Adaptive model fitting with time-varying input variables

Consider the long-standing problem of fitting a model to multivariate data. In many control systems, we are interested in models that are associated with tracking a nonstationary process with time-varying input variables. It is often hopeless to produce a globally valid model over the whole domain in such a setting. Further, a globally valid model is not likely to be even needed in practice since some combinations of input variables are highly unlikely to occur. For this reason, we consider an adaptive model estimation method that emphasizes local fitting. This can be implemented in an elegant way using recursive methods such as stochastic approximation. The application motivating the general approach is the construction of real-time (or faster) training simulators for use by Navy personnel; the approach would apply in many other control and tracking applications