GPS multipath and NLOS mitigation for relative positioning in urban environments

Multipath interference and non-line-of-sight (NLOS) reception are major error sources when using global navigation satellite system-based cooperative positioning (CP) in urban environments. In this paper, we develop a multipath and NLOS mitigation algorithm that significantly improves the relative positioning accuracy in urban environments, compared with the absolute positioning and conventional tight CP technique, respectively. In this proposed method, each receiver fuses the Global Positioning System (GPS) pseudorange and Doppler shift measurements, and the linear cooperative navigation observation model is formulated by considering the multipath and NLOS biases as additive sparse errors. We investigate a sparse estimation algorithm to solve the navigation problem and estimate the multipath and NLOS biases, with the weighting matrix designed as function of satellite carrier-to-noise density ratio and the regularization parameter selected by Bayesian information criterion. Based on a least absolute shrinkage and selection operator problem, an ℓ₁ regularization is introduced to enforce sparsity in the biases estimation model, which can be solved by the reweighted-ℓ₁ algorithm. The GPS measurements can be corrected by subtracting the estimated multipath and NLOS biases, and the relative positioning performance of proposed method is verified by analytical and experimental results.