In Global Navigation Satellite System (GNSS) precise positioning and navigation, integer ambiguity resolution is a prerequisite. However, how to correctly resolve integer ambiguities, especially in complex environments, is a tricky problem. In this article, an integrated approach for GNSS precise positioning and navigation mainly including the best integer equivariant (BIE) estimation based on unsupervised machine learning (ML) is proposed. Specifically, considering the unsupervised ML strategy, the K-means++ algorithm is applied to the BIE estimation, where the ambiguity candidates are selected by the K-means++ algorithm. Then, by combing the float, fixed, and ML BIE solutions, an integrated precise positioning and navigation approach is given. By conducting two field experiments in challenging conditions, the positioning accuracy and reliability are improved after using the ML BIE solutions. Specifically, in the monitoring experiment, centimeter-level and even millimeter-level accuracy can be obtained. According to the results of the vehicle experiment, the positioning reliability is improved to a great extent.