A priori analysis of allowable interval between measurements as a test of model validity

摘要

The variance of predicted states can be computed by a Kalman filter for linear models, or by a linear approximation in a neighborhood for nonlinear models. Using these procedures, variances can be projected forward in time until allowable probabilities for statistical errors are exceeded. At this time the model is no longer useful as a predictive device, and a measurement of the system is required. The allowable interval between measurements is suggested as an indicator of model validity. Several statistical procedures for testing the suitability of models as a predictive device are discussed. A useful test must indicate that probability of model rejection increases as the projected variance increases. In usual applications of model testing the process variance is not known and an adaptive calculation of process variance is required in order to calculate the allowance interval between measurements. A new algorithm for calculating process variance is reported and compared with previously reported algorithms.