A nonparametric adaptive nonlinear statistical filter

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system´s process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the system´s prior distribution. The system´s prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.