The Volterra integral-functional series is the classic approach for nonlinear black box dynamical systems modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many other. Identifying the time-varying functional parameters, also known as Volterra kernels, poses a difficulty due to the curse of dimensionality. This refers to the exponential growth in the number of model parameters as the complexity of the input-output response increases. The least squares method (LSM) is widely acknowledged as the standard approach for tackling the issue of identifying parameters. Unfortunately, the LSM suffers with many drawbacks such as the sensitivity to outliers causing biased estimation, multicollinearity, overfitting and inefficiency with large datasets. This paper presents alternative approach based on direct estimation of the Volterra kernels using the collocation method. Two model examples are studied. It is found that the collocation method presents a promising alternative for optimization, surpassing the traditional least squares method when it comes to the Volterra kernels identification including the case when input and output signals suffer from considerable measurement errors.

翻译：Volterra积分-泛函级数是非线性黑箱动态系统建模的经典方法，广泛应用于无线电物理、空气动力学、电子与电气工程等诸多领域。辨识时变泛函参数（即Volterra核）因维数灾难而面临困难，这指的是随着输入-输出响应复杂度的增加，模型参数呈指数级增长。最小二乘法（LSM）被公认为解决参数辨识问题的标准方法。然而，LSM存在诸多缺陷，如对异常值敏感导致有偏估计、多重共线性、过拟合以及处理大数据集时效率低下。本文提出一种基于配置法直接估计Volterra核的替代方法，研究了两个模型示例。结果表明，配置法在Volterra核辨识（包括输入和输出信号存在显著测量误差的情况）中展现出优于传统最小二乘法的优化潜力。