arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2201.04342cs.ITmath.IT
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雷达目标联合检测与估计的理论界限

Theoretical Limits of Joint Detection and Estimation for Radar Target

Nan Wang, Dazhuan Xu

摘要:

提出了一种基于互信息的雷达联合检测与估计(JDE)方案,其目标是在目标存在和目标不存在之间选择真实的目标,并在目标存在时估计未知的距离参数。受Shannon信息论思想的启发,建立了复高斯白噪声环境下的JDE系统模型。本文的主要工作有:(1)根据噪声、目标散射和联合目标参数的先验统计特性,推导了联合估计估计的等效信道和后验概率密度函数,(2)用联合熵偏差和联合信息(定义为接收信号与联合目标参数之间的互信息)来衡量联合估计估计系统的性能,(3)用联合熵偏差和联合信息来衡量联合估计系统的性能。(3)提出了抽样后验概率和级联JDEer,并通过经验联合熵与经验联合信息的偏差来衡量其性能:(4)证明了联合信息是整体性能的可用极限,即联合信息是可用的,且任一JDEer的经验联合信息不大于联合信息;(5)级联定理证明了经验检测信息与经验估计信息之和可以逼近联合信息,即,级联JDEer的性能极限是可用的。仿真结果验证了联合定理和级联定理的正确性,并表明采样后验概率JDEer的性能是渐近最优的。此外,级联的JDEer的性能可以接近JDE系统的系统性能。

英文摘要:

This paper proposes a joint detection and estimation (JDE) scheme based on mutual information for the radar work, whose goal is to choose the true one between target existent and target absence, and to estimate the unknown distance parameter when the target is existent. Inspired by the thoughts of Shannon information theory, the JDE system model is established in the presence of complex white Gaussian noise. We make several main contributions: (1) the equivalent JDE channel and the posterior probability density function are derived based on the priori statistical characteristic of the noise, target scattering and joint target parameter; (2) the performance of the JDE system is measured by the joint entropy deviation and the joint information that is defined as the mutual information between received signal and the joint target parameter; (3) the sampling a posterior probability and cascaded JDEers are proposed, and their performance is measured by the empirical joint entropy deviation the empirical joint information; (4) the joint theorem is proved that the joint information is the available limit of the overall performance, that is, the joint information is available, and the empirical joint information of any JDEer is no greater than the joint information; (5) the cascaded theorem is proved that the sum of empirical detection information and empirical estimation information can approximate the joint information, i.e., the performance limit of cascaded JDEer is available. Simulation results verify the correctness of the joint and the cascaded theorems, and show that the performance of the sampling a posterior probability JDEer is asymptotically optimal. Moreover, the performance of cascaded JDEer can approximate the system performance of JDE system.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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