Algebraic solution for three‐dimensional TDOA/AOA localisation in multiple‐input–multiple‐output passive radar

Abstract

The problem of estimating the location of a single target from time difference of arrival (TDOA) and angle of arrival (AOA) measurements using multi-transmitter multi-receiver passive radar system with widely separated antennas is discussed. A closed-form two-step target position estimator is presented and analysed. Using the measured AOAs, the method is able to resolve the weakness of the TDOA-based methods in estimating the target height. Several weighted least-squares minimisations are employed by the method to produce a location estimate. A weighting matrix in each step is employed to provide a significant improvement in the performance of the algorithm. The Cramer-Rao lower bound (CRLB) for target localisation accuracy is also developed. The proposed estimator is analytically shown to reach the CRLB for Gaussian TDOA and AOA noises at moderate noise level. Simulation studies indicate that the proposed hybrid TDOA/AOA location scheme performs better than any of the other algorithms, especially in the z -direction.