Optimal Sensor Placement for Source Localization: A Unified ADMM Approach

Abstract

Source localization plays a key role in many applications including radar, wireless and underwater communications. Among various localization methods, the most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), Angle-Of-Arrival (AOA) and Received Signal Strength (RSS) based. Since the Cramér-Rao lower bounds (CRLB) of these methods depend on the sensor geometry explicitly, sensor placement becomes a crucial issue in source localization applications. In this paper, we consider finding the optimal sensor placements for the TOA, TDOA, AOA and RSS based localization scenarios. We first unify the three localization models by a generalized problem formulation based on the CRLB-related metric. Then a unified optimization framework for optimal sensor placement (UTMOST) is developed through the combination of the alternating direction method of multipliers (ADMM) and majorizationminimization (MM) techniques. Unlike the majority of the stateof-the-art works, the proposed UTMOST neither approximates the design criterion nor considers only uncorrelated noise in the measurements. It can readily adapt to to different design criteria (i.e. A, D and E-optimality) with slight modifications within the framework and yield the optimal sensor placements correspondingly. Extensive numerical experiments are performed to exhibit the efficacy and flexibility of the proposed framework.

Optimal Sensor Placement for Hybrid Source Localization Using Fused TOA-RSS-AOA Measurements

“…Hybrid measurements Correlated noise Non-uniform noise variances Optimality criteria [28] No No No A [22], [24], [27], [29], [30] No No No D [34]- [38] No No Yes A [31]- [33] No No Yes D [40] No Yes Yes A, D and E [39], [41] Yes No No A, D [42] Yes No No D [23], [43] Yes No No A Proposed Algorithm Yes Yes Yes A, D and E optimality criteria. Section IV gives the details of numerical simulations and the results.…”

“…Similar to the derivation of C TOA , the CRLB for RSS and AOA can be derived, and their FIM are given by [40]:…”

“…b) Update Φ using Algorithm 2 (for Aand D-optimal design) and Algorithm 3 (for E-optimal design). c) Compute Z. d) Solve (40) to obtain J t+1 . e) If J t+1 − J t F / J t F < ǫ, stop and return J t+1 .…”

“…The authors in [39] derived the optimal sensing directions for target localization for different types of measurements while considering the uncertainty in the prior knowledge of the target position. A unified framework for designing optimal sensor orientations based on A, D and E optimal criteria was developed for different types of measurement models in [40].…”

“…We would like to note that the ADMM based approach proposed in [40] is not extendable for hybrid source localiza-tion model, as extending the framework in [40] to handle the hybrid CRLB is not straightforward due to the presence of additional rotation matrix in the FIM of the AOA model. On the other hand, the proposed algorithm can easily handle the design objective based on CRLB for the hybrid measurement model.…”