Non Linear AR-Noise Investigated Via a Kalman Filter

  • G. Cojazzi
  • M. Marseguerra
  • C. M. Porceddu


The use of autoregressive (AR) models for extracting the information contained in the fluctuating component of a stationary signal represents a well established technique, widely used in the nuclear reactor engineering field. The possibility of treating non stationary fluctuations via a time varying autoregressive (TV AR) model is here considered in the framework of the Kaiman filters theory. Firstly, the vanishing of the covariance matrix of the state vector is prevented by slightly increasing the matrix at each time step. Moreover the forecasting guess of the state vector is improved by the use of a least squares technique. The results of numerical experiments, made on AR models of increasing order up to four are encouraging and suggest the convenience of further investigating the features of the present approach to this non linear noise problem.


State Vector Kalman Filter Filter Theory True Coefficient Gaussian White Noise Process 
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  1. 1.
    SMORN V, 12 – 16th October 1987, Munich, FRG.Google Scholar
  2. 2.
    G.E.P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control, Holden Day Inc., San Francisco,USA, (1976).MATHGoogle Scholar
  3. 3.
    M. B. Priestley, Spectral Analysis and Time Series, Academic Press, London, (1981).MATHGoogle Scholar
  4. 4.
    P. C. Young, A Recursive Approach to Time Series Analysis, Bull. Inst. Math. Appl.. 10: 209 (1974).Google Scholar
  5. 5.
    A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, N. Y., (1970).MATHGoogle Scholar
  6. 6.
    R. F. Kaiman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, ASME Jour. Basic Eng. Series D, 83:85 (1961).CrossRefGoogle Scholar
  7. 7.
    M. Marseguerra and C. M. Porceddu, An Example of Utilization of Kaiman Filters in Time Series Analysis, 19th IMORN, 4 – 16th June 1986, Rome, Italy.Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • G. Cojazzi
    • 1
  • M. Marseguerra
    • 1
  • C. M. Porceddu
    • 2
  1. 1.Politecnico di MilanoMilanoItaly
  2. 2.Centro “E. Clementel”ENEABolognaItaly

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