Performance Bound Approximation for Bearing Estimation with Bias Correction

Array-based bearing estimation often displays a threshold behavior, that is, below certain signal-to-noise ratio (SNR) the estimation mean-square error (MSE) increases dramatically. The error increase is known to be largely attributed to sidelobe ambiguities in signal field correlation along with estimation bias at low SNR. This paper investigates the bias-related contribution from the perspective of local performance bounds. The first-order bias of the maximum likelihood estimate is first derived for a complex multivariate Gaussian data model, which is then incorporated into the Cramer-Rao bound and Barankin bound respectively to obtain MSE approximations. The simulations show an improved threshold region error prediction compared to the same bounds without bias correction.