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- W2330266296 abstract "This paper designs the new fixed-point smoother, which estimates a stationary stochastic signal, based on the innovations theory by the covariance information of the signal and observation noise processes. Two kinds of observation noises are considered here, which are the stationary white noise and the stationary white plus stationary coloured noise. We design the sub-optimal fixed-point smoother for each noise. The new smoother has the two advantages: 1) The linear stationary stochastic signal can be estimated, with a simple initial-value system, directly by the curve-fitted functions of the covariance information, and by the observed values. So we do not have any trouble of finding an approximating state space model by the spectral factorization method, using covariance information. 2) The calculation of the algorithm for the fixed-point smoothing estimate is easy. The reason is that the covariance function of the stationary stochastic signal and coloured-noise processes are assumed to be semi-degenerate. Semi-degenerate kernels can express the general kind of covariance information in the form of finite sums of products of nonrandom functions.The originality of this paper lies in the idea that we first derived the fixed-point smoother, which estimates a linear stationary stochastic signal, based on the innovations theory by the covariance information. In comparison with the fixed-point smoother for the stationary white noise case by the Wiener-Hopf integral equation approach using the information in nonstationary systems, the present fixed-point smoother in this paper for stationary systems also has the numerical merit that the given algorithms contain fewer number of differential equations than those by the Wiener-Hopf integral equation approach.The effectiveness of the new fixed-point smoother was assured by some numerical examples." @default.
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- W2330266296 date "1980-01-01" @default.
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- W2330266296 title "Design of Linear Stationary Fixed-Point Smoother by Covariance Information Based on the Innovations Theory" @default.
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- W2330266296 doi "https://doi.org/10.9746/sicetr1965.16.804" @default.
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