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首页> 外文期刊>Information Theory, IEEE Transactions on >Error Exponents for Neyman-Pearson Detection of a Continuous-Time Gaussian Markov Process From Regular or Irregular Samples
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Error Exponents for Neyman-Pearson Detection of a Continuous-Time Gaussian Markov Process From Regular or Irregular Samples

机译：用于从规则或不规则样本中进行连续时间高斯马尔可夫过程的Neyman-Pearson检测的误差指数

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摘要

This paper addresses the detection of a stochastic process in noise from a finite sample under various sampling schemes. We consider two hypotheses. The noise only hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables (noise only). The signal plus noise hypothesis models the observations as the samples of a continuous time stationary Gaussian process (the signal) taken at known but random time-instants and corrupted with an additive noise. Two binary tests are considered, depending on which assumptions is retained as the null hypothesis. Assuming that the signal is a linear combination of the solution of a multidimensional stochastic differential equation (SDE), it is shown that the minimum Type II error probability decreases exponentially in the number of samples when the False Alarm probability is fixed. This behavior is described by error exponents that are completely characterized. It turns out that they are related to the asymptotic behavior of the Kalman Filter in random stationary environment, which is studied in this paper. Finally, numerical illustrations of our claims are provided in the context of sensor networks.
机译：本文讨论了在各种采样方案下从有限样本中检测噪声中的随机过程的问题。我们考虑两个假设。仅噪声假设相当于将观测值建模为i.i.d.高斯随机变量（仅噪声）。信号加噪声假设将观察结果建模为连续时间固定的高斯过程（信号）的样本，该过程是在已知但随机的时间瞬间获取的，并被加性噪声破坏。根据保留的原假设，考虑了两个二元检验。假设信号是多维随机微分方程（SDE）的解的线性组合，则表明当固定了虚警概率时，最小II型错误概率在样本数量中呈指数下降。此行为由完全表征的错误指数来描述。事实证明，它们与卡尔曼滤波器在随机平稳环境中的渐近行为有关，本文对此进行了研究。最后，在传感器网络的上下文中提供了我们的权利要求的数字图示。

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