On the distributed estimation of rank-deficient dynamical systems: A generic approach

In this paper, we consider distributed estimation when the communication time-scale is restricted to the time-scale of the dynamics. It can be shown that this restriction may not guarantee a stable estimation error when the data fusion is implemented only in the observation-space. To address this issue, one has to rely on fusion in the predictor-space, which alone may lead to a stable error only when the system matrix is full S-rank (maximal rank of the zero/non-zero structure). In this paper, we show that when the system matrix is S-rank deficient, predictor-space fusion is insufficient, i.e., the distributed estimator is not observable. In order to recover distributed observability, we provide a novel measurement-based agent classification, and subsequently, define inter-agent communication derived from this classification. The results are based on structured systems theory and the notion of generic observability. Finally, we provide an illustrative example to show the applicability of the proposed schemes using an iterative Linear Matrix Inequality (LMI) approach.