Geometry-Dependent PCRLB for Target Tracking in Clutter With Radar Measurement Uncertainty

초록

In realistic radar tracking scenarios, the target measurement uncertainty (TMU)—encompassing both detection probability and measurement error covariance—is strongly influenced by the target-to-radar (T2R) geometry. However, the existing posterior Cramér–Rao lower bounds (PCRLBs) largely overlook the fundamental impact of T2R geometry on the TMU and, consequently, on the mean square error (MSE) of state estimation, often leading to overly conservative bounds. To bridge this gap, this paper first develops a generalized model of target measurement error covariance for bistatic radar systems with moving transmitters and receivers, in which the impact of T2R geometry on the error covariance is explicitly characterized. Based upon this TMU formulation, we subsequently derive a geometry-dependent PCRLB (GD-PCRLB) that fully incorporates both measurement origin uncertainty and geometry-dependent TMU. In this derivation, both detection probability and measurement error covariance are treated as state-dependent parameters when differentiating the log-likelihood function with respect to the target state. Unlike existing PCRLBs that partially or completely ignore the geometry-dependent nature of TMU, the proposed GD-PCRLB captures substantial performance benefits by extracting additional Fisher information arising from geometry-dependent TMU. The resulted GD-PCRLB provides a significantly less conservative MSE lower bound compared to existing bounds that only partially or fully neglect the influence of T2R geometry on TMU. Numerical results demonstrate that the improvement offered by the GD-PCRLB becomes more pronounced as the level of TMU increases. © 1965-2011 IEEE.

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