Linear Statistical Model Fitting to Discrete Measurement Data for Kalman Filtering

In this paper, we propose a method for state estimation that uses data samples that may be irregularly distributed as learning data. We assume that there is no known mathematical measurement model that could be fitted to these samples. The proposed algorithm fits a local linear model that uses sample information within the prior. In linearisation, we fit according to the prior an affine model and also compute its residual covariance. The resulting linearisation can be used directly in the Kalman Filter (KF) for state estimation. We show in examples how the proposed method can be used for creating local linearisations based on non-uniform sample points within prior.