UNCERTAINTIES FOR RECURSIVE ESTIMATORS IN NONLINEAR STATE-SPACE MODELS, WITH APPLICATIONS TO EPIDEMIOLOGY

Consider a nonlinear dynamic system where one wishes to estimate a sta te vector using noisy measurements, Many algorithms have been proposed to address this problem, among them the extended Kalman filter (and i ts variants) and constant-gain stochastic approximation. To quantify t he efficacy of these algorithms, it is necessary to describe the distr ibution of the state estimation error. Typically, performance has been measured by the estimation error covariance alone, which does not pro vide enough information to probabilistically quantify the estimation a ccuracy. By casting the estimation error in an autoregressive-type for m, this paper addresses the broader question of the distribution of th e error for a general class of recursive algorithms. We illustrate the distributional results in an epidemiological problem of disease monit oring.