A Kalman filter extension for the analysis of imprecise time series

The Kalman filter combines given physical information for a linear system and external observations of its state in an optimal way. Conventionally, the uncertainty is assessed in a stochastic framework: measurement and system errors are modelled using random variables and probability distributions. However, the quantification of the uncertainty budget of 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 required which is closer to the situation in real-world applications. Here, the Kalman filter is extended with respect to non-stochastic data imprecision which is caused by hidden systematic errors. The paper presents both the theoretical formulation and a numerical example.