Nonlinear State Space Model Identification Using a Regularized Basis Function Expansion

TL;DR

This paper introduces a regularized basis function expansion method for nonlinear state space model identification, utilizing particle methods and expectation maximization to improve flexibility and prevent overfitting.

Contribution

It presents a novel approach combining basis function expansion, particle filtering, and regularization for nonlinear state space model identification.

Findings

Effective in simulation and real-data scenarios

Regularization improves model generalization

Closed-form parameter updates enhance computational efficiency

Abstract

This paper is concerned with black-box identification of nonlinear state space models. By using a basis function expansion within the state space model, we obtain a flexible structure. The model is identified using an expectation maximization approach, where the states and the parameters are updated iteratively in such a way that a maximum likelihood estimate is obtained. We use recent particle methods with sound theoretical properties to infer the states, whereas the model parameters can be updated using closed-form expressions by exploiting the fact that our model is linear in the parameters. Not to over-fit the flexible model to the data, we also propose a regularization scheme without increasing the computational burden. Importantly, this opens up for systematic use of regularization in nonlinear state space models. We conclude by evaluating our proposed approach on one simulation example and two real-data problems.