Guaranteed Estimation Algorithms for Prediction and Interpolation of Random Processes

Abstract

Prediction and interpolation of a process is investigated for known covariance functions of measurement error and perturbations belonging to a set ℜ of nonnegative-definite functions. Guaranteed estimation is studied, assuming that the guaranteed estimate is the best estimate of the parameters of the useful signal in the sense of the minimum of the mean-square error under the worst behavior of measurement errors and perturbations with covariance functions belonging to the set ℜ. Depending on the type of constraints, i.e., characteristics of the set ℜ, different approaches and methods are applied to guaranteed estimation. Papers concerned with this topic are reviewed. Prediction and interpolation are analytically investigated for the case in which covariance functions are bounded by the constraints imposed on their variance matrices. For the continuous case, the weight function and its equations are derived. Prediction and interpolation accuracies are evaluated and compared with the least-squares filters.