PCRLB for batch discrete‐time estimation through state decoupling

Abstract

This letter aims to obtain a closed‐form performance metric using the smoothing posterior Cramér–Rao lower bound (PCRLB) for a class of direct discrete‐time kinematic models. By decoupling the state‐space model into separate position, velocity and acceleration components using an independent dynamic representation, the velocity component in the a priori distribution is converted into a position component. Based on the above derivations, the closed‐form PCRLB is developed. The effectiveness of the proposed bound is demonstrated by contrasting the proposed smoothing PCRLB with the traditional recursive PCRLB in a bearings‐only target tracking scenario.