Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

Optimal Geometries for AOA Localization in the Bayesian Sense

This paper considers the optimal sensor placement problem for angle-of-arrival (AOA) target localization in the 2D plane with a Gaussian prior. Optimal sensor locations are analytically determined for a single AOA sensor using the D- and A-optimality criteria and an approximation of the Bayesian Fisher information matrix (BFIM). Optimal sensor placement is shown to align with the minor axis of the prior covariance error ellipse for both optimality criteria. The approximate BFIM is argued to be valid for a sufficiently small prior covariance compared with the target range. Optimal sensor placement results obtained for Bayesian target localization are extended to manoeuvring target tracking. For sensor trajectory optimization subject to turn-rate constraints, numerical search methods based on the D- and A-optimality criteria as well as a new closed-form projection algorithm that aims to achieve alignment with the minor axis of the prior error ellipse are proposed. It is observed that the two optimality criteria generate significantly different optimal sensor trajectories despite having the same optimal sensor placement for the localization of a stationary target. Analysis results and the performance of the sensor trajectory optimization methods are demonstrated with simulation examples. It is observed that the new closed-form projection algorithm achieves superior tracking performance compared with the two numerical search methods.

Sensor Selection for Optimal Target localization with 3-D Angle of Arrival Estimation in Underwater Wireless Sensor Networks

This paper investigates a sensor selection scheme for optimal target localization with three-dimensional (3-D) Angle of Arrival (AOA) estimation in Underwater Wireless Sensor Networks (UWSN). Specifically, we present a new 3-D AOA-based localization measurement model, which considers correlated noises and Gaussian priors. The trace of Cramer–Rao lower bound (CRLB) for the 3-D AOA measurement model is derived by introducing a special vector to denote the selected sensors with the azimuth and elevation angle measurements. Based on the presenting expressions of the CRLB, we formulate the sensor selection problem as an optimization problem, which has been transformed into the semidefinite problem program by convex relaxation, and a randomization method is adopted to improve the quality of the SDP solution. Simulation results illustrate that the proposed method receives better estimation performance over the reference methods and approaches the exhaustive search method.