Robust detection and tracking algorithms for time reversal matched field processing

在时间反转、匹配场处理（TR/MFP）中，传输到环境中的信号的反向散射被记录、延迟、能量归一化，并重新传输到介质中。TR/MFP提供了传统检测器的替代方案，例如一维信号处理中的匹配滤波器和多维匹配场处理（MFP）。MFP的难点在于，用于对通道进行建模的格林函数是未知的，因此，必须通过数值计算。根据其固有的性质，只要接收换能器阵列提供足够的通道采样，TR/MFP本质上派生通道的格林函数。TR/MFP的第二个优点在于对信道多径的有效处理。众所周知，多路径严重影响传统探测器的性能，被认为是有害的和负面的，其影响应尽量减少。《TR/MFP》呈现了相反的机会：多路径是积极的，越多越好。虽然TR/MFP技术并不新颖，但缺乏对这种情况的彻底检测理论。我们的初步工作解决了这一差距，并分析地证明了我们认为是第一次用TR/MFP观察到的超分辨率聚焦现象。在本提案中，我们试图进一步扩展这一分析，以提供以下问题的定量答案：TR/MFP如何用于经典信号处理应用，例如：(i)在丰富的杂波环境中进行目标检测；（ii）通过某种形式的空分多址（SDMA），在无线通信中提高信道容量并使之均衡；（三）反层析问题，以确定通道特征，仅举几例。我们还将研究TR/MFP在目标定位、跟踪和识别方面有多好？TR/MFP的基本限制是什么？为了获得准确的TR/MFP，信道必须有多稳定？

In time reversal, matched field processing (TR/MFP), the backscatter of a signal transmitted into an environment is recorded, delayed, energy normalized, and retransmitted into the medium. TR/MFP offers an alternative to traditional detectors, e.g. the matched filter in one dimensional signal processing and the matched field processing (MFP) in multidimensions. The difficulty with MFP is that the Green's function used to model the channel is not known and, therefore, has to be computed numerically. By its inherent nature, TR/MFP intrinsically derives the Green's function of the channel as long as the receiving transducer array provides an adequate sampling of the channel. A second advantage of TR/MFP lies in the productive treatment of the channel multipaths. As is generally known, multipath significantly affects the performance of traditional detectors and is considered to be a detrimental and a negative whose effects should be minimized. TR/MFP presents the opposite opportunity: multipath as a positive, the more the better. Though the technique of TR/MFP is not new, but a thorough theory of detection for this setting is lacking. Our initial work addresses this gap and proves analytically, we believe for the first time, the phenomena of super resolution focusing observed with TR/MFP. In this proposal, we seek to extend this analysis further to provide quantitative answers to the following questions: How can TR/MFP be used in classical signal processing applications, such as: (i) target detection in a rich cluttering environment; (ii) channel capacity enhancement and equalization in wireless communications by some form of space division multiple access (SDMA); and (iii) inverse tomographic problems to determine channel characteristics, to name a few. We will also investigate how good TR/MFP is for target localization, tracking, and identification? What are the fundamental limits of TR/MFP? How stationary does the channel have to be for accurate TR/MFP?