Linear Least-squares EstimationThomas Kailath 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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Editors Comments on Paper 1 | 9 |
Editors Comments on Papers 2 Through 6 | 48 |
On a Fundamental Approximation Problem in | 94 |
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analytic applications assumed coefficients components condition consider constant covariance matrix defined denote derived determined differential equation dynamic system elements extrapolation factorization filtration finite follows formula Fourier Gaussian given Hilbert space IEEE Trans innovations input integral equation Kailath Kalman filter Kolmogorov Krein least-squares estimation Lemma limiter linear equations linear filter loop Math mathematical maximal matrix mean square method minimizing multivariate stationary nonlinear nonstationary observations obtained operator optimal estimate optimum orthogonal output paper parameter phase jitter poles polynomials prediction predictor problem Proc process x(t quadratic random processes random variables rational spectrum recursive Riccati Riccati equation satisfied sequence x(t signal and noise smoothing solution spectral density stagewise state-space stationary processes stationary random stationary sequence statistical stochastic processes theorem tion transformation transient error upper half-plane values vector Wiener Wiener filter Wiener-Hopf equation zero