Barankin Bound for Bearing Estimation with Bias Correction

Array-based bearing estimation is commonly used in many sonar/radar applications. Typical performance of a practical implementation displays a threshold behavior, that is, below certain signal-to-noise ratio (SNR) the estimation mean- square error 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, and some performance bounds are exploited to capture the ambiguities and predict the threshold SNR. Research in the past often ignores the bias-related contribution due to evaluation difficulty. Recently a complete Cramer-Rao bound (CRB) has been derived to include both the Fisher information and the bias contribution using a first-order approximation of the MLE bias. The revised CRB has shown some threshold behavior, however it is still far less tight compared to the simulations, first because it cannot capture the sidelobe ambiguities; second because the expression of the first-order bias given in a referred paper was later found incorrect in terms of the sample size order. This paper further develops the concept of local performance bounds with bias correction in two aspects. First a closed-form expression of the MLE first-order bias is derived for a complex multivariate Gaussian data model. Second, the Barankin bound is derived and evaluated for the bearing estimation problem, which is optimized through a set of test points in the parameter space to capture the sidelobe ambiguities. The simulations show that the resulted bound is much tighter than the CRB. Together with the bias correction, the bound is also able to close the gap from the large-error global bounds yet with much less computations.