On the genericity properties in networked estimation: Topology design and sensor placement

TL;DR

This paper investigates how to design network topology and sensor placement for efficient, power-constrained estimation of linear systems, highlighting limitations of measurement and state-estimate fusion under different system matrix structures.

Contribution

It characterizes the effectiveness of measurement and state-estimate fusion in networked estimation with limited communication, especially under structured-rank deficiencies.

Findings

Measurement fusion alone can lead to unbounded errors without local observability.

State-estimate fusion may not recover observability in S-rank deficient systems.

The paper provides conditions under which fusion strategies succeed or fail.

Abstract

In this paper, we consider networked estimation of linear, discrete-time dynamical systems monitored by a network of agents. In order to minimize the power requirement at the (possibly, battery-operated) agents, we require that the agents can exchange information with their neighbors only \emph{once per dynamical system time-step}; in contrast to consensus-based estimation where the agents exchange information until they reach a consensus. It can be verified that with this restriction on information exchange, measurement fusion alone results in an unbounded estimation error at every such agent that does not have an observable set of measurements in its neighborhood. To over come this challenge, state-estimate fusion has been proposed to recover the system observability. However, we show that adding state-estimate fusion may not recover observability when the system matrix is structured-rank ($S$-rank) deficient. In this context, we characterize the state-estimate fusion and measurement fusion under both full $S$-rank and $S$-rank deficient system matrices.