Identification of MIMO ARX models from small samples using sparse matrix optimization

System identification (SI) using small samples is a problem of interest in several applications. However, parameter estimation in these situations is a challenge since classical identification techniques (based on prediction-error methods) are guaranteed to be efficient and consistent only under asymptotic (large sample) conditions. In addition these techniques need the knowledge of delay and order of the process prior to estimation of parameters which is difficult to obtain especially when dealing with multi-input multi-output (MIMO) systems. This paper presents a method for identifying MIMO models which have auto-regressive with exogenous (ARX) input structure without the knowledge of delay and order of the process, using the ideas of sparse matrix optimization (SMO). The formulation of the proposed method consists of a constrained one norm minimization on the parameter matrix to induce sparsity. Three case studies, including one on real time data, are discussed to present the efficacy of the proposed method. Results show that the estimates obtained using the proposed algorithm have lower variance than the traditional least square estimates.