A Nonparametric Adaptive Nonlinear Statistical Filter
This work addresses state estimation for nonlinear stochastic systems, offering an adaptive approach that could be useful in domains like control or signal processing, but it appears incremental as it builds on existing Kalman filter concepts with a nonparametric twist.
The paper tackles the problem of optimal state estimation in nonlinear stochastic systems by proposing a nonparametric adaptive filter that estimates process and measurement uncertainties from past data without prior distribution assumptions, using jackknife sampling on sub-sampled data to update state estimates and uncertainties as new data is acquired.
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.