The best linear approximation (BLA) framework has already proven to be a valuable tool to analyze nonlinear systems and to start the nonlinear modeling process. The existing BLA framework is limited to systems with additive (colored) noise at the output. Such a noise framework is a simplified representation of reality. Process noise can play an important role in many real-life applications.This paper generalizes the best linear approximation framework to account also for the process noise, both for the open-loop and the closed-loop setting, and shows that the most important properties of the existing BLA framework remain valid. The impact of the process noise contributions on the robust BLA estimation method is also analyzed.

中文翻译：

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将最佳线性逼近框架扩展到过程噪声情况

最佳线性逼近 (BLA) 框架已被证明是分析非线性系统和启动非线性建模过程的宝贵工具。现有的 BLA 框架仅限于在输出端具有附加（有色）噪声的系统。这种噪声框架是现实的简化表示。过程噪声可以在许多实际应用中发挥重要作用。 本文概括了最佳线性逼近框架，以考虑开环和闭环设置的过程噪声，并表明最重要的属性现有的 BLA 框架仍然有效。还分析了过程噪声贡献对稳健 BLA 估计方法的影响。