Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-28T15:30:48.499Z Has data issue: false hasContentIssue false
  • English
  • Français

Prediction of a noise-distorted, multivariate, non-stationary signal

Published online by Cambridge University Press:  14 July 2016

Eugene Sobel
Eugene Sobel*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

Extract

This paper deals with the problem of predicting or extracting a certain type of non-stationary sequence or signal from another sequence composed of the signal and a stationary noise. The noise is assumed to be uncorrelated with the signal. Although all sequences in the body of this paper are multivariate, for purposes of discussion, this introduction will deal with only the univariate case.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 330 - 342
Copyright
Copyright © Sheffield: Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Frazer, R. A., Duncan, W. J. and Collar, A. R. (1947) Elementary Matrices. Cambridge Univ. Press, Cambridge.Google Scholar
[2] Hannan, E. J. (1964) The estimation of a changing seasonal pattern. J. Amer. Statist. Ass. 59, 1063–1077.Google Scholar
[3] Hannan, E. J. Measurement of a wandering signal amid noise. J. Appl. Prob. 4, 90–102.Google Scholar
[4] Jones, R. H. (1966) Exponential smoothing for multivariate time series. J. R. Statist. Soc. B 28, 241–251.Google Scholar
[5] Kalman, R. E. (1960) A new approach to linear filtering and prediction problems. ASME Trans. 82, Part D, 35–45.Google Scholar
[6] Kalman, R. E. (1962) New methods and results in linear filtering and prediction theory. Proc. of Symposium on Applications of Random Functions and Probability Theory. Wiley, New York.Google Scholar
[7] Masani, P. (1966) Book review. J. Amer. Statist. Ass. 61, 268–273.Google Scholar
[8] Sobel, E. (1966) Extraction of Slowly Changing Seasonals and of Sums of Accumulating Sequences. Ph.D. Thesis. Johns Hopkins University.Google Scholar
[9] Sobel, E. (1966) Prediction of a sum of accumulating sequences. Technical Report No. 49, Dept. of Statistics, Johns Hopkins University.Google Scholar
[10] Wiener, N. and Masani, P. (1957) The prediction theory of multivariate stochastic processes. Acta Math. 98, 111–150.Google Scholar
[11] Whittle, P. (1963) Prediction and Regulation. English Universities Press Ltd., London.Google Scholar