Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method

摘要

This article investigates parameter and order identification of a block-oriented Hammerstein system by using the orthogonal matching pursuit method in the compressive sensing theory which deals with how to recover a sparse signal in a known basis with a linear measurement model and a small set of linear measurements. The idea is to parameterize the Hammerstein system into the linear measurement model containing a measurement matrix with some unknown variables and a sparse parameter vector by using the key variable separation principle, then an auxiliary model based orthogonal matching pursuit algorithm is presented to recover the sparse vector. The standard orthogonal matching pursuit algorithm with a known measurement matrix is a popular recovery strategy by picking the supporting basis and the corresponding nonzero element of a sparse signal in a greedy fashion. In contrast to this, the auxiliary model based orthogonal matching pursuit algorithm has unknown variables in the measurement matrix. For a K-sparse signal, the standard orthogonal matching pursuit algorithm takes a fixed number of K stages to pick K columns (atoms) in the measurement matrix, while the auxiliary model based orthogonal matching pursuit algorithm takes steps larger than K to pick K atoms in the measurement matrix with the process of picking and deleting atoms, due to the gradually accurate estimates of the unknown variables step by step. The auxiliary model based orthogonal matching pursuit algorithm can simultaneously identify parameters and orders of the Hammerstein system, and has a high efficient identification performance.