On sequential Kalman filtering with scheduled measurements

The stability problem of Kalman filtering for linear stochastic systems with scheduled measurements in [1] is reconsidered in this paper. The transmission of a vector observation from the sensor to the remote estimator is realized by sequentially transmitting each component of the observation to the estimator in one time step. The communication of each component is triggered if and only if the corresponding component of normalized measurement innovation vector is larger than a given threshold. As a complementary to [1], we extend the measurement data scheduler to have different thresholds assigned to different components of the normalized measurement innovation vector and similarly derive the sequential Kalman filter. Moreover, the sufficient and necessary conditions for guaranteeing the stability of mean squared estimation error are established for general linear systems by explicitly investigating the convergence properties of a specially constructed axillary function.

[1]  Lihua Xie,et al.  Multiple-Level Quantized Innovation Kalman Filter , 2008 .

[2]  Keyou You,et al.  Quantized filtering of linear stochastic systems , 2011 .

[3]  Andrea J. Goldsmith,et al.  LQG Control for MIMO Systems Over Multiple Erasure Channels With Perfect Acknowledgment , 2012, IEEE Transactions on Automatic Control.

[4]  Ling Shi,et al.  Optimal Sensor Power Scheduling for State Estimation of Gauss–Markov Systems Over a Packet-Dropping Network , 2012, IEEE Transactions on Signal Processing.

[5]  Ling Shi,et al.  Event-Based Sensor Data Scheduling: Trade-Off Between Communication Rate and Estimation Quality , 2013, IEEE Transactions on Automatic Control.

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

[7]  Lihua Xie,et al.  Kalman filtering with scheduled measurements - Part I: Estimation framework , 2012, Proceedings of the 10th World Congress on Intelligent Control and Automation.

[8]  Young Soo Suh,et al.  Modified Kalman filter for networked monitoring systems employing a send-on-delta method , 2007, Autom..

[9]  J.P. Hespanha,et al.  A Constant Factor Approximation Algorithm for Event-Based Sampling , 2007, 2007 American Control Conference.

[10]  Lihua Xie,et al.  Kalman Filtering With Scheduled Measurements , 2013, IEEE Transactions on Signal Processing.

[11]  T. Başar,et al.  Optimal Estimation with Limited Measurements , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  Shan Gao,et al.  Sensor Scheduling for k-Coverage in Wireless Sensor Networks , 2006, MSN.

[13]  Stergios I. Roumeliotis,et al.  SOI-KF: Distributed Kalman Filtering With Low-Cost Communications Using The Sign Of Innovations , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

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

[15]  A. Casavola,et al.  Proofs of "LQG Control For MIMO System Over Multiple TCP-like Erasure Channels" , 2009, 0909.2172.