A General Theory for Distributed Signal Detection

噪声中信号的检测是许多实际信号处理和通信系统的关键任务。通过使用在多个传感器上进行的观测可以获得的性能收益是众所周知的。然而，通常将每个传感器产生的所有数据传输到某个中央位置以用于做出信号检测决策的成本太高。因此，研究分布式检测方案是非常有意义的，它在提供可接受的性能的同时只需要有限的传输。对于相关观测情况下的分布式信号检测方案的研究一直很缺乏。这个项目的目标是为理解分布式检测方案奠定理论基础，这些方案适用于具有从传感器到传感器的依赖观测的情况。该理论将预测何时最优分布式处理方案将不同于最优隔离传感器处理方案。这一理论也将解释为什么会发生这种情况。这种方法在很大程度上依赖于我们已经开发的弱信号结果和最近的初步结果。具体地说，我们试图用已知函数和未知常数来表示最优传感器处理，就像我们在弱信号情况下所做的那样。使用这种表示法应该能够确定最佳隔离传感器处理何时是最佳的，并解释为什么最佳隔离传感器处理在某些情况下不是最佳的。虽然重点是发展急需的理论，但结果将立即在许多应用中有用。此外，一些重点是致力于开发设计算法和研究非参数分布式检测方案，用于不确定统计模型的情况。这样的研究将产生解决实际问题的工具和技术。

The detection of signals in noise is a critical task for a number of practical signal processing and communication systems. The performance gains that can be achieved by using observations taken at multiple sensors are well known. However, generally is too costly to transmit all the data generated by each sensor to some central location to use in making a signal detection decision. It is therefore of great interest to study distributed detection schemes, which provide acceptable performance while requiring only limited transmissions. Research on distributed signal detection schemes for cases with dependent observations has been lacking. The goal of this project is to develop the foundation of a theory for understanding distributed detection schemes for cases with dependent observations from sensor to sensor. The theory will predict when the optimum distributed processing schemes will be different from the optimum isolated sensor processing schemes. The theory will also explain why this occurs. The approach draws heavily on weak-signal results we have already developed and on recent preliminary results. Specifically, we are attempting to represent the optimum sensor processing in terms of known functions and unknown constants, as we have done in the weak signal cases. Using such a representation should allow one to determine when the optimum isolated sensor processings will be optimum and to explain why the optimum isolated sensor processings are not optimum in some cases. While the focus is on developing much needed theory, the results will be immediately useful in many applications. Furthermore, some emphasis is being devoted to developing design algorithms and to the study of nonparametric distributed detection schemes for cases with uncertain statistical models. Such studies will produce tools and techniques for pressing practical problems.