## 1 Introduction  
System modeling and identification of single variable processes have been well studied. However, most industrial processes are multivariable systems [1; 2; 3], including multiple-input multiple-output (MIMO) systems and multiple-input single-output (MISO) systems. For example, in chemical and process industries, the heat exchangers are MIMO systems, in which the state of a heat exchanger often is represented by four field input variables: the cold inlet temperature, the hot inlet temperature, the cold mass flow and the hot mass flow; the outputs are respectively the cold outlet temperature and hot outlet temperature [4]. In wireless communication systems, the MIMO technology can increase wireless channel capacity and bandwidth by using the multiple antennas without the need of additional power [5]. In computing system technology, the power consumption model for host servers can be identified using a MISO model, in which the system inputs have different forms, such as the rate of the change in the CPU frequency and the rate of the change in the CPU time share, and the system outputs are the changes in power consumption [6]. With the development of the industrial process, the identification of multivariable processes is in great demand. Researchers have studied the problem of identification for multichannel systems from different fields [7; 8; 9], and many methods have been proposed for multivariable cases [10; 11]. Recursive algorithms and iterative algorithms have wide applications in system modeling and system identification [12; 13; 14]. For example, [PERSON] et al. derived the hierarchical least squares based iterative algorithm for the Box-Jenkins system [15]; and [PERSON] and [PERSON] presented the iterative method for solving systems of linear matrix equations over reflexive and anti-reflexive matrices [16]. Compared with the recursive identification algorithm, the iterative identification algorithm uses all the measured data to refresh parameter estimation, so the parameter estimation accuracy can be greatly improved, and the iterative identification methods have been successfully applied to many different models [17; 18; 19]. In the field of system identification, the filtering technique is efficient to improve the computational efficiency [20; 21; 22], and it has been widely used in parameter estimation of different models [23; 24]. Particularly, [PERSON] et al. discussed the parameter estimation for linear stochastic time-delay systems based state filtering [25]; [PERSON] et al. discussed the identification of Wiener-type nonlinear systems using the adaptive filter [26]; and [PERSON] et al. presented a gradient based iterative algorithm for identification of a class nonlinear systems by filtering the input-output data [27]. This paper combines the filtering technique with the auxiliary model identification idea to estimate parameters of multi-input output error autoregressive (OEAR) systems. By using a linear filter to filter the input-output data, a multi-input OEAR system is transformed into two identification models, and the dimensions of the covariance matrices of the decomposed two models become smaller than that of the original OEAR model. The contributions of this paper are as follows:  
* By using the data filtering technique and the auxiliary model identification idea, a data filtering based recursive generalized least squares (F-RGLS) identification algorithm is derived for the multi-input OEAR system. * A data filtering based iterative least squares (F-LSI) identification algorithm is developed for the multi-input OEAR system. * The proposed F-LSI identification algorithm updates the parameter estimation by using all of the available data, and can produce highly accurate parameter estimates compared to the F-RGLS identification algorithm. The rest of this paper is organized as follows: Section 2 gives a description for multi-input OEAR systems. Section 3 gives an F-RGLS algorithm for the multi-input OEAR system by using the data filtering technique.