Novel Adaptive Filtering Techniques for Multidimensional Signals

多维信号的新颖自适应滤波技术

• 批准号: EP/H026266/1
• 负责人: Danilo Mandic
• 金额: $ 42.03万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH026266%2F1
• 关键词: Novel; Adaptive; Filtering; Techniques; Multidimensional

This proposal seeks to develop a rigorous theoretical and computational framework for statistical signal processing of three- and four-dimensional real world signals. This will be achieved in the quaternion domain, benefiting from its division algebra, and thus promising a quantum improvement in the modelling of such signals. Particular emphasis will be on solutions for adaptive signal processing problems, whose accuracy will be enhanced through the use of quaternion statistics and the associated special forms of correlation- and eigen-structures. Current algorithms are less than adequate for the very large class of processes with noncircular (rotation dependent) probability distributions, and for signals whose components exhibit coupling and large unbalanced dynamics; these are common in array signal processing, wind modelling, motion tracking, and chaos engineering.The proposed research will enable unified modelling of three- and four-dimensional signals, together with better understanding of the associated nonlinear dynamics and geometry of learning, and will also serve as a framework for simultaneous modelling of heterogeneous data sources. The fundamental novelty of this work is our recently proposed quaternion least mean square (QLMS) algorithm, which makes full use of quaternion algebra, and thus allows for additional degrees of freedom and enhanced accuracy in the modelling of real world phenomena. This will also serve as a framework to design a suite of novel adaptive filtering and tracking algorithms, based on both standard and widely linear models, which will be suitable to deal with the generality of quaternion valued signals. Comprehensive theoretical evaluation and practical testing will be performed in order to prove the worthwhileness of the proposed approach. Practical applications considered will be short term wind forecasting in renewable energy and trajectory tracking from motion sensors in smart environments; particular gains are expected when dealing with large and intermittent dynamics at multiple scales (turbulence, gusts, multiple coupled rotation trajectories).This research proposal, based at Imperial College and in collaboration with an internationally leading research group from University of Tokyo Japan, will find solutions to these problems and will also open new possibilities for advances in a number of emerging areas dealing with uncertainty, complexity and multidimensional data natures.

该建议旨在为三维和四维真实的世界信号的统计信号处理开发一个严格的理论和计算框架。这将在四元数域中实现，受益于其除法代数，从而有望在此类信号的建模中实现量子改进。特别强调的是自适应信号处理问题的解决方案，其准确性将通过使用四元数统计和相关的特殊形式的相关性和本征结构得到提高。目前的算法是不够的，为非常大的一类过程的非循环（旋转相关的）概率分布，以及其分量表现出耦合和大的不平衡动态的信号;这些在阵列信号处理、风建模、运动跟踪和混沌工程中是常见的。拟议的研究将使三维和四维信号的统一建模成为可能，以及更好地理解相关的非线性动力学和几何学的学习，也将作为一个框架，同时建模的异构数据源。这项工作的基本新奇是我们最近提出的四元数最小均方（QLMS）算法，它充分利用四元数代数，从而允许额外的自由度和提高精度的建模真实的世界现象。这也将作为一个框架，设计一套新的自适应滤波和跟踪算法，基于标准和广泛的线性模型，这将是适合于处理的四元数值信号的一般性。为了证明所提出的方法的可行性，将进行全面的理论评估和实际测试。考虑的实际应用将是可再生能源的短期风预测和智能环境中运动传感器的轨迹跟踪;当处理多尺度的大的和间歇性的动态时，预期会有特别的收获（湍流，阵风，多个耦合旋转轨迹）。这项研究计划，基于帝国理工学院，并与日本东京大学的国际领先研究小组合作，将为这些问题找到解决方案，并将为处理不确定性，复杂性和多维数据性质的一些新兴领域的进步开辟新的可能性。