Non-Parametric GNSS Integer Ambiguity Estimation via Positional Likelihood Field Marginalization

Abstract

In this paper, we propose a non-parametric method for estimating the posterior distribution of global positioning satellite systems (GNSS) integer ambiguity. It is difficult to estimate the posterior probability of discrete integer ambiguities directly from carrier phase observations due to the unclear domain definition. We thus introduce a positional likelihood field that accumulates the ambiguity function method values in the position space and then estimate the integer ambiguity distributions by marginalizing the likelihood over the entire position. Defining the positional likelihood field in the position space facilitates carrier phase likelihood accumulation. To correctly estimate the posterior distribution, however, a sufficient density of samples is required, which results in a large computational cost. The proposed method enables large-scale sampling by taking advantage of GPU parallel processing. Experimental results demonstrate that the proposed method enables accurate and robust estimation of integer ambiguity distributions, contributing to improved centimeter-level position estimation accuracy. In addition, the histograms provide quantitative evidence of events in urban environments where integer ambiguity is not uniquely determined.