Shi J, Sun H H
Electrical and Computer Engineering Department, Drexel University, Philadelphia, PA 19104.
Ann Biomed Eng. 1991;19(4):457-72. doi: 10.1007/BF02584320.
An approach for decomposing of a Nonlinear Non-Gaussian Process (NNGP) is presented. A set of adjoin processes alpha's are first constructed based on the orthogonal principle so that the linear and nonlinear part of the process can be completely separated by a correlation operation without the statistical assumption on the process (i.e., it is not necessarily a Gaussian Process). The linear and nonlinear filters or predictors can then be designed and implemented independently and the consistency of parameters is guaranteed. An algorithm is given for a second order nonlinear process, and it can easily be extended to higher order cases if necessary. The method is first demonstrated by applying it to a nonlinear filter design problem, i.e., system identification. Finally, the necessity of a proposed decomposition procedure is proven by applying it to an example in which the parameters of a signal model are extracted from a version which is distorted due to the nonlinearity of the channel.
提出了一种分解非线性非高斯过程（NNGP）的方法。首先基于正交原理构造一组伴随过程α，使得该过程的线性部分和非线性部分能够通过相关运算完全分离，而无需对该过程进行统计假设（即它不一定是高斯过程）。然后可以独立设计和实现线性和非线性滤波器或预测器，并保证参数的一致性。给出了针对二阶非线性过程的算法，如有必要，该算法可轻松扩展到高阶情况。该方法首先通过将其应用于非线性滤波器设计问题（即系统辨识）进行了演示。最后，通过将其应用于一个示例来证明所提出分解过程的必要性，在该示例中，从因信道非线性而失真的版本中提取信号模型的参数。
