A KALMAN FILTER EXTENSION FOR THE ANALYSIS OF IMPRECISE TIMESERIES

摘要

The Kalman filter combines given physical information for alinear system and external observations of its state in an optimalway. Conventionally, the uncertainty is assessed in astochastic framework: measurement and system errors aremodelled using random variables and probability distributions.However, the quantification of the uncertainty budgetof empirical measurements is often too optimistic due to, e.g.,the ignorance of non-stochastic errors in the analysis process.For this reason a more general formulation is requiredwhich is closer to the situation in real-world applications.Here, the Kalman filter is extended with respect to nonstochasticdata imprecision which is caused by hidden systematicerrors. The paper presents both the theoretical formulationand a numerical example.