Application of Minimum Distortion Filtering to Identification of Linear Systems Having Non-uniform Sampling Period

We consider the problem of identification of continuous time systems when the data is collected using non-uniform sampling periods. We formulate this problem in the context of Nonlinear Filtering. We show how a new class of nonlinear filtering algorithm (Minimum Distortion Filtering) can be applied to this problem. A simple example is used to illustrate the performance of the algorithm. We also compare the results with those obtained from (a particular realization) of Particle Filtering.

[1]  G. Pagès,et al.  Optimal quantization methods for nonlinear filtering with discrete-time observations , 2005 .

[2]  D. Mayne,et al.  Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering† , 1969 .

[3]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Hiromitsu Kumamoto,et al.  Random sampling approach to state estimation in switching environments , 1977, Autom..

[5]  G. Kitagawa Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[6]  John Geweke,et al.  Monte carlo simulation and numerical integration , 1995 .

[7]  Tomas McKelvey,et al.  State-space parametrizations of multivariable linear systems using tridiagonal matrix forms , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[9]  Hisashi Tanizaki Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques , 2001 .

[10]  Graham C. Goodwin,et al.  Control System Design , 2000 .

[11]  Christos Georgakis,et al.  18th IFAC World Congress: Milano, Italy, August 28 to September 2, 2011 , 2013 .

[12]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[13]  Torsten Söderström,et al.  Identification of continuous-time AR processes from unevenly sampled data , 2002, Autom..

[14]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[15]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[16]  Lennart Ljung,et al.  Frequency domain identification of continuous-time output error models, Part II: Non-uniformly sampled data and B-spline output approximation , 2010, Autom..

[17]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..

[18]  Graham C. Goodwin,et al.  A Novel Technique based on up-sampling for addressing Modeling Issues in Sampled Data Nonlinear Filtering , 2011 .

[19]  J. E. Handschin Monte Carlo techniques for prediction and filtering of non-linear stochastic processes , 1970 .

[20]  Thomas B. Schön,et al.  Estimation of Nonlinear Dynamic Systems : Theory and Applications , 2006 .

[21]  Graham C. Goodwin,et al.  Sampling and sampled-data models , 2010, Proceedings of the 2010 American Control Conference.

[22]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[23]  Niclas Bergman,et al.  Recursive Bayesian Estimation : Navigation and Tracking Applications , 1999 .

[24]  Vipin Kumar,et al.  Introduction to Data Mining , 2022, Data Mining and Machine Learning Applications.

[25]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[26]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[27]  Thomas F. Edgar,et al.  Process Dynamics and Control , 1989 .

[28]  Jun S. Liu,et al.  Metropolized independent sampling with comparisons to rejection sampling and importance sampling , 1996, Stat. Comput..

[29]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[30]  T. Grundy,et al.  Progress in Astronautics and Aeronautics , 2001 .

[31]  Michael Isard,et al.  A Smoothing Filter for CONDENSATION , 1998, ECCV.

[32]  S. Haykin Kalman Filtering and Neural Networks , 2001 .

[33]  A. Isidori Nonlinear Control Systems , 1985 .

[34]  S. Graf,et al.  Foundations of Quantization for Probability Distributions , 2000 .

[35]  Graham C. Goodwin,et al.  Sampling in Digital Sig-nal Processing and Control , 1996 .

[36]  Paul Zarchan,et al.  Fundamentals of Kalman Filtering: A Practical Approach , 2001 .

[37]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[38]  Brett Ninness,et al.  Maximum Likelihood estimation of state space models from frequency domain data , 2009, 2007 European Control Conference (ECC).

[39]  S. Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[40]  H. Kushner On the Differential Equations Satisfied by Conditional Probablitity Densities of Markov Processes, with Applications , 1964 .

[41]  Robert J. Elliott,et al.  Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature , 2007, Proceedings of the IEEE.

[42]  Torsten Söderström,et al.  Identification of Continuous-Time ARX Models From Irregularly Sampled Data , 2007, IEEE Transactions on Automatic Control.

[43]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.