Spectral Clustering on Subspace for Parameter Estimation of Jump Linear Models

TL;DR

This paper introduces the spectral clustering on subspace (SCS) algorithm for estimating parameters, switching epochs, and model input of jump linear models, achieving exact identification without noise and near optimality at high SNR.

Contribution

The paper proposes a novel spectral clustering on subspace algorithm that effectively estimates parameters and switching times in jump linear models, improving over existing methods.

Findings

Exact parameter estimation in noise-free case.

Achieves Cramér-Rao bound at high SNR.

Partitions observation space into subspaces for each linear model.

Abstract

The problem of estimating parameters of a deterministic jump or piecewise linear model is considered. A subspace technique referred to as spectral clustering on subspace (SCS) algorithm is proposed to estimate a set of linear model parameters, the model input, and the set of switching epochs. The SCS algorithm exploits a block diagonal structure of the system input subspace, which partitions the observation space into separate subspaces, each corresponding to one and only one linear submodel. A spectral clustering technique is used to label the noisy observations for each submodel, which generates estimates of switching time epoches. A total least squares technique is used to estimate model parameters and the model input. It is shown that, in the absence of observation noise, the SCS algorithm provides exact parameter identification. At high signal to noise ratios, SCS attains a clairvoyant Cram\'{e}r-Rao bound computed by assuming the labeling of observation samples is perfect.