New Conditional Posterior Cramér-Rao Lower Bounds for Nonlinear Sequential Bayesian Estimation

• Published in: IEEE transactions on signal processing 2012-10, Vol.60 (10), p.5549-5556
• Main Authors: Yujiao Zheng, Ozdemir, O., Ruixin Niu, Varshney, P. K.
• Format: Article
• Language: English
• Subjects: Applied sciences; Approximation methods; Bayesian analysis; Bayesian methods; Detection, estimation, filtering, equalization, prediction; Dynamical systems; Exact sciences and technology; Filtering; Information, signal and communications theory; Lower bounds; Noise measurement; Nonlinear dynamics; Nonlinear filtering; Nonlinearity; On-line systems; Online; particle filters; posterior Cramér-Rao lower bounds; Radar tracking; Signal and communications theory; Signal, noise; Target tracking; Telecommunications and information theory; Time measurement; Vectors
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2012.2205686

The recursive procedure to compute the posterior Cramér-Rao lower bound (PCRLB) for sequential Bayesian estimators, derived by Tichavsky , provides an off-line performance bound for a general nonlinear filtering problem. Since the corresponding Fisher information matrix (FIM) is obtained by taking the expectation with respect to all the random variables, this PCRLB is not well suited for online adaptive resource management for dynamic systems. For online estimation performance evaluation in a nonlinear system, the concept of conditional PCRLB was proposed by Zuo in 2011. In this paper, two other online conditional PCRLBs are proposed which are alternatives to the one proposed by Zuo Numerical examples are provided to show that the three online bounds, namely the conditional PCRLB proposed by Zuo and the two conditional PCRLBs proposed in this paper, are very close to one another.