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。提出用于衡量系统性能的检测信息（DI），该方法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，当观测间隔足够大时，虚警概率等于存在状态的先验概率。本文还提出了一种随机检测方法——采样后验概率。通过数学证明的目标检测定理表明，DI是目标检测可达的理论极限。具体而言，当从采样后验检测方法获得的经验DI趋近于DI时，决策失败概率趋于零；反之，不存在任何检测器能使经验DI超过DI。数值仿真验证了定理的正确性，结果表明最大后验检测法和奈曼-皮尔逊检测法均受限于该理论极限。