
Accession Number : AD0699217
Title : ON THE OPTIMAL SMOOTHING OF PIECEWISE CONTINUOUS FUNCTIONS,
Corporate Author : SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
Personal Author(s) : Blum,Marvin
Report Date : 12 NOV 1969
Pagination or Media Count : 27
Abstract : Noisy observations on a piecewise continuous function f(t) are made at a set of sample points. The function f(t) is assumed to be represented by a linear function of unknown parameters x sub ij in the ith interval or stage. Besides the continuity condition, other linear constraints such as continuity of derivatives may be imposed at the points of discontinuity. In this paper the optimum estimate in the sense of the minimum variance unbiased estimate or best linear unbiased estimate is obtained based on processing all the data over all stages in a batch. This solution known as the classical solution is compared with a stagewise solution which has operational and computation advantages. Both estimators are unbiased. A necessary and sufficient condition under which the two estimators have equal covariance matrices is demonstrated. (Author)
Descriptors : (*DECISION THEORY, FUNCTIONS(MATHEMATICS)), INFORMATION THEORY, CONTROL SYSTEMS, ANALYSIS OF VARIANCE, MATRICES(MATHEMATICS)
Subject Categories : Statistics and Probability
Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE