Theoretical performance bounds for reduced-order linear and nonlinear distributed estimation

In sensor networks deployed over large-scale, multidimensional physical systems with limited spatial observability, reduced-order, distributed estimation is a practical alternative to centralized estimation. For such reduced-order systems, centralized computation of the posterior Cramér Rao lower bound (CRLB) is not possible as the global estimate of the entire state vector is not accessible at a single processing node. We derive the distributed PCRLB (dPCRLB) implementations encompassing both linear and nonlinear reduced-order dynamical systems and verify their optimality through Monte Carlo simulations.