TOA-based direct localization in shallow water multipath environments: CRLB analysis and optimal sensor deployment

Abstract

Existing research explores the optimal sensing deployment in line-of-sight conditions, leveraging Cramér-Rao Lower Bound (CRLB) for optimization analysis. However, determining an optimal sensing deployment for direct localization in shallow water, characterized by distinctive multipath effects, poses a more significant challenge. This paper studies the optimal sensor deployment for direct localization grounded on the Time of Arrival (TOA) in a shallow water multipath environment. To address this problem, an initial derivation of the CRLB for accurate source localization is conducted, bearing in mind a multipath signal loss model. Subsequently, an optimization problem is articulated to minimize the trace of CRLB while adhering to the angular and range constraints to ascertain optimal sensor placement. Two necessary conditions for the objective function to attain a theoretical minimum are drawn out to find the closed-form solution. Nevertheless, it is impractical to satisfy these conditions concurrently under multipath circumstances. To swiftly attain the (sub-)optimal solution, an improved Particle Swarm Optimization (IPSO) algorithm is proposed, employing the previously derived conditions to initialize and update the inertia weights. Extensive simulation results based on the BELLHOP toolbox corroborate the theoretical analysis and the superior performance of the suggested sensor deployment scheme.