Topology design in networked estimation: A generic approach

In this paper, we consider networked estimation where asymptotic consensus is replaced with only one fusion iteration between every two successive steps of system dynamics. With this restriction on the fusion, we show that the topology of the communication network plays a key role in the observability (and the error stability) of the estimator. For arbitrary system matrices, algebraic design of the communication topology is challenged with (i) large-scale computation, and (ii) particular fusion rules. To avoid these, structured systems theory and the notion of generic observability are implemented, which are computationally tractable and do not rely on exact fusion rules. We show the stability under weak network connectivity as compared to strong connectivity in the literature. In particular, we do not constrain the system matrix to be generically full rank compared to earlier works and show that for system matrices with rank deficiency (in the generic sense), implementing only state-estimate fusion does not recover the networked observability; thus, output fusion is required.