An application of system identification in metrology

Abstract Metrology is advancing by development of new measurement techniques and corresponding hardware. A given measurement technique, however, has fundamental speed and precision limitations. In order to overcome the hardware limitations, we develop signal processing methods based on the prior knowledge that the measurement process dynamics is linear time-invariant. Our approach is to model the measurement process as a step response of a dynamical system, where the input step level is the quantity of interest. The solution proposed is an algorithm that does real-time processing of the sensor's measurements. It is shown that when the measurement process dynamics is known, the input estimation problem is equivalent to state estimation. Otherwise, the input estimation problem can be solved as a system identification problem. The main underlying assumption is that the measured quantity is constant and the measurement process is a low-order linear time-invariant system. The methods are validated and compared on applications of temperature and weight measurement.

[1]  Ivan Markovsky,et al.  Structured low-rank approximation and its applications , 2008, Autom..

[2]  B. Friedland.  Treatment of bias in recursive filtering , 1969 .

[3]  Clemens Elster,et al.  Deconvolution filters for the analysis of dynamic measurement processes: a tutorial , 2010 .

[4]  Ivan Markovsky,et al.  Software for weighted structured low-rank approximation , 2014, J. Comput. Appl. Math..

[5]  Rik Pintelon,et al.  Identification of Linear Time-Invariant Systems From Multiple Experiments , 2015, IEEE Transactions on Signal Processing.

[6]  Jan C. Willems,et al.  A Behavioral Approach to Estimation and Dead-Beat Observer Design With Applications to State–Space Models , 2006, IEEE Transactions on Automatic Control.

[7]  W. Willman,et al.  On the linear smoothing problem , 1969 .

[8]  Jan C. Willems,et al.  From time series to linear system - Part III: Approximate modelling , 1987, Autom..

[9]  Bart De Moor,et al.  A note on persistency of excitation , 2005, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[10]  Ali H. Sayed,et al.  Linear Estimation (Information and System Sciences Series) , 2000 .

[11]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[12]  S. Van Huffel,et al.  Exact and Approximate Modeling of Linear Systems: A Behavioral Approach , 2006 .

[13]  I. Markovsky.  A software package for system identification in the behavioral setting , 2013 .

[14]  Sabine Van Huffel,et al.  Exact and Approximate Modeling of Linear Systems: A Behavioral Approach (Mathematical Modeling and Computation) (Mathematical Modeling and Computation) , 2006 .

[15]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[16]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[17]  Daniel E. Rivera,et al.  System identification: A Wiener-Hammerstein benchmark , 2012 .

[18]  Wei-Qun Shu.  Dynamic weighing under nonzero initial conditions , 1993 .

[19]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[20]  Sun-Yuan Kung,et al.  A new identification and model reduction algorithm via singular value decomposition , 1978 .

[21]  Jan C. Willems,et al.  From time series to linear system - Part II. Exact modelling , 1986, Autom..

[22]  Paolo Rapisarda,et al.  Data-driven simulation and control , 2008, Int. J. Control.

[23]  David L. Donoho,et al.  WaveLab and Reproducible Research , 1995 .

[24]  A. Antoniadis,et al.  Wavelets and Statistics , 1995 .

[25]  Ivan Markovsky,et al.  Recent progress on variable projection methods for structured low-rank approximation , 2014, Signal Process..

[26]  Ivan Markovsky.  Comparison of Adaptive and Model-Free Methods for Dynamic Measurement , 2015, IEEE Signal Processing Letters.

[27]  M. Budin.  Minimal realization of discrete linear systems from input-output observations , 1971 .

[28]  M. Niedźwiecki,et al.  Application of adaptive filtering to dynamic weighing of vehicles , 1996 .

[29]  B. Gopinath.  On the identification of linear time-invariant systems from input-output data , 1969 .