Linear least-squares estimation
The topic of linear least-squares estimation, apparently a very specaial one, has ramifications in a large number of problems, both specific and general, stochastic and deterministic. Among these, we might mention the detection of Gaussian signals in Gaussian noise, quadratic minimization problems in modern control theory, polynomial factorization problems in network theory, computation of spline functions, solution of fredholm integral equations and two-point linear boundary-value problems, Pade approximation problems, system identification techniques, the theory of invariant subspaces and Hiilbert-space operators, inverse Sturm-Liouville problems, and so on.
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A. N. Kolmogorov adaptive loop algorithms analysis analytic applications arbitrary assume coefficients condition consider constant Contr covariance defined denote derived determined differential equation discrete-time dynamic system elements estimation theory extrapolation finite follows formula Fourier Gaussian given half-plane Hilbert space IEEE IEEE Trans innovations input integral equation Kailath Kalman filter Karhunen Kolmogorov Krein least-squares estimation Lemma linear equations linear filtering linear systems Masani Math mathematical matrix mean-square method minimal models nonlinear observations obtained operator optimal filter optimum orthogonal output paper parameter polynomials prediction problem Proc proof quadratic random function random processes random variables rational spectrum recursive relation representation Riccati equation satisfied sequence x(t smoothing solution solved spectral density squares state-space stationary processes stationary random stationary sequence statistical stochastic processes theorem theory tion transfer function transformation uniquely upper half-plane values vector Wiener Wiener filter Wiener-Hopf equation York zero