ROBUST RECURSIVE ESTIMATION IN THE PRESENCE OF HEAVY-TAILED OBSERVATION NOISE

• 成果类型: Review
• 署名作者: SCHICK, IC; MITTER, SK
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325511
• 发表日期: 1994
• 页码: 1045-1080
• 关键词: GENERALIZED LINEAR-MODELS; nonstationary time-series; Kalman filter; Bayesian estimation; systems; SPACE; identification

摘要

Under the usual assumptions of normality, the recursive estimator known as the Kalman filter gives excellent results and has found an extremely broad field of application-not only for estimating the state of a stochastic dynamic system, but also for estimating model parameters as well as detecting abrupt changes in the states or the parameters. It is well known, however, that significantly nonnormal noise, and particularly the presence of outliers, severely degrades the performance of the Kalman filter. This results in poor state estimates, nonwhite residuals and invalid inference. A first-order approximation is derived for the conditional prior distribution of the state of a discrete-time stochastic linear dynamic system in the presence of epsilon-contaminated normal observation noise. This distribution is then used to derive a first-order approximation of the conditional mean (minimum-variance) estimator. If the observation noise distribution can be represented as a member of the epsilon-contaminated normal neighborhood, then the conditional prior is also, to first order, an analogous perturbation from a normal distribution whose first two moments are given by the Kalman filter. Moreover, the perturbation is itself of a special form, combining distributions whose parameters are given by banks of parallel Kalman filters and optimal smoothers.