Effective bias reduction methods for passive source localization using TDOA and GROA

Abstract

For passive source localization based on both TDOA and GROA, this paper proposes two bias reduction methods for the well-known Weighted-Least-Squares (WLS) estimator. We first derive the passive source localization bias from the two-step algebraic closed-form solution. This bias is found to be considerably larger than the Maximum Likelihood Estimator (MLE) and limits the WLS estimator’s practical applications. In this paper, We develop two methods to reduce the bias. The first one called Bias-Subtraction-Method (BSM) directly subtracts the expected bias from the solution of the WLS estimator, and the second one called Bias-Reduction-Method (BRM) imposes a constraint to the equation error formulation to improve the source location estimate. The noise covariance matrix must be known exactly in calculating the expected bias in BSM, and we only need to know the structure of it in BRM. For far-field sources localization when the noise is Gaussian and not too large, both of the two proposed methods can reduce the localization bias effectively and achieve the Cramér-Rao Lower Bound (CRLB) performance very well, and the BRM almost has the same performance as the MLE estimator. Simulations corroborate the performance of the two proposed methods.