Higher Order Statistical Signal Processing and Analysis

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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.