# Stable spline identification of linear systems under missing data

## TL;DR

This paper introduces a nonparametric Bayesian approach using stable spline kernels for identifying linear systems with missing data, improving model prediction accuracy over traditional methods.

## Contribution

It presents a novel class of radial basis function kernels derived from stable spline kernels, enabling effective system identification with incomplete data.

## Key findings

- The new kernel approach outperforms standard parametric methods in prediction accuracy.
- The method is applicable to both discrete and continuous-time systems.
- Numerical experiments validate the effectiveness of the proposed approach.

## Abstract

A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian framework as zero-mean Gaussian processes. Their covariances are given by the so-called stable spline kernels encoding information on regularity and BIBO stability. In this paper, we demonstrate that these kernels also lead to a new family of radial basis functions kernels suitable to model system components subject to disturbances given by filtered white noise. This novel class, in cooperation with the stable spline kernels, paves the way to a new approach to solve missing data problems in both discrete and continuous-time settings. Numerical experiments show that the new technique may return models more predictive than those obtained by standard parametric Prediction Error Methods, also when these latter exploit the full data set.