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首页> 外文期刊>IEEE Transactions on Information Theory >Recursive Distributed Detection for Composite Hypothesis Testing: Nonlinear Observation Models in Additive Gaussian Noise
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Recursive Distributed Detection for Composite Hypothesis Testing: Nonlinear Observation Models in Additive Gaussian Noise

机译：复合假设检验的递归分布式检测：加性高斯噪声中的非线性观测模型

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摘要

This paper studies recursive composite hypothesis testing in a network of sparsely connected agents. The network objective is to test a simple null hypothesis against a composite alternative concerning the state of the field, modeled as a vector of (continuous) unknown parameters determining the parametric family of probability measures induced on the agents’ observation spaces under the hypotheses. Specifically, under the alternative hypothesis, each agent sequentially observes an independent and identically distributed time-series consisting of a (nonlinear) function of the true but unknown parameter corrupted by Gaussian noise, whereas, under the null, they obtain noise only. Two distributed recursive generalized likelihood ratio test type algorithms of the consensus+innovations form are proposed, namely, CIGLRT−L and CIGLRT−NL , in which the agents estimate the underlying parameter and in parallel also update their test decision statistics by simultaneously processing the latest local sensed information and information obtained from neighboring agents. For CIGLRT−NL , for a broad class of nonlinear observation models and under a global observability condition, algorithm parameters which ensure asymptotically decaying probabilities of errors (probability of miss and probability of false detection) are characterized. For CIGLRT−L , a linear observation model is considered and upper bounds on large deviations decay exponent for the error probabilities are obtained.
机译：本文研究稀疏连接的主体网络中的递归复合假设检验。该网络的目标是针对涉及领域状态的复合备选方案测试一个简单的零假设，该虚假假设被建模为（连续）未知参数的向量，这些向量确定了假设下在代理商的观察空间上诱发的概率测度的参数族。具体来说，在替代假设下，每个代理依次观察到一个独立的且分布均匀的时间序列，该时间序列由真实但未知的参数（由高斯噪声破坏）的（非线性）函数组成，而在零值下，它们仅获得噪声。提出了两种共识+创新形式的分布式递归广义似然比测试类型算法，即CIGLRT-L和CIGLRT-NL，其中代理估计基础参数，同时还通过同时处理最新参数来并行更新其测试决策统计信息。本地感知的信息以及从邻近代理获取的信息。对于CIGLRT-NL而言，对于广泛的非线性观测模型以及在全局可观测性条件下，表征了确保误差渐近衰减的概率（未命中概率和错误检测概率）的算法参数。对于CIGLRT-L，考虑线性观测模型，并针对误差概率获得大偏差衰减指数的上限。

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