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A nonlinear optimum-detection problem. II. Simple numerical examples

机译：非线性最佳检测问题。二。简单的数值示例

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For pt.I see ibid., vol.36, no.2, p.347-57 (1990). Simple numerical examples are presented to illustrate the effect of the previously derived nonlinear filters for combating nonlinear Gaussian noise in detecting deterministic signals. The nonlinear Gaussian noise is expressed as a quadratic form in stationary Gaussian noise that is also present in the data, together with white Gaussian noise. Thus the nonlinear noise is referred to as the quadratic noise and the stationary noise as the linear noise. The former is assumed to be an order of magnitude smaller than the latter. When the signal overlaps with both the linear and the quadratic noise, use of both nonlinear filters for the small quadratic-noise region improves the detection performance well beyond the optimum level achievable in the absence of the quadratic noise. As the quadratic noise increases, this improvement diminishes and the performance eventually deteriorates below the level achievable by the linear and the first nonlinear filter combination.
机译：关于第一部分，见同上，第36卷，第2期，第347-57页（1990年）。给出了简单的数值示例，以说明先前导出的非线性滤波器在检测确定性信号中对抗非线性高斯噪声的作用。非线性高斯噪声在稳态高斯噪声中也以二次形式表示，该高斯噪声也与白高斯噪声一起出现在数据中。因此，非线性噪声被称为二次噪声，静止噪声被称为线性噪声。假定前者比后者小一个数量级。当信号与线性噪声和二次噪声都重叠时，对于较小的二次噪声区域使用两个非线性滤波器都将改善检测性能，远远超过不存在二次噪声时可达到的最佳水平。随着二次噪声的增加，这种改善减弱，并且性能最终恶化到线性滤波器和第一个非线性滤波器组合所能达到的水平以下。

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