Distributed posterior Cramér-Rao lower bound for nonlinear sequential Bayesian estimation

In distributed sensor networks, the posterior Cramér-Rao lower bound (PCRLB) has recently been used [1] as a selection criteria for sensor management decisions, where new sensor nodes are deployed or existing ones reactivated to optimize the network´s performance. Previous algorithms to compute the PCRLB are derived for the centralized [2] and hierarchical architectures [3] using a fusion centre that makes them inappropriate for distributed sensor management. Only recently a suboptimal expression [1] for the distributed architecture has been proposed, which can at times lead to large errors especially in systems with highly non-linear dynamics. The paper derives the optimal PCRLB for the distributed architecture. In other words, we derive a recursive procedure to determine the overall Fisher information matrix (FIM), i.e., the inverse of the PCRLB, from local FIMs of the distributed estimators. The proposed distributed PCRLB is independent of the filtering mechanism used and closely follows its centralized counterpart.