Kalman filtering with intermittent observations

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.

[1]  Peter Seiler,et al.  Estimation with lossy measurements: jump estimators for jump systems , 2003, IEEE Trans. Autom. Control..

[2]  Bruno Sinopoli,et al.  Distributed control applications within sensor networks , 2003, Proc. IEEE.

[3]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[4]  Qiang Ling,et al.  Soft real-time scheduling of networked control systems with dropouts governed by a Markov chain , 2003, Proceedings of the 2003 American Control Conference, 2003..

[5]  Christoforos N. Hadjicostis,et al.  Feedback control utilizing packet dropping network links , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  Oswaldo Luiz V. Costa,et al.  Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems , 2002, IEEE Trans. Autom. Control..

[7]  Andrey V. Savkin,et al.  The problem of state estimation via asynchronous communication channels with irregular transmission times , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[8]  M. Micheli.  Random Sampling of a Continuous-time Stochastic Dynamical System: Analysis, State Estimation, and Applications , 2001 .

[9]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[10]  John Lygeros,et al.  Verified hybrid controllers for automated vehicles , 1998, IEEE Trans. Autom. Control..

[11]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[12]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[15]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[16]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[17]  Y. Bar-Shalom,et al.  Detection thresholds for tracking in clutter--A connection between estimation and signal processing , 1985 .

[18]  Mohamed T. Hadidi,et al.  Linear recursive state estimators under uncertain observations , 1978 .

[19]  M. Athans,et al.  Further results on the uncertainty threshold principle , 1977 .

[20]  M. Athans,et al.  The uncertainty threshold principle: Fundamental limitations of optimal decision making under dynamic uncertainty , 1976 .

[21]  Nasser E. Nahi,et al.  Optimal recursive estimation with uncertain observation , 1969, IEEE Trans. Inf. Theory.

[22]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .