A WOLD-KOLMOGOROV APPROACH TO LINEAR LEAST SQUARES ESTIMATION. PART I. THE FILTERING PROBLEM. PART II. THE SMOOTHING PROBLEM.
STANFORD UNIV CALIF STANFORD ELECTRONICS LABS
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The Wold-Kolmogorov approach to linear least-squares approximation problems is first to whiten the observed data by a causal and invertible operation and then to treat the resulting simpler white-noise observations problem. This technique was successfully used by Bode and Shannon to obtain a simple derivation of the classical Wiener filtering problem for stationary processes over a semi-infinite interval. This report extends the technique to handle nonstationary continuous-time processes over finite intervals. In Part I this method is used to obtain a simple derivation of the Kalman-Bucy recursive filtering formulas for both continuous-time and discrete-time processes and also some minor generalizations thereof. In Part II the method is used to obtain a new, simple and general solution to the smoothing problem. Author