H∞-minimum error state estimation of linear stationary processes

A state estimator is derived which minimizes the H_∞-norm of the estimation error power spectrum matrix. Two approaches are presented. The first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution. The second approach establishes a duality between the problem of H_∞-filtering and the problem of unconstrained input H_∞-optimal regulation. Using this duality, previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding Kalman filter. The two approaches usually lead to different results. They are compared by a simple example which also demonstrates a clear advantage of the H_∞-estimate over the conventional l ₂-estimate