Bayesian hybrid estimation of LTI networked systems using finite set statistics

In this paper, we develop a Bayesian approach to estimating the state and connectivity topology of a set of networked linear time invariant systems. The connectivity of the network is assumed simple, undirected and constant in time. Each node's state, in turn, is assumed to satisfy linear discrete-time dynamics corrupted by Gaussian process noise. Measurements are assumed to be some linear transformation of the state at each node and are also corrupted by Gaussian noise. We use a Bayesian hybrid estimation approach based on the general theory of finite set statistics, which was developed for multi-target detection and tracking, to estimate the nodes' states as well as the topology of the network. Due to the linearity of the nodes' dynamics and the Gaussianity of the process and measurement noise signals, we are able to obtain algebraic closed-form solutions to the hybrid estimation problem. We demonstrate the effectiveness of our approach on a simple multi-agent consensus network from the literature. This approach promises to solve, in closed-form, more general hybrid network estimation problems in the future, including but not limited to: dynamic topologies that are coupled with nonlinear node dynamics.