Presidential Young Investigator Award: Detection and Estimation in Low Dimensional Subspaces

这项研究涉及开发和评估用于信号估计和检测的高效、高性能的信号处理算法。用于处理传感器阵列收集的数据和分析时间序列的算法尤其令人感兴趣。一种用于降低信号处理算法的复杂性并提高其性能的技术是基于在处理之前将数据映射到子空间。数据到子空间的映射适用于几乎所有的信号处理问题，尤其适用于必须处理大量数据的问题，如果不是强制性的话。正在研究的一个关键问题是线性变换的设计，它在最小化子空间维度的同时最大化性能。在自适应波束形成、自适应滤波、谱估计和信源位置估计问题以及更一般的非线性信号处理算法中，正在探索映射到子空间的数据的处理。正在研究为转换设计确定适当的性能标准，以及在性能和复杂性之间进行权衡。利用统计分析和模拟来分析所得到的算法的性能。

Van Veen This research involves the development and evaluation of efficient, high performance signal processing algorithms for signal estimation and detection. Algorithms for processing data collected at arrays of sensors and for analysis of time series are of particular interest. One technique for reducing the complexity and improving the performance of signal processing algorithms is based on mapping data into subspaces prior to processing. Mapping of data into subspaces is appropriate for almost all signal processing problems, and is especially applicable, if not mandatory, to problems in which large quantities of data must be processed. A key issue under study is the design of linear transformations which maximize performance while minimizing subspace dimension. Processing of data mapped into subspaces is being explored in adaptive beamforming, adaptive filtering, spectrum estimation, and source location estimation problems, as well as in more general nonlinear signal processing algorithms. Determination of appropriate performance criteria for transformation design and tradeoffs between performance and complexity are under investigation. Statistical analysis and simulation are being utilized to analyze the performance of the resulting algorithms.