# The Use of Gaussian Processes in System Identification

## TL;DR

This paper reviews how Gaussian processes are applied in system identification, including modeling techniques like NFIR, NARX, and state-space models, highlighting their role in learning dynamic input-output relationships.

## Contribution

It provides a concise overview of Gaussian process-based methods in system identification, emphasizing recent developments and applications.

## Key findings

- Gaussian processes enable flexible nonlinear modeling.
- They facilitate probabilistic predictions with uncertainty quantification.
- Various models like NFIR, NARX, and state-space are discussed.

## Abstract

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to form time series prediction models such as non-linear finite-impulse response (NFIR) models as well as non-linear autoregressive (NARX) models. Gaussian process state-space models (GPSS) can be used to learn the dynamic and measurement models for a state-space representation of the input-output data. Temporal and spatio-temporal Gaussian processes can be directly used to form regressor on the data in the time domain. The aim of this article is to briefly outline the main directions in system identification methods using Gaussian processes.