TY - JOUR
T1 - Approximating the Lower Bound on the Arithmetic Average-Based Distributed State Estimation
AU - Yuan, Ye
AU - Liu, Xinyu
AU - Li, Wujun
AU - Yi, Wei
AU - Varshney, Pramod K.
N1 - Publisher Copyright:
© 1965-2011 IEEE.
PY - 2024
Y1 - 2024
N2 - In multi-sensor state estimation, existing posterior Cramér-Rao lower bounds (PCRLBs) are generally derived under the measurement independence assumption (MIA). When correlations among measurements are unknown, the true PCRLB can not be computed due to the inability to compute the likelihood function corresponding to the local measurements. Motivated by the random variables-based arithmetic average (RV-AA) fusion rule, which combines the local variables with unknown correlations as a linear mixture variable (LMV), an LMV-based approximation to the performance lower bound (LMV-A-LB) on RV-AA is derived in this paper to provide a more refined performance indicator for it. This approximation uses the posterior obtained from the LMV along with the Bayes' rule to estimate the true but unavailable likelihood function. We show that the LMV-A-LB generally lacks a closed-form solution, so it is approximated using sequential Monte Carlo approaches. Further, by limiting the system model to the commonly used additive Gaussian noise case, we compute the exact expression of the derived bound with the aid of the Kalman filters. Numerical simulation experiments demonstrate that the LMV-A-LB obtains a tighter performance lower bound for RV-AA fusion by comparing with existing bounds.
AB - In multi-sensor state estimation, existing posterior Cramér-Rao lower bounds (PCRLBs) are generally derived under the measurement independence assumption (MIA). When correlations among measurements are unknown, the true PCRLB can not be computed due to the inability to compute the likelihood function corresponding to the local measurements. Motivated by the random variables-based arithmetic average (RV-AA) fusion rule, which combines the local variables with unknown correlations as a linear mixture variable (LMV), an LMV-based approximation to the performance lower bound (LMV-A-LB) on RV-AA is derived in this paper to provide a more refined performance indicator for it. This approximation uses the posterior obtained from the LMV along with the Bayes' rule to estimate the true but unavailable likelihood function. We show that the LMV-A-LB generally lacks a closed-form solution, so it is approximated using sequential Monte Carlo approaches. Further, by limiting the system model to the commonly used additive Gaussian noise case, we compute the exact expression of the derived bound with the aid of the Kalman filters. Numerical simulation experiments demonstrate that the LMV-A-LB obtains a tighter performance lower bound for RV-AA fusion by comparing with existing bounds.
KW - Distributed state estimation
KW - posterior cramér-rao lower bound
KW - random variables-based arithmetic average fusion
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U2 - 10.1109/TAES.2024.3510236
DO - 10.1109/TAES.2024.3510236
M3 - Article
AN - SCOPUS:85211495224
SN - 0018-9251
JO - IEEE Transactions on Aerospace and Electronic Systems
JF - IEEE Transactions on Aerospace and Electronic Systems
ER -