A comparison of classical stochastic estimation and deterministic robust estimation

The formulation and solution of two linear parameter estimation problems are compared. The basic distinction in the problem formulation is the nature of the uncertainty. In one case, the uncertainty is generated by white Gaussian noise, and the solution is the Kalman filter. In the other case, the uncertainty is unmodeled dynamics in the unit ball in H^∞ or its nonlinear cover, and the particular solution studied is a deterministic robust estimator. Certain parallels between classical stochastic estimation (Kalman filtering) and the deterministic robust estimation are examined. The similarities and differences are discussed in geometric terms, in philosophical terms, and in terms of the estimator´s recursive implementation