Filtering Problem for Functionals of Stationary Sequences
نویسندگان
چکیده
In this paper, we consider the problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations with noise. In the case of spectral certainty in which the spectral densities of the sequences are exactly known, we propose formulas for calculating the spectral characteristic and value of the mean-square error of the estimate by using the Fourier coefficients of some functions from the spectral densities. When the spectral densities are not exactly known but a class of admissible spectral densities is given, the minimax-robust method of estimation is applied. Formulas for determining the least favourable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of the functionals are proposed for some specific classes of admissible spectral densities.
منابع مشابه
Minimax-robust filtering problem for stochastic sequences with stationary increments and cointegrated sequences
The problem of optimal estimation of the linear functionals Aξ = ∑∞ k=0 a(k)ξ(−k) and AN ξ = ∑N k=0 a(k)ξ(−k) which depend on the unknown values of a stochastic sequence ξ(k) with stationary nth increments is considered. Estimates are based on observations of the sequence ξ(k) + η(k) at points of time k = 0,−1,−2, . . ., where the sequence η(k) is stationary and uncorrelated with the sequence ξ...
متن کاملMinimax-robust prediction problem for stochastic sequences with stationary increments and cointegrated sequences
The problem of optimal estimation of the linear functionals Aξ = ∑∞ k=0 a(k)ξ(k) and AN ξ = ∑N k=0 a(k)ξ(k) which depend on the unknown values of a stochastic sequence ξ(m) with stationary nth increments is considered. Estimates are obtained which are based on observations of the sequence ξ(m) + η(m) at points of time m = −1,−2, . . ., where the sequence η(m) is stationary and uncorrelated with...
متن کاملChange Point Estimation of the Stationary State in Auto Regressive Moving Average Models, Using Maximum Likelihood Estimation and Singular Value Decomposition-based Filtering
In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change...
متن کاملRenewal Theorem for a Class of Stationary Sequences
A renewal theorem is obtained for stationary sequences of the form ~,=~( . . . , Xn_ ~, X,, X,+I , ...), where X,, n~Z, are i.i.d.r.v.s, valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling ...
متن کاملRobust Noise Filtering in Image Sequences
Image sequences filtering have recently become a very important technical problem especially with the advent of new technology in multimedia and video systems applications. Often image sequences are corrupted by some amount of noise introduced by the image sensor and therefore inherently present in the imaging process. The main problem in the image sequences is how to deal with spatio-temporal ...
متن کامل