State Estimation in Spatially Distributed Cyber-Physical Systems: Bounds on Critical Measurement Drop Rates

In this paper, we analyze Kalman filter (KF) based state estimation in spatially distributed cyber-physical systems. We consider a practical scenario, where sensors are arbitrarily deployed over an area to jointly sense a linear dynamical system. The sensors directly communicate their observations to a central state estimation unit over a lossy network resulting in: (1) random measurement losses; (2) partial observation updates in the Kalman filter. We analyze the stability of the state estimation process in this scenario, by establishing the conditions under which its steady state error covariance matrix is bounded. In contrast to previous pioneering work with intermittent observations [1], we consider a dispersed measurement scenario and establish bounds on critical measurement loss rates of individual sensor communication links. The analysis illustrates the trade-off between state estimation accuracy and the quality of underlying communication network. Our analysis is critical to quantify the stability of control operation for safe and efficient operation of a cyber-physical system.