On Event Based State Estimation

To reduce the amount of data transfer in networked control systems and wireless sensor networks, measurements are usually taken only when an event occurs, rather than at each synchronous sampling instant. However, this complicates estimation and control problems considerably. The goal of this paper is to develop a state estimation algorithm that can successfully cope with event based measurements. Firstly, we propose a general methodology for defining event based sampling. Secondly, we develop a state estimator with a hybrid update, i.e. when an event occurs the estimated state is updated using measurements; otherwise the update makes use of the knowledge that the monitored variable is within a bounded set that defines the event. A sum of Gaussians approach is employed to obtain a computationally tractable algorithm.

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

[2]  Robert V. Brill,et al.  Applied Statistics and Probability for Engineers , 2004, Technometrics.

[3]  Petar M. Djuric,et al.  Gaussian sum particle filtering , 2003, IEEE Trans. Signal Process..

[4]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[5]  Anton Cervin,et al.  Sporadic event-based control of first-order linear stochastic systems , 2008, Autom..

[6]  H. Lebesgue,et al.  Intégrale, Longueur, Aire , 1902 .

[7]  M. Hautus.  Stabilization, controllability and observability of linear autonomous systems , 1970 .

[8]  Xiaofeng Wang,et al.  State Based Self-triggered Feedback Control Systems with ℒ2 Stability , 2008 .

[9]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[10]  S. Coraluppi,et al.  Advances in asynchronous and decentralized estimation , 2001, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542).

[11]  L. Meier.  Estimation and control with quantized measurements , 1971 .

[12]  Paulo Tabuada,et al.  Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks , 2007, IEEE Transactions on Automatic Control.

[13]  W. P. M. H. Heemels,et al.  Analysis of event-driven controllers for linear systems , 2008, Int. J. Control.

[14]  Manel Velasco,et al.  On the Timing of Discrete Events in Event-Driven Control Systems , 2008, HSCC.

[15]  K. Åström,et al.  Comparison of Riemann and Lebesgue sampling for first order stochastic systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[16]  M.L.J. Hautus,et al.  Controllability and observability conditions of linear autonomous systems , 1969 .

[17]  Marek Miskowicz,et al.  Asymptotic Effectiveness of the Event-Based Sampling according to the Integral Criterion , 2007, Sensors (Basel, Switzerland).

[18]  Robert J. Elliott,et al.  Measure Theory and Filtering: Preface , 2004 .

[19]  Bruno Sinopoli,et al.  A characterization of the critical value for Kalman filtering with intermittent observations , 2008, 2008 47th IEEE Conference on Decision and Control.

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

[21]  Young Soo Suh,et al.  Improving Estimation Performance in Networked Control Systems Applying the Send-on-delta Transmission Method , 2007, Sensors.

[22]  H. Sorenson,et al.  Recursive bayesian estimation using gaussian sums , 1971 .

[23]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[24]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[25]  A. V. Balakrishnan,et al.  Kalman Filtering Theory , 1984 .

[26]  Ali Saberi,et al.  Filtering theory , 2007 .

[27]  Marek Miskowicz,et al.  Send-On-Delta Concept: An Event-Based Data Reporting Strategy , 2006, Sensors (Basel, Switzerland).