# Realization and identification algorithm for stochastic LPV state-space models with exogenous inputs

## TL;DR

This paper introduces a new realization and identification algorithm for stochastic LPV state-space models with exogenous inputs, combining correlation analysis and covariance realization for efficient and consistent estimation.

## Contribution

It presents a novel algorithm that integrates deterministic LPV realization with stochastic covariance methods, improving model estimation accuracy and computational efficiency.

## Key findings

- Algorithm is computationally efficient.
- Estimates LPV model matrices accurately from empirical data.
- Validated through a numerical case study.

## Abstract

In this paper, we present a realization and an identification algorithm for stochastic Linear Parameter-Varying State-Space Affine (LPV-SSA) representations. The proposed realization algorithm combines the deterministic LPV input output to LPV state-space realization scheme based on correlation analysis with a stochastic covariance realization algorithm. Based on this realization algorithm, a computationally efficient and statistically consistent identification algorithm is proposed to estimate the LPV model matrices, which are computed from the empirical covariance matrices of outputs, inputs and scheduling signal observations. The effectiveness of the proposed algorithm is shown via a numerical case study.