Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

A new approach is proposed for the design of approximate, fixed-order, discrete time realizations of stochastic processes from the output covariance 'R(i,j) over a finite time interval. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed-order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measu-e of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. The models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorelogical wind profiles from the statistical analysis of historical data.