Stochastic modeling of mean-wind profiles for in-flight wind estimation--A new approach to lower order stochastic realization schemes

A new approach has been proposed for the design of approximate, lower order discrete time realizations of stochastic processes from the output covariance matrix over a finite time interval. No restrictive assumptions are imposed on the process, that is, it can be nonstationary and also can lead to higher dimension realization. Classes of fixed order models ("guaranteed models") are defined having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater than or equal to the process covariance matrix. The design is achieved by minimizing, in one of those classes, the approximation between the model and the process measured by the trace of the difference of the respective covariance matrices. The method has been employed in a practical problem of developing lower order wind models from a higher order covariance matrix in numerical form. The wind model is intended to be incorporated on board an aircraft maneuvering according to a four-dimensional guidance scheme in the neighborhood of the terminus of a flight. Choice of the order of the model and the resulting accuracies of the estimation schemes are compared.