Sparse Parameter-Assisted Bias-Robust Localization Based on Concave-Convex Programming Without Priors

Ranging bias mitigation is a critical technique for improving localization accuracy, and it becomes especially challenging when prior state information is unavailable. In this paper, we propose a robust estimator that leverages the sparsity of measurement biases to address the lack of prior information and achieves position estimation based on convex-concave programming (CCP). Specifically, we introduce an auxiliary variance amplification parameter to identify measurement anomalies and construct the optimization problem based on maximum likelihood estimation (MLE), which can be equivalently transformed into an ℓ1-regularized form. To address the non-convexity challenge, the original problem is transformed into difference-of-convex-functions (DC) programming using second-order cone relaxation (SOCR) and semidefinite relaxation (SDR), and solved by CCP. On this basis, we propose a joint SOCR-CCP and SDR-CCP (JSSC) algorithm that leverages the respective advantages of SOCR and SDR. The Rao test is incorporated into this algorithm to reduce complexity and enhance stability. Finally, numerical results demonstrate that the proposed methods outperform various state-of-the-art competing methods.