×

Signal polynomial smoothing from correlated interrupted observations based on covariances. (English) Zbl 1129.60040

Summary: The least-squares polynomial smoothing problem of discrete-time signals from uncertain observations is addressed, when the variables describing the uncertainty are correlated at consecutive sampling times. Defining suitable augmented signal and observation vectors, the polynomial estimation problem is reduced to the linear estimation problem of the augmented signal. By an innovation approach, recursive algorithms are derived for the augmented linear estimators without requiring the knowledge of the state-space model generating the signal, but only covariance information of the processes involved.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
62M20 Inference from stochastic processes and prediction
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] De Santis, IEEE Transactions on Automatic Control AC-40 pp 1274– (1995)
[2] Carravetta, SIAM Journal on Control and Optimization 34 pp 1666– (1996)
[3] Dalla Mora, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48 pp 859– (2001)
[4] Bondon, IEEE Transactions on Information Theory IT-40 pp 960– (1994)
[5] Uppala, IEEE Transactions on Image Processing 6 pp 608– (1997)
[6] Laakso, Signal Processing 80 pp 567– (2000)
[7] NaNacara, Signal Processing 62 pp 215– (1997)
[8] Caballero, International Journal of Modelling and Simulation 23 pp 22– (2003)
[9] Jackson, IEEE Transactions on Information Theory 22 pp 376– (1976)
[10] Hadidi, IEEE Transactions on Automatic Control 24 pp 944– (1979)
[11] Nakamori, Applied Mathematics and Computation 135 pp 429– (2003)
[12] Nakamori, Applied Mathematics and Computation 143 pp 319– (2003)
[13] Nakamori, Digital Signal Processing 15 pp 207– (2005)
[14] Nakamori, International Journal of Systems Science 36 pp 617– (2005)
[15] Nakamori, International Journal of Systems Science 34 pp 439– (2003)
[16] Nakamori, IEICE Transactions on Fundamentals of Electronics, Communication and Computer Sciences E86-A pp 1240– (2003)
[17] , , , . Polynomial estimation of signals from non-independent uncertain observations using covariance information. International Conference on Numerical Analysis and Applied Mathematics 2005, Proceedings. Wiley-VCH: New York, 2005; 390–393. · Zbl 1083.62078
[18] . Matrix Differential Calculus with Applications in Statistics and Econometrics (revised edn). Wiley: New York, 1999.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.