被动声纳粒子滤波检测前跟踪的检测门限设置方法

doi:10.12263/DZXB.20201274

摘要/Abstract

摘要：

对于粒子滤波检测前跟踪算法，在被动声纳观测量满足指数分布的情况下，本文提出一种按照系统要求的虚警概率设置检测门限的方法.首先，利用贝叶斯定理推导了后验概率比表达式；然后，设置对数后验概率比为检验统计量，通过积分运算离散化处理和Jacobian定理对其进行简化；最后，在不存在目标的情况下分析检验统计量的概率分布特性，得到一定虚警概率要求下检测门限的解析表达式，利用有目标和没有目标情况下观测单元的统计特性差异，证明了在控制虚警概率的同时可以实现对目标的检测.蒙特卡洛仿真结果表明，利用所提的门限设置方法得到的虚警概率与系统要求的虚警概率之间偏差小于0.01，检测概率大于0.95.

关键词: 检测前跟踪, 粒子滤波, 检测门限, 指数分布

Abstract:

This paper proposes a method of determining detection threshold according to the demanded false alarm probability for particle filter track-before-detect, in the case of the passive sonar observables are all exponential distributions. Firstly, the expression of posterior probability ratio is derived based on the Bayesian theorem. Secondly, the logarithmic posterior probability ratio is set as the test statistic, and it is simplified by the discretization of the integral operation and the Jacobian logarithm. Finally, the probability distribution characteristics of the test statistic is analysed in the absence of a target, and the analytical expression of the detection threshold is obtained according to the demanded false alarm probability. Using the difference in statistical characteristics of the observables with and without a target, it is proved that the detection of the target can be achieved while controlling the false alarm probability. The Monte-Carlo simulation results show that using the proposed method, the deviation between the calculated value of false alarm probability and the required value of false alarm probability is less than 0.01 and the detection probability is greater than 0.95.

Key words: track-before-detect, particle filter, detection threshold, exponential distributions

中图分类号:

TN973

奚畅, 蔡志明, 袁骏. 被动声纳粒子滤波检测前跟踪的检测门限设置方法[J]. 电子学报, 2022, 50(7): 1722-1734.

Chang XI, Zhi-ming CAI, Jun YUAN . A Method of Determining Detection Threshold for Particle Filter Track-Before-Detect in Passive Sonar[J]. Acta Electronica Sinica, 2022, 50(7): 1722-1734.

图/表 9

参考文献 29

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虚警概率设置值	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09	0.1
虚警概率计算值	0.014 0	0.025 6	0.036 7	0.048 4	0.058 4	0.068 4	0.078 9	0.087 4	0.096 9	0.106 0
检测概率计算值	0.998 5	0.980 2	0.968 8	0.957 4	0.970 7	0.996 2	0.981 4	0.967 0	0.985 3	0.989 9

虚警概率设置值	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09	0.1
虚警概率计算值	0.014 0	0.025 6	0.036 7	0.048 4	0.058 4	0.068 4	0.078 9	0.087 4	0.096 9	0.106 0
检测概率计算值	0.998 5	0.980 2	0.968 8	0.957 4	0.970 7	0.996 2	0.981 4	0.967 0	0.985 3	0.989 9

虚警概率设置值	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09	0.1
虚警概率计算值	0.016 5	0.025 0	0.040 4	0.053 5	0.059 6	0.067 5	0.068 3	0.083 3	0.092 2	0.102 7
检测概率计算值	0.918 4	0.927 6	0.934 8	0.940 4	0.939 3	0.946 5	0.946 7	0.946 1	0.950 0	0.952 1

虚警概率设置值	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09	0.1
虚警概率计算值	0.016 5	0.025 0	0.040 4	0.053 5	0.059 6	0.067 5	0.068 3	0.083 3	0.092 2	0.102 7
检测概率计算值	0.918 4	0.927 6	0.934 8	0.940 4	0.939 3	0.946 5	0.946 7	0.946 1	0.950 0	0.952 1

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