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On Minimax Robust Detection of Stationary Gaussian Signals in White Gaussian Noise

机译：高斯白噪声中平稳高斯信号的最小极大鲁棒检测

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摘要

The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, in which the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a Neyman–Pearson criterion with a fixed false alarm probability, as the length of the observation interval grows without bound. A stochastic suppression condition is identified for the uncertainty set of spectral density functions, and it is established that, under the stochastic suppression condition, the resulting minimax problem possesses a saddle point, which is achievable by the likelihood ratio tests matched to a so-called suppressing power spectral density in the uncertainty set. No convexity condition on the uncertainty set is required to establish this result.
机译：研究了检测嵌入在高斯白噪声中的广义高斯平稳信号过程的问题，在该过程中信号过程的功率谱密度呈现不确定性。最小极大鲁棒检测的性能特征在于，随着观察间隔的长度无限制地增长，在Neyman–Pearson准则下具有固定误报概率的未命中概率的指数衰减率。对于频谱密度函数的不确定性集合，确定了一个随机抑制条件，并确定在该随机抑制条件下，所得的极小极大问题具有一个鞍点，这可以通过与所谓的似然比检验匹配来实现。抑制不确定度集中的功率谱密度。无需不确定性集上的凸度条件即可建立该结果。

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