Higher Order Statistical Signal Processing and Analysis

本研究项目涉及开发和评估 信号处理和分析的算法， 除了，或者代替， 通常的二阶统计。 而第二阶 信号的统计仅是基础系统的函数 传递函数大小，高阶统计量取决于 系统传递函数幅度以及其相位。 时间序列（仅观察系统输出）和系统 识别（观察输入和输出）公式 正在考虑。 问题的几个方面包括 正反演建模、反褶积和参数化 估计，正在调查中。 本项目的重点是 关于适当定义的第四累积量的优化 标准结合，或代替，通常的第二 阶误差准则，从而避免了对显式数据的需要 累积量匹配 正在调查的应用包括 1)未知空间不相关高斯时延估计 噪声，2）未知的，可能非最小的盲反卷积 相位、通道和3）具有噪声输入的系统识别。

This research project is concerned with development and evaluation of algorithms for signal processing and analysis that exploit higher order statistics of signals in addition to, or in lieu of, the usual second order statistics. Whereas the second order statistics of signals are a function of only the underlying system transfer function magnitude, higher order statistics depend upon both the system transfer function magnitude as well as its phase. Both time series (only system output is observed) and system identification (both input and output are observed) formulations are being considered. Several aspects of the problem including inverse and direct modeling, deconvolution and parameter estimation, are being investigated. Emphasis in this project is on optimization of an appropriately defined fourth cumulant criterion in conjunction with, or in lieu of, the usual second order error criterion, thereby obviating the need for explicit data cumulant matching. Among the applications being investigated are 1) time delay estimation in unknown spatially uncorrelated Gaussian noise, 2) blind deconvolution with unknown, possibly nonminimum phase, channels, and 3) system identification with noisy inputs.