An Iteratively Extended Target Tracking by Using Decorrelated Unbiased Conversion of Nonlinear Measurements

Extended target tracking (ETT) based on random matrices typically assumes that the measurement model is linear. However, nonlinear measurements (such as range and azimuth) depending on locations of a series of unknown scattering centers always exist in many practical tracking applications. To address this issue, this paper proposes an iteratively extended target tracking based on random matrices by using decorrelated unbiased conversion of nonlinear measurements (ETT-IDUCM). First, we utilize a decorrelated unbiased converted measurement (DUCM) method to convert nonlinear measurements depending on unknown scatters of target extent in polar coordinates into the ones in Cartesian coordinates with equivalent measurement noise covariances. Subsequently, a novel method, combining iteratively extended Kalman filter (IEKF) updates with variational Bayesian (VB) cycles is developed for precise estimation of the target's kinematic state and extension. This method leverages the synergy between external IEKF iterations, which use the estimated state as a new prediction and input for DUCM, and internal VB iterations, which realize a closed-form approximation of the joint posterior probability. This approach progressively enhances estimation accuracy. Simulation results demonstrate the ETT-IDUCM algorithm's superior precision in estimating the target's kinematic state and extension compared to existing methods.