Generalized Conditional PCRLB Fully Accounting for Geometry-Dependent Target Measurement Uncertainty

초록

The conditional posterior Cramér-Rao lower bound (CPCRLB) incorporating historical measurements from particular realizations of target states, is regarded as a more accurate and faithful online lower bound compared to the unconditional PCRLB. In general radar, especially bistatic radar tracking, the target measurement uncertainty (TMU) in terms of both target detection probability and measurement error covariance is significantly determined by the target-to-radar (T2R) geometry. However, the existing CPCRLBs assume perfect target detection, and lead to over-optimistic conditional MSE error lower bounds for radar tracking with miss-detection. Morever, they completely ignore the impact of geometry-dependent TMU on the conditional bound, and inevitably discard valuable target Fisher information which makes the bounds over-conservative. This paper rigorously derives a generalized CPCRLB (GCPCRLB) to fully account for the impact of both the miss-detection and geometry-dependent TMU on the conditional bound. Furthermore, we prove that the proposed GCPCRLB coincides with existing CPCRLB under the assumption of both perfect detection and geometry-independent TMU. Based on the general recursion of the proposed GCPCRLB, an implementable GCPCRLB is further derived for bistatic radar tracking with explicit geometry-dependent TMU. The proposed implementable GCPCRLB is then applied to radar trajectory control to optimize the T2R geometry for improved tracking. Numerical results demonstrate that the proposed GCPCRLB provides a much more accurate conditional MSE lower bound for radar tracking with miss-detection and geometry-dependent TMU. Compared to state-of-the-art radar trajectory control methods, our proposed control method acquires the target measurement with the least uncertainty and achieves the most accurate tracking result. © 2026 IEEE. All rights reserved.

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