Optimal linear estimators for systems with multiple random measurement delays and packet dropouts

• Published in: International journal of systems science Vol. 44; no. 2; pp. 358 - 370
• Main Authors: Sun, Shuli, Xiao, Wendong
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.02.2013; Taylor & Francis
• Subjects: Applied sciences; Augmentation; Bernoulli distribution, innovation analysis approach; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control system analysis; Control theory. Systems; Delay; Difference equations; Dropouts; Estimators; Exact sciences and technology; Mathematical models; Modelling and identification; optimal linear estimators; Optimization; packet dropouts; random measurement delays; Software; Stochastic systems; Lossy channel; Multiple delay; Difference equation; Optimal estimation; Modeling; Innovation; Linear prediction; Efficiency; Least squares method; Observer; Bernoulli distribution; random measurement delays; Linear estimation; System identification; State estimation; Random variable; Packet switching; innovation analysis approach; Probabilistic approach; Optimal filter; Delay system; packet dropouts; Random distribution; optimal linear estimators; Steady state; Transmission time; Lyapunov equation; Linear filter; Discrete time; Riccati equation; Transmission loss
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2011.601347

This article is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with possible multiple random measurement delays and packet dropouts, where the largest random delay is limited within a known bound and packet dropouts can be infinite. A new model is constructed to describe the phenomena of multiple random delays and packet dropouts by employing some random variables of Bernoulli distribution. By state augmentation, the system with random delays and packet dropouts is transferred to a system with random parameters. Based on the new model, the least mean square optimal linear estimators including filter, predictor and smoother are easily obtained via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state estimators is given. An example shows the effectiveness of the proposed algorithms.