Multipath Mitigation in Global Navigation Satellite Systems Using a Bayesian Hierarchical Model with Bernoulli Laplacian Priors

Abstract

A new sparse estimation method was recently introduced in a previous work to correct biases due to multipath (MP) in GNSS measurements. The proposed strategy was based on the resolution of a LASSO problem constructed from the navigation equations using the reweighted-$\ell_1$ method. This strategy requires to adjust the regularization parameters balancing the data fidelity term and the involved regularizations. This paper introduces a new Bayesian estimation method allowing the MP biases and the unknown model parameters and hyperparameters to be estimated directly from the GNSS measurements. The proposed method is based on Bernoulli Laplacian priors, promoting sparsity of MP biases