Kalman Filtering Over A Packet Dropping Network: A Probabilistic Approach

We consider the problem of state estimation of a discrete time process over a packet dropping network. Previous pioneering work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M, and we derive lower and upper bounds on Pr[P_k ≤ M]. We are also able to recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper

On the steady-state performance of Kalman filtering with intermittent observations for stable systems

Many recent problems in distributed estimation and control reduce to estimating the state of a dynamical system using sensor measurements that are transmitted across a lossy network. A framework for analyzing such systems was proposed in and called Kalman filtering with intermittent observations. The performance of such a system, i.e., the error covariance matrix, is governed by the solution of a matrix-valued random Riccati recursion. Unfortunately, to date, the tools for analyzing such recursions are woefully lacking, ostensibly because the recursions are both nonlinear and random, and hence intractable if one wants to analyze them exactly. In this paper, we extend some of the large random matrix techniques first introduced in to Kalman filtering with intermittent observations. For systems with a stable system matrix and i.i.d. time-varying measurement matrices, we obtain explicit equations that allow one to compute the asymptotic eigendistribution of the error covariance matrix. Simulations show excellent agreement between the theoretical and empirical results for systems with as low as n = 10, 20 states. Extending the results to unstable system matrices and time-invariant measurement matrices is currently under investigation

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area