To estimate the Wiener nonlinear systems with process noise, a recursive Bayesian algorithm based on cu-bic spline approximation is proposed. It's well known that the polynomial approximation does not extrapolate well and high degree polynomials have oscillatory behavior, etc. To overcome these drawbacks, a cubic spline function is used to approximate the inverse function of the output nonlinearity. And then the original Wiener system is parameterized to be a pseudo-linear regression model. The estimated variance of the noise is also integrated in the algorithm to estimate the pa-rameters. In order to approximate the inverse nonlinearity, a mean-value based variable knot-selection method is employed. After the convergence is analyzed, a numerical simulation and a case study validate the algorithm.%为了辨识过程噪声干扰的Wiener非线性系统,提出了一种基于三样条函数逼近的递推贝叶斯算法.众所周知,传统的多项式逼近具有不能外推、高阶易震荡等缺点.为了克服这些缺点,首先利用三样条函数对Wiener系统的非线性反函数进行逼近,在此基础上将待辨识系统参数化为伪线性回归系统.然后把估计到的噪声方差融入算法,接着使用递推贝叶斯算法对参数进行了估计.为了提高三样条函数对非线性反函数的逼近能力,一种基于均值的变聚点选择方法被应用于算法.文中还对算法的收敛性进行了分析,并用数值仿真和案例建模验证了算法的有效性.
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