On-line estimation of smooth signals with partial observation
P. L. Chow, Rafail Zalmanovich Khas'minskii · Problems of Information Transmission · 2006
The paper concerns the estimation of a smooth signal S ( t ) and its derivatives in the presence of a noise depending on a small parameter ε based on a partial observation. A nonlinear Kalman-type filter is proposed to perform on-line estimation. For the signal S in a given class of smooth functions, the convergence rate for the estimation risks, as ε → 0, is obtained. It is proved that such rates are optimal in a minimax sense. In contrast to the complete observation case, the rates are reduced, due to incomplete information.