Function space approach to state estimation for a class of uncertain systems

A joint detection-estimation scheme is derived for the estimation of the state of a linear system subject to white noise disturbances whose covariance function is known up to a parameter. The unknown parameter is assumed to satisfy at least one of several bounds indicating different levels of uncertainty about the model. Since no a priori information about the parameter, other than the bounds is known, a weighted minimax criterion is used. Function space techniques are used to determine the solution.