Optimal averaging time for improving observer accuracy of stochastic dynamical systems.

In the problem of remote estimation by a centralized observer, improvements to the accuracy of observer estimates come at a cost of higher communication bandwidth and energy consumption. In this article we improve observer estimation accuracy by reducing the measurement variance on the sensor node before its transmission to the centralized observer node. The main contribution is to show that measurement variance is a trade-off between dynamical system variance and sensor variance. As a result there is an optimal averaging time that minimizes measurement variance, providing more accurate measurement to the observer. The optimal averaging time is computable by solving a univariate optimization problem.

[1]  S. C. Dutta Roy.  A state of the art survey on linear phase digital filter design , 1976 .

[2]  Renjith V. Ravi,et al.  Optimization algorithms, an effective tool for the design of digital filters; a review , 2019, Journal of Ambient Intelligence and Humanized Computing.

[3]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[4]  Ling Shi,et al.  Optimal Periodic Sensor Scheduling With Limited Resources , 2011, IEEE Transactions on Automatic Control.

[5]  Daniel E. Quevedo,et al.  Sensor Scheduling in Variance Based Event Triggered Estimation With Packet Drops , 2015, IEEE Transactions on Automatic Control.

[6]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[7]  Tri Tran,et al.  Dependable control systems with Internet of Things. , 2015, ISA transactions.

[8]  Neelam Singh,et al.  A review of different optimization algorithms for a linear phase FIR filter , 2017, 2017 International Conference on Recent Innovations in Signal processing and Embedded Systems (RISE).

[9]  J. Junkins,et al.  Optimal Estimation of Dynamic Systems , 2004 .

[10]  A.H. Haddad,et al.  Applied optimal estimation , 1976, Proceedings of the IEEE.

[11]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[12]  Ling Shi,et al.  Event-Based State Estimation , 2016 .

[13]  Qing-Long Han,et al.  Distributed networked control systems: A brief overview , 2017, Inf. Sci..

[14]  Alireza Fatehi,et al.  State Estimation and Fusion in the Presence of Integrated Measurement , 2017, IEEE Transactions on Instrumentation and Measurement.

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

[16]  F. Lewis,et al.  Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition , 2007 .

[17]  Biao Huang,et al.  State estimation incorporating infrequent, delayed and integral measurements , 2015, Autom..

[18]  Tore Hägglund,et al.  Signal filtering in PID control , 2012 .

[19]  Jun Zheng,et al.  Wireless Sensor Networks: A Networking Perspective , 2009 .

[20]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .