A Robust Position Estimator Using Bayesian Sparse Prior Against GNSS MP/NLOS Outliers

In urban environments, frequent multipath (MP) and non-line-of-sight (NLOS) occurrences introduce significant measurement outliers, posing challenges for accurate and robust positioning via global navigation satellite system (GNSS). This paper proposes a robust position estimator that capitalizes on the fact that MP/NLOS typically affect only a subset of satellites, leading to sparsity of the unknown MP/NLOS bias vector. The method employs real-time estimation and correction of the MP/NLOS bias vector from a Bayesian perspective, leveraging a kinematic model, measurement quality, and sparsity. Initially, the augmented linear representation of the extended Kalman filter (EKF) is used to transform the mixed dense-sparse problem into a standard Bayesian sparse regression form through a subspace projection technique. Subsequently, a reweighting scheme is developed to assess the likelihood of individual elements in the bias vector being zero, and a horseshoe prior is applied to represent their sparsity. Finally, using Bayes’ rule, the maximum a posteriori (MAP) estimation for the bias vector is formulated, and non-convex optimization is solved via local linear approximation (LLA) to quickly obtain the sparse solution for bias correcting and robust positioning. Experimental results on a typical urban environmental dataset demonstrate that the proposed method effectively mitigates the impact of MP/NLOS outliers, reducing root mean square (RMS) value of positioning errors by 78.14%, 75.46%, and 85.09% in the east, north, and vertical directions, respectively, compared to the classical EKF positioning method.