ON OPTIMAL AND SUBOPTIMAL LINEAR SMOOTHING.
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
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Recursive form of results on smoothing for linear dynamic systems were first given by Bryson and Frazier 1962. Alternate formulations of the problem were given by Rauch et al 1965, Mayne 1966, Fraser 1967 and Kailath 1968. The present report shows that the results of Mayne and Fraser can be derived in a more general setting using the Orthogonality Principle of Linear Estimation. The form of the results is particularly useful for the sensitivity analysis of the optimal smoother. Explicit equations are derived for the actual covariance of a suboptimal smoother which uses wrong information about the mean square values of noise inputs. Conditions are established under which the calculated values of the covariances provide upper bounds on the actual covariances of the smoothed estimates. Author