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

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.