In this paper, we solve the optimal target detection problem employing the thoughts and methodologies of Shannon's information theory. Introducing a target state variable into a general radar system model, an equivalent detection channel is derived, and the a posteriori probability distribution is given accordingly. Detection information (DI) is proposed for measuring system performance, which holds for any specific detection method. Moreover, we provide an analytic expression for the false alarm probability concerning the a priori probability. In particular, for a sufficiently large observation interval, the false alarm probability equals the a priori probability of the existing state. A stochastic detection method, the sampling a posteriori probability, is also proposed. The target detection theorem is proved mathematically, which indicates that DI is an achievable theoretical limit of target detection. Specifically, when empirical DI is gained from the sampling a posteriori detection method approaches the DI, the probability of failed decisions tends to be zero. Conversely, there is no detector whose empirical DI is more than DI. Numerical simulations are performed to verify the correctness of the theorems. The results demonstrate that the maximum a posteriori and the Neyman-Pearson detection methods are upper bounded by the theoretical limit.

翻译：本文运用香农信息论的思想与方法解决了最优目标检测问题。通过将目标状态变量引入通用雷达系统模型，推导出等效检测信道，并据此给出后验概率分布。本文提出检测信息（DI）作为衡量系统性能的指标，该指标适用于任何特定检测方法。此外，我们给出了关于先验概率的虚警概率解析表达式。特别地，当观测间隔足够长时，虚警概率等于存在状态的先验概率。还提出了一种随机检测方法——采样后验概率。通过数学证明目标检测定理表明：检测信息是目标检测可达的理论极限。具体而言，当通过采样后验概率检测方法获得的经验检测信息趋近于检测信息时，错误决策概率趋于零；反之，不存在任何检测器的经验检测信息能超过检测信息。通过数值仿真验证了定理的正确性。结果表明，最大后验检测方法与奈曼-皮尔逊检测方法均受此理论极限约束。