Kalman Filtering of Time Series Data
We introduce the method of Kalman filtering of time series data for linear systems and its nonlinear variant the extended Kalman filter. We demonstrate how the filter can be applied to nonlinear systems and reconstructions of nonlinear systems for the purposes of noise reduction, state estimation and parameter estimation. We discuss issues such as implementation of the filter equations and choices of filter parameters within the context of reconstructing nonlinear systems from data. Several examples illustrating the use of the filter are presented inlcuding a preliminary use of the filter as applied to economic time series data.
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