Nondefinite least squares and its relation to H∞-minimum error state estimation

The problem of recursive nondefinite least-squares state estimation of continuous-time stationary processes is solved, by applying Pontryagin´s maximum principle. A comparison of the derived solution to the result that is obtained for the H_∞ -minimum error estimation suggests a new interpretation for the H_∞-optimal estimation mechanism. According to this interpretation, the estimator tries to optimally estimate the required combination of the states, in the l₂-norm sense, against the worst disturbance signal that stems from a fictitious measurement of this combination