Abstract-Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.

Abstract-When data are transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network, both observation and control packets may be lost or delayed. This process can be modeled by assigning probabilities to successfully receive packets. Determining the impact of this uncertainty on the feedback-loop requires a generalization of classical control theory. This paper presents the foundations of such new theory.Motivations and overview of the efforts of different research groups are described first. Then, novel contributions of the authors are presented. These include showing threshold behaviors which are governed by the uncertainty parameters of the communication network: for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g. TCP-like protocols), there exists critical probabilities for the successful delivery of packets, below which the optimal controller fails to stabilize the system. Furthermore, for these protocols, the separation principle holds and the optimal LQG control is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear.

Abstract-Motivated by our experience in building sensor networks for navigation as part of the Networked Embedded Systems Technology (NEST) project at Berkeley, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multi-hop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded error occurs.

Abstract

In this paper we study the effect of false data injection attacks on state estimation carried over a sensor network monitoring a discrete-time linear time-invariant Gaussian system. The steady state Kalman filter is used to perform state estimation while a failure detector is employed to detect anomalies in the system. An attacker wishes to compromise the integrity of the state estimator by hijacking a subset of sensors and sending altered readings. In order to inject fake sensor measurements without being detected the attacker will need to carefully design his actions to fool the estimator as abnormal sensor measurements would result in an alarm. It is important for a designer to determine the set of all the estimation biases that an attacker can inject into the system without being detected, providing a quantitative measure of the resilience of the system to such attacks. To this end, we will provide an ellipsoidal algorithm to compute its inner and outer approximations of such set. A numerical example is presented to further illustrate the effect of false data injection attack on state estimation.