## 1 Introduction  
System modeling and system identification are the prerequisite and foundation of all control issues. System identification has a significant effect on the filtering [1; 2; 3], state estimation [4; 5; 6], system control [7; 8; 9] and optimization [10]. For example, [PERSON] _et al._ proposed a nonlinear filtering approach based on spline nonlinear functions [11]; [PERSON] _et al._ presented an algorithm to estimate the parameters and states for linear systems with canonical state-space descriptions [12]; [PERSON] _et al._ discussed the theoretical implementation of robust attitude estimation for a rigid spacecraft system under measurement loss [13]. As system identification becomes widely available, many identification methods have been raised, e.g., the gradient identification methods [14, 15], the hierarchical identification methods [16, 17, 18], the auxiliary model identification methods [19, 20] and the multi-innovation identification methods [21].  
In all of these identification methods, the recursive identification [22, 23, 24] and the iterative identification methods [25, 26, 27] constitute two categories of important parameter estimation methods [28]. The variable of the recursive identification is about time, so it can be used to estimate the system parameters online. [PERSON] _et al._ derived the recursive identification algorithm to identify the parameters in the parameterized Hammerstein-Wiener system model [29]; [PERSON] presented a robust recursive algorithm for identification of a Hammerstein model with a static nonlinear block in polynomial form and a linear block described by the ARMAX model [30]; [PERSON] _et al._ studied constrained two-dimensional recursive least squares identification problems for batch processes, which can improve the identification performance by incorporating a soft constraint term in the cost function to reduce the variation of the estimated parameters [31]. [PERSON] and [PERSON] derived the mathematical models and presented a least squares-based iterative algorithm for multi-input multirate systems with colored noises by replacing the unknown noise terms in the information vector with their estimates [32].  
Some estimation methods focus on the estimation problems of equation error type systems [33, 34, 35], including the equation-error autoregressive (EEAR) systems, the equation-error moving average systems and the equation-error autoregressive moving average systems. For example, [PERSON] and [PERSON] derived a filtering-based recursive least squares identification algorithm for nonlinear dynamical adjustment models [36]; [PERSON] developed a maximum likelihood estimation algorithm to estimate the parameters of Hammerstein nonlinear CARARMA systems by using the Newton iteration [37]; [PERSON] presented a recursive generalized extended least squares algorithm for identifying controlled ARMA systems [28]; the basic idea is to replace the unknown terms in the information vector with their estimates. On the basis of the work in [28, 32], the objective of this paper is to develop new identification algorithms using the model equivalent transformation and to provide more accurate parameter estimates.  
The rest of this paper is organized as follows. Section 2 gives the identification model for EEAR systems. Section 3 gives a recursive generalized least squares algorithm, and Section 4 gives a model equivalence-based recursive least squares algorithm. Section 5 computes the parameter estimates of the original system. Section 6 provides numerical examples to prove the validity of the proposed algorithms. Finally, some concluding remarks are made in Section 7.