The correlation properties of gamma and other non-Gaussian processes generated by memoryless nonlinear transformation
The correlation properties of gamma and other non-Gaussian processes generated by memoryless nonlinear transformation
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DOI：
10.1088/0022-3727/32/23/314
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发表时间：
1999-12
期刊：
影响因子：
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通讯作者：
R. Tough;K. Ward
中科院分区：
文献类型：
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作者：
R. Tough;K. Ward
非高斯随机过程的自相关函数 (ACF) 是通过对已知 ACF 的高斯过程进行无记忆非线性变换获得的，计算为幂级数，系数表示为一维积分。一般来说，必须对这些进行数值评估；还考虑了两个分析上易于处理的特殊情况。在实际感兴趣的情况下，我们发现该级数快速收敛。然后将这些结果用于模拟具有指定 ACF 的非高斯过程，该 ACF 的值可以小于其平均值的平方。我们的方法与公开文献中的其他方法进行了比较。给出了具有伽玛单点统计的时间序列和随机场的示例，这些统计提供了高分辨率雷达杂波的受控模型。
The autocorrelation function (ACF) of a non-Gaussian random process, obtained by the memoryless nonlinear transformation of a Gaussian process with a known ACF, is calculated as a power series with coefficients expressed as one-dimensional integrals. In general these must be evaluated numerically; two analytically tractable special cases are also considered. In cases of practical interest the series has been found to converge rapidly. These results are then used in the simulation of a non-Gaussian process with a specified ACF, which can take values less than the square of its mean. Our approach is compared with other methods in the open literature. Examples are given of time series and random fields with gamma single-point statistics that provide controlled models of high-resolution radar clutter.