Numerically Stable Centered Error Entropy and Mixture Minimum Error Entropy Estimators for Bearings-Only Target Tracking Problem

This letter focuses on tracking a moving target using only bearing measurements obtained by a moving observer, commonly termed bearings-only tracking (BOT) or target motion analysis (TMA). The accuracy of popular nonlinear state estimators, such as the unscented Kalman filter (UKF), is affected by non-Gaussian noises in the measurements and uncertainties in the observer path. To address this, maximum correntropy (MC) and minimum error entropy (MEE) criteria have been recently reported in the literature. Even though the MEE criteria have the potential to produce more accurate estimates, the estimation framework tends to become unstable. Hence, to deal with the complexities of noise in the model and the instability in numerical computations, a robust mixture MEE (MMEE) with UKF is proposed in this letter. In addition to MMEE, a robust centered error entropy-based estimator (RCEE) is also proposed. The RCEE-UKF and MMEE-UKF methods are compared with MEE-UKF and MC-UKF estimators through simulations, and it is found that the RCEE-UKF provides the best estimation accuracy.