Sparsity-Driven Robust Passive Elliptic Positioning

With the recent accelerated advancements in multistatic sensing and localization technologies, elliptic positioning (EP), aimed at locating a signal-reflecting target based on bistatic ranges (BRs), has captured the interest of many researchers in the area. An expanded scenario of EP, termed passive EP (PEP), emerges when the transmitter position is no longer assumed known, but the direct transmitter-to-receiver ranges are available alongside BRs. This contribution studies robust PEP (RPEP) under anomalous range measurements caused by practical operational conditions. To handle outliers, we adopt the concept of sparse representation by exploiting the rare and infrequent characteristics that the deviant range readings usually display and leveraging the ℓ₀-norm to promote sparsity. We then develop a customized projected gradient descent algorithm to tackle the ℓ₀-constrained ℓ₂-minimization problem arising from such a sparsity-driven RPEP formulation. As a theoretical result, we rigorously establish the convergence of the iterates produced to a critical point. Additionally, a two-layer exploratory mechanism is included to more effectively navigate the nonconvex optimization landscape. In the simulations, our proposed technique demonstrates its performance reaching the Cramér–Rao lower bound benchmark under Gaussian noise environments, and exhibits strong potential to outperform existing PEP and RPEP methods in terms of robustness when outliers are introduced.