The identification of Piecewise Affine Output-Error (PWA-OE) model from input-output data involves estimating a finite set of parameters for the affine output-error submodels and partitioning the regressor space accordingly. Traditional least squares methods fail to provide consistent estimates in the presence of output-error noise, whereas prediction error methods ensure parameter consistency. This paper introduces an enhanced Outer Bounding Ellipsoid (OBE) algorithm tailored for PWA-OE model identification under bounded noise, leveraging the prediction error approach. This class of algorithms is recognized for its computational efficiency. Furthermore, through a numerical example, the proposed method demonstrates excellent performance, achieving accurate parameter estimation with high reliability.

The present study deals with a new identification algorithm from binary output measurements. The study focuses on the class of Finite Impulse Response (FIR) systems. The proposed algorithm is based on the estimation of correlation functions. A geometric interpretation is proposed and leads to a formulation of the algorithm using a Singular Value Decomposition (SVD). A convergence analysis is proposed showing the mean-square convergence with a rate of$\mathscr{O}\left(N^{-1}\right)$, Monte Carlo simulations are proposed to confirm performance.

This paper presents a subspace identification al-gorithm in the case of binary measurements on the output. The algorithm is a three-step algorithm. It requires the input signal to be periodic and the knowledge of the noise distribution. An analysis is provided and introduces to the well behavior of the algorithm. Numerical simulations confirm the analysis and good performance of the proposed algorithm.

In this study, the authors consider the identification of auto‐regressive (AR) models for time‐series from one‐bit quantised observation sequences. The only available information is the fact that the samples of the time‐series are lower or higher than a threshold of quantisation. This threshold may be different from zero. An identification algorithm is presented and analysed. A recursive formulation is proposed, an extension for the identification of a non‐linear time‐series is also proposed.