TY - JOUR
T1 - Exponential Mixture Density Based Approximation to Posterior Cramr-Rao Lower Bound for Distributed Target Tracking
AU - Yuan, Ye
AU - Yi, Wei
AU - Varshney, Pramod K.
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China under Grants 61771110, U19B2017 and 61871103, in part by the Fundamental Research Funds of Central Universities under Grant ZYGX2020ZB029, and in part by Chang Jiang Scholars Program and the 111 Project under Grant B17008.
Publisher Copyright:
© 1991-2012 IEEE.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - distributed data fusion
KW - multi-sensor target tracking
KW - PCRLB
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U2 - 10.1109/TSP.2022.3148540
DO - 10.1109/TSP.2022.3148540
M3 - Article
AN - SCOPUS:85124712068
SN - 1053-587X
VL - 70
SP - 862
EP - 877
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
ER -