The design of on-line linear least-squares estimators given covariance specifications via an imbedding method

The method of invariant imbedding is employed to develop on-line algorithms for all types of linear least-squares estimators (filter; fixed-point, fixed-lag, and fixed-interval smoothers; fixed-point, fixed-lead, and fixed-interval predictors) using covariance specifications for nonstationary stochastic signals in the presence of white Gaussian plus colored noise. Two design procedures are given. One is based on the initial-value solution of the function I"y(t) which is the solution to a Fredholm integral equation of the second kind, and the other on that of the function h(t,s) which is the impulse response function obeyed by a generalized Wiener-Hopf integral equation.

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