Tianju Sui

Tianju Sui, Damian Marelli, Ximing Sun et al.

This paper focuses on a networked state estimation problem for a spatially large linear system with a distributed array of sensors, each of which offers partial state measurements, and the transmission is lossy. We propose a measurement coding scheme with two goals. Firstly, it permits adjusting the communication requirements by controlling the dimension of the vector transmitted by each sensor to the central estimator. Secondly, for a given communication requirement, the scheme is optimal, within the family of linear causal coders, in the sense that the weakest channel condition is required to guarantee the stability of the estimator. For this coding scheme, we derive the minimum mean-square error (MMSE) state estimator, and state a necessary and sufficient condition with a trivial gap, for its stability. We also derive a sufficient but easily verifiable stability condition, and quantify the advantage offered by the proposed coding scheme. Finally, simulations results are presented to confirm our claims.

Tianju Sui, Damián Marelli, Minyue Fu et al.

Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on local measurements as well as information received from its neighbours. A recent algorithm has been proposed, which yields the optimal solution (i.e., the one that would be obtained using a centralized method) in finite time, provided the communication network forms an acyclic graph. If instead, the graph is cyclic, the only available alternative algorithm, which is based on iterative matrix inversion, achieving the optimal solution, does so asymptotically. However, it is also known that, in the cyclic case, the algorithm designed for acyclic graphs produces a solution which, although non optimal, is highly accurate. In this paper we do a theoretical study of the accuracy of this algorithm, in communication networks forming cyclic graphs. To this end, we provide bounds for the sub-optimality of the estimation error and the estimation error covariance, for a class of systems whose topological sparsity and signal-to-noise ratio satisfy certain condition. Our results show that, at each node, the accuracy improves exponentially with the so-called loop-free depth. Also, although the algorithm no longer converges in finite time in the case of cyclic graphs, simulation results show that the convergence is significantly faster than that of methods based on iterative matrix inversion. Our results suggest that, depending on the loop-free depth, the studied algorithm may be the preferred option even in applications with cyclic communication graphs.

Damián Marelli, Tianju Sui, Eduardo Rohr et al.

Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement equation, i.e., the measurement matrix and the measurement error covariance, are random. Our result also generalizes existing ones in the sense that it does not require the system matrix to be diagonalizable. For this general setting, we state a necessary and a sufficient condition for stability, and address its numerical computation. An important application of our generalization is a networking setting with multiple sensors which transmit their measurement to the estimator using a sensor scheduling protocol over a lossy network. We demonstrate how our result is used for assessing the stability of a Kalman filter in this multi-sensor setting.