State Estimation Over a Lossy Network in Spatially Distributed Cyber-Physical Systems

In this paper, we analyze stochastic stability of Kalman filter (KF) based state estimation over a lossy network in spatially distributed cyber-physical systems. We study a practical scenario in which sensors are arbitrarily deployed over an area to jointly sense the state of underlying physical system. The sensors directly communicate observations to a central state estimation unit over a network resulting in random loss in measurements and partial observation updates in KF. We analyzed stability of state estimation process in this scenario by establishing conditions under which steady state error covariance matrix is bounded. In contrast to previous work on gathered measurement scenario with intermittent loss, we considered a dispersed measurement scenario and established bounds on critical probability of receiving measurements over individual sensor communication links. Our analysis later exploited possible existence of spatial correlation among states in the filtering process and characterized its impact on the bounds. We further extended our analysis by considering correlated loss among sensor measurements. The overall analysis quantifies the trade-off between state estimation accuracy and the quality of underlying communication network. In addition, our analysis demonstrates that by exploiting spatial correlation among states, a higher degree of information loss (or lower network quality) can be tolerated to achieve a certain estimation accuracy. Since estimation accuracy directly impacts the stability of control operation, this analysis is critical for architecture and network planing design of cyber-physical systems.