Improved Weighted Instrumental Variable Estimator for Doppler-Bearing Source Localization in Heavy Noise

Abstract

In Doppler-bearing source localization, pseudolinear estimators are appealing alternatives to the divergence-prone and computationally-demanding iterative maximum likelihood estimator. Among the existing pseudolinear estimators, the weighted instrumental variable estimator (WIVE) is the most attractive option as it is asymptotically unbiased and efficient. However, the asymptotic unbiasedness of the WIVE relies on the approximation that the second-order noise term in the Doppler pseudolinear noise is zero, which is only valid for sufficiently small noise. In large noise, the second-order noise term can no longer be neglected, thereby leading to biased estimates. In this paper, we analyze the WIVE bias and propose a new improved version of the WIVE, called the I-WIVE, that overcomes the WIVE bias problems at large noise levels. The superior performance of the I-WIVE over the WIVE and other pseudolinear estimators is demonstrated by way of simulations. Specifically, we observe that the I-WIVE exhibits a negligible bias and produces a mean-squared error closest to the Cramér-Rae lower bound among the simulated estimators.