Kalman filtering with intermittent observations: Bounds on the error covariance distribution

When measurements are subject to random losses, the covariance of the estimation error of a state estimator becomes a random variable. In this paper we present bounds on the cumulative distribution function of the covariance of the estimation error for a discrete time linear system. We also show that the bounds can be arbitrarily tight if sufficient computational power is available. Numerical simulations show that the proposed method provides tighter bounds than the ones available in the literature.

[1]  A. Goldsmith,et al.  Kalman filtering with partial observation losses , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[2]  Bruno Sinopoli,et al.  Kalman Filtering With Intermittent Observations: Tail Distribution and Critical Value , 2012, IEEE Transactions on Automatic Control.

[3]  Hamid M. Faridani,et al.  Performance of kalman filter with missing measurements , 1986, Autom..

[4]  Bruno Sinopoli,et al.  Foundations of Control and Estimation Over Lossy Networks , 2007, Proceedings of the IEEE.

[5]  Babak Hassibi,et al.  On the steady-state performance of Kalman filtering with intermittent observations for stable systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[6]  Minyue Fu,et al.  Statistical properties of the error covariance in a Kalman filter with random measurement losses , 2010, 49th IEEE Conference on Decision and Control (CDC).

[7]  Ling Shi,et al.  Probabilistic performance of state estimation across a lossy network , 2008, Autom..

[8]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[9]  Ling Shi,et al.  Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective , 2010, IEEE Transactions on Automatic Control.

[10]  Luca Schenato,et al.  Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop , 2008, IEEE Transactions on Automatic Control.

[11]  Soummya Kar,et al.  Moderate Deviations of a Random Riccati Equation , 2012, IEEE Transactions on Automatic Control.

[12]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[13]  Andrea Censi,et al.  Kalman Filtering With Intermittent Observations: Convergence for Semi-Markov Chains and an Intrinsic Performance Measure , 2011, IEEE Transactions on Automatic Control.

[14]  Soummya Kar,et al.  Kalman Filtering With Intermittent Observations: Weak Convergence to a Stationary Distribution , 2009, IEEE Transactions on Automatic Control.

[15]  Andrea Censi,et al.  On the performance of Kalman filtering with intermittent observations: A geometric approach with fractals , 2009, 2009 American Control Conference.