基于连续信任函数理论的鲁棒雷达目标检测方法

doi:10.12305/j.issn.1001-506X.2021.09.12

Abstract

Abstract:

Target detection is the basic function of radar, and its robustness directly determines the success or failure of radar application. Aiming at the problem of Rayleigh target detection, a robust radar target detection method is proposed by making full use of the advantages of continuous belief function theory in uncertain information representation and reasoning. The belief of prior model noise, real target and external interference can be quantified accurately in the detection decision space. In view of the fact that the proposed method does not have analytical solution, through the transformation of random variables, the arbitrary Rayleigh target amplitude fluctuation model is transformed into the standard Rayleigh model.And then, the numerical calculation of the belief function is realized by using the look-up table method. Finally, the detection decision is completed or used for subsequent fusion reasoning. Rayleigh target detection experiments verify the robustness of the proposed method.

Key words: radar target detection, Rayleigh target amplitude fluctuation model, continuous belief function theory

CLC Number:

TN951

Wei YANG, Yongxiang LIU, Yaowen FU, Xiang LI. Robust radar target detection method based on continuous belief function theory[J]. Systems Engineering and Electronics, 2021, 43(9): 2463-2469.

Figures/Tables 7

Fig.1

Table 1

Table 2

Robust radar target detection algorithm based on trust function theory"

步骤	操作	备注
先验信息	标准瑞利概率密度函数的等投注概率表	根据应用需求选择近似精度
步骤1	获得点观测z∈R⁺	雷达幅度观测
步骤2	当$ z\ge \sqrt{{\bar{\sigma }}}$时, 对$ \forall \theta_{c} \in \Theta$, 按照式(17)计算条件观测似然函数: $\text{p}{{\text{l}}^{\bf{R}}}\left[ {{\theta }_{c}} \right](z)\approx \sum\limits_{{{\eta }_{i}}=\frac{z}{\sqrt{{\bar{\sigma }}}}, \Delta \eta >0}^{\text{CO}{{\text{V}}_{\text{rls}}}}{2}\left[ \bar{\gamma }\left( {{\eta }_{i}} \right)-{{\eta }_{i}} \right]\left( 1-2\eta _{i}^{2} \right)\exp \left( -\eta _{i}^{2} \right)\Delta \eta $	定理1
步骤2	当$ z <\sqrt{{\bar{\sigma }}}$时, 对$ \forall \theta_{c} \in \Theta$, 按照式(17)~式(20)计算条件观测似然函数: $\text{p}{{\text{l}}^{\bf{R}}}\left[ {{\theta }_{c}} \right](z)\approx \sum\limits_{{{\eta }_{i}}={{{\bar{\gamma }}}^{-1}}\left( \frac{z}{\sqrt{{\bar{\sigma }}}} \right), \Delta \eta >0}^{\text{CO}{{\text{V}}_{\text{rls}}}}{2}\left[ \bar{\gamma }\left( {{\eta }_{i}} \right)-{{\eta }_{i}} \right]\left( 1-2\eta _{i}^{2} \right)\exp \left( -\eta _{i}^{2} \right)\Delta \eta $	定理1
步骤3	对$ \forall S \subset \Theta, m^{\Theta}[z](S)=\prod\limits_{\left\{\theta_{c} \mid \theta_{c} \in S\right\}} \mathrm{p} l^{\bf{R}}\left[\theta_{c}\right](z) \prod\limits_{\left\{\theta_{d} \mid \theta_{d} \in \bar{S}\right\}}\left\{1-\mathrm{pl}^{\bf{R}}\left[\theta_{d}\right](z)\right\}$	GBT
步骤4	对$ \forall \theta_{c} \in \Theta$, 计算投注概率值$\operatorname{BetP}[z]\left(\theta_{c}\right)=\sum\limits_{\left\{S \mid \theta_{c} \subset S\right\}} \frac{m^{\Theta}[z](S)}{\left\{1-m^{\Theta}[z](\phi)\right\}\|S\|} $	投注概率计算
步骤5	用于决策硬判决时, 选择最大投注概率假设$ \theta_{d}=\arg \max \limits_{\forall \theta_{c} \in \Theta} \operatorname{Bet} \mathrm{P}[z]\left(\theta_{c}\right)$；或将m^Θ[z](S)和BetP[z](θ_c)输出给下一级, 待进一步融合后决策。	参考文献[27]

Table 2

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$\bar{\gamma }\left( {{u}_{i}} \right) $	u_i	p^rls(u_i)	$\bar{\gamma }\left( {{u}_{i}} \right) $	u_i	p^rls(u_i)
0.05	1.91	0.099 8	0.45	1.00	0.735 0
0.10	1.68	0.198 0	0.50	0.94	0.778 8
0.15	1.53	0.293 1	0.55	0.88	0.812 9
0.20	1.41	0.384 3	0.60	0.82	0.837 2
0.25	1.31	0.469 7	0.65	0.77	0.852 0
0.30	1.22	0.548 4	0.70	0.71	0.857 7
0.35	1.14	0.619 3	⋮	⋮	⋮
0.40	1.07	0.681 7

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Robust radar target detection method based on continuous belief function theory

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