Exponential Mixture Density Based Approximation to Posterior Cramr-Rao Lower Bound for Distributed Target Tracking

Ye Yuan, Wei Yi, Pramod K. Varshney

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The posterior Cramr-Rao lower bound (PCRLB) and a number of its extensions including the unconditional PCRLB (U-PCRLB) and the conditional PCRLB (C-PCRLB) have been widely studied in multi-sensor target tracking (MSTT). Previous MSTT works assume that the measurements are conditionally independent, which is often not the case in practice. When the correlations of the measurements are unknown, the standard Bayes update and PCRLB computations cannot be performed. Inspired by geometric average (GA) fusion that implements data fusion with unknown data correlations by employing exponential mixture density (EMD) to compute the global posterior, EMD-based approximations to U-PCRLB and C-PCRLB are derived in this paper for two classic distributed fusion architectures, namely the hierarchical and consensus architectures. The PCRLB can be decomposed into two parts, one coming from the prior information and the other from the information contained in the data. The data information part of PCRLB is approximated via EMD-based posterior, leading to the approximation of the PCRLB. We present a sequential Monte Carlo solution to recursively compute the proposed approximation to the PCRLB for nonlinear non-Gaussian estimation problems. Numerical simulations are provided to show that the proposed approximation to the bound on the estimation mean square error (MSE) is tighter compared to the existing bounds based on likelihood fusion obtained under the measurement independence assumption.

Original languageEnglish (US)
Pages (from-to)862-877
Number of pages16
JournalIEEE Transactions on Signal Processing
StatePublished - 2022
Externally publishedYes


  • distributed data fusion
  • multi-sensor target tracking

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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