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.