Kalman Filtering With Intermittent Observations: Tail Distribution and Critical Value

In this paper, we analyze the performance of Kalman filtering for discrete-time linear Gaussian systems, where packets containing observations are dropped according to a Markov process modeling a Gilbert-Elliot channel. To address the challenges incurred by the loss of packets, we give a new definition of non-degeneracy, which is essentially stronger than the classical definition of observability, but much weaker than one-step observability, which is usually used in the study of Kalman filtering with intermittent observations. We show that the trace of the Kalman estimation error covariance under intermittent observations follows a power decay law. Moreover, we are able to compute the exact decay rate for non-degenerate systems. Finally, we derive the critical value for non-degenerate systems based on the decay rate, improving upon the state of the art.

I. Introduction

A large wealth of applications demands wireless communication among small embedded devices. Wireless Sensor Network (WSN) technology provides the architectural paradigm to monitor and control systems with a high degree of temporal and spatial granularity. Applications of sensor networks are becoming ubiquitous, ranging from environmental monitoring and control, to building automation, surveillance along with many others [1]. Given their low power nature and the requirement of long lasting deployment, communication between devices is limited in both range and reliability. Changes in the environment, such as the simple relocation of a large metal object in a room or the presence of people, inevitably affect the propagation properties of the wireless medium. Channels are time-varying, unreliable and difficult to characterize. Spurred by this consideration, our effort concentrates on the design and analysis of estimation and control algorithms over unreliable networks.