Reduced state estimator for systems with parametric inputs

A reduced state estimator is derived for systems with bounded parameters as inputs. Optimal filter gains are derived for minimizing the total covariance of the estimation error due to measurement noise and parameter uncertainty. It is shown that these filter gains for a two-state system with a Gaussian parameter satisfy the Kalata relation in steady state. Equations are also derived for optimally filtering measurements in arbitrary time order. This reduced state estimator offers novelties over a traditional Kalman filter in its application to the class of problems considered. The total error covariance, which is minimized, makes no use of plant noise. Furthermore, the filter is easier to optimize in high dimensional and multiple sensor applications as well as in processing out-of-sequence measurements.