## 1 Introduction  
In actual industry processes, block-oriented nonlinear systems are often introduced to model nonlinear systems. Block-oriented nonlinear systems can be commonly divided into Hammerstein systems and Wiener systems [1; 2; 3]. Hammerstein systems consist of a linear block following a static nonlinear block [4; 5; 6]. Wiener systems are composed of a linear block preceding a static nonlinear block [7; 8; 9]. The output of Wiener systems is nonlinear, so the modeling for Wiener systems is more sophisticated than that for Hammerstein systems. Differing from the work in [8; 9], this paper focuses on the identification problem for Wiener nonlinear systems with moving average noises which are called Wiener output error moving average (OEMA) systems. In most existing works, the nonlinear part of Wiener systems is assumed a linear combination or a piecewise-linear function [10], or has a invertible and monotone function representation over the operating range [11, 12]. [PERSON] and [PERSON] derived a least squares-based and a gradient-based iterative identification algorithms for Wiener nonlinear systems by separating one bilinear cost function into two linear cost functions [13]. [PERSON] _et al._ presented a maximum likelihood method to identify Wiener models [14].  
The stochastic gradient (SG) algorithm has less computational burden and slower convergence rate than the recursive least squares algorithm [15, 16, 17]. Some new algorithms were presented to improve the convergence rate of the SG algorithm [18, 19, 20]. For example, [PERSON] _et al._ introduced the convergence index to the SG algorithm and obtained a faster convergence rate than stochastic gradient algorithm [21]; [PERSON] _et al._ derived the multi-innovation extended stochastic gradient algorithm for controlled autoregressive moving average models by expanding the scalar innovation to an innovation vector and analyzed its performance in detail [22]. Recently, the gradient-based iterative (GI) algorithm was also presented to improve the convergence rate of the SG algorithm [23, 24, 25]. By making sufficient use of all the measured information, the GI algorithm can obtain a faster convergence rate than the SG algorithm. [PERSON] _et al._ presented a gradient-based iterative identification algorithms for Box-Jenkins systems with finite measurement input-output data [26]. [PERSON] _et al._ proposed a gradient based iterative algorithm to determine the parameters of a nonlinear system by using the negative gradient search [27]. [PERSON] _et al._ derived a hierarchical gradient based iterative estimation algorithm for multivariable output error moving average systems using the hierarchical identification principle [28].  
To the best of our knowledge, few contributions have addressed the modeling and estimation issues for Wiener nonlinear OEMA systems, which are the focus of this work. For Wiener nonlinear OEMA systems, our objectives are as follows:  
* To establish the identification model of the Wiener nonlinear OEMA system from input to output.
* To present a gradient-based iterative identification algorithm for the Wiener nonlinear OEMA model.
* To analyze the performances of the proposed algorithm using a numerical simulation, including the convergence rates and the estimation errors of this algorithm.  
The rest of this paper is organized as follows. Section 2 establishes the identification model of the Wiener nonlinear OEMA system. Section 3 presents a gradient-based iterative identification algorithm for the Wiener nonlinear OEMA model. Section 4 provides an example to illustrate the effectiveness of the proposed algorithm. The conclusions of the paper are summarized in Section 5.