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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Page 272
... loop could be modified as shown in the third figure'thus introducing one additional integrator . Proceeding as ... ADAPTIVE FILTERS The discussion which follows will concern adaptive systems , i.e. , those which change parameters or ...
... loop could be modified as shown in the third figure'thus introducing one additional integrator . Proceeding as ... ADAPTIVE FILTERS The discussion which follows will concern adaptive systems , i.e. , those which change parameters or ...
Page 273
... loop is fast , paper analysis is impossible that f and simulation techniques are needed . In On func designing an adaptive system it is necessary eplace to consider the response and stability of the loop as well as the source of ...
... loop is fast , paper analysis is impossible that f and simulation techniques are needed . In On func designing an adaptive system it is necessary eplace to consider the response and stability of the loop as well as the source of ...
Page 275
... adaptive system just described forms a very sophis- ticated tracking loop . = Fig . 5 is a block diagram of the zero velocity lag tracking loop in which we do not know the signal or noise spectra although we assume the noise to be ...
... adaptive system just described forms a very sophis- ticated tracking loop . = Fig . 5 is a block diagram of the zero velocity lag tracking loop in which we do not know the signal or noise spectra although we assume the noise to be ...
Contents
Preface | 1 |
On a Problem of Extrapolation of A N Kolmogoroff | 90 |
Editors Comments on Papers 7 Through 13 | 130 |
Copyright | |
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analytic application assumed B₁ coefficients components condition consider constant covariance matrix defined denote derived determined differential equation dynamic system elements equal extrapolation factorization filtration finite follows formula Fourier Gaussian given Hilbert space IEEE Trans innovations input integral equation interval Kailath Kalman filter Kolmogorov Krein least-squares estimation Lemma limiter linear equations linear filter loop Math mathematical maximal matrix mean square method minimizing Nauk nonlinear observations obtained operator optimal estimate optimal filter optimum orthogonal output paper parameter phase jitter poles polynomials prediction predictor problem Proc process x(t quadratic random processes random variables rational spectrum recursive respect Riccati equation satisfied sequence x(t signal and noise smoothing solution spectral density stagewise stationary processes stationary random statistical stochastic processes Theorem tion transformation transient error upper half-plane values vector Wiener Wiener filter Wiener-Hopf equation zero