A greedy iterative least squares algorithm for multivariable systems

This paper considers the joint estimation of parameters and time-delays for multi-input output-error systems. By introducing the noise-free outputs and setting an input regression length, an over-parameterization linear sparse identification model can be obtained. A greedy iterative least squares algorithm based on the Householder transformation and auxiliary model is proposed. The proposed algorithm can estimate the multiple time-delays and parameters of the multivariable systems from a few number of sampled data, and has the advantage of avoiding computing the inverse of a high-dimensional matrix at each iteration compared to existing methods. Finally, a numerical simulation example demonstrates the effectiveness of the proposed algorithm.