A COMPARISON OF CLASSICAL STOCHASTIC ESTIMATION AND DETERMINISTIC ROBUST ESTIMATION

This note compares the formulation and solution of two linear parameter estimation problems. The basic distinction in the problem formulations 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 infinity or its nonlinear cover, and the particular solution studied here is a deterministic robust estimator which was introduced circa 1987. This note examines certain parallels between classical stochastic estimation (Kalman filtering) and the deterministic robust estimation. The similarities and differences are discussed in geometric terms, in philosophical terms, and in terms of the estimator's recursive implementation.