A Nonparametric Adaptive Nonlinear Statistical Filter

TL;DR

This paper introduces an adaptive nonlinear state estimator that leverages statistical learning to estimate uncertainties from data without prior distribution assumptions, improving upon traditional Kalman filters.

Contribution

It presents a novel nonparametric, data-driven approach for adaptive state estimation in nonlinear stochastic systems, avoiding prior distribution assumptions.

Findings

Effective estimation of process and measurement uncertainties from data.

Adaptive updates improve state estimation accuracy.

Applicable to nonlinear stochastic systems without prior distribution knowledge.

Abstract

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.