﻿ 基于DOD和PTD的北斗欺骗式干扰检测技术研究
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 应用科技  2019, Vol. 46 Issue (2): 35-41  DOI: 10.11991/yykj.201807010 0

### 引用本文

ZHANG Guoli, ZHANG Yao, TIAN Ye. Research of Beidou navigation satellite system spoofing detection based on DOD and PTD[J]. Applied Science and Technology, 2019, 46(2), 35-41. DOI: 10.11991/yykj.201807010.

### 文章历史

1. 中国人民解放军92941部队，辽宁 葫芦岛 125000;
2. 哈尔滨工程大学 自动化学院，黑龙江 哈尔滨 150001

Research of Beidou navigation satellite system spoofing detection based on DOD and PTD
ZHANG Guoli1, ZHANG Yao2, TIAN Ye2
1. The People’s Liberation Army 92941 Troops, Huludao 125000, China;
2. College of Automation, Harbin Engineering University, Harbin 150001, China
Abstract: In order to detect spoofing attacks of Beidou navigation signals in the signal-tracking phase, we analyzed Beidou navigation signal system model in the tracking phase, then proposed the spoofing attacks algorithm based on power threshold detection (PTD) and Doppler offset detection (DOD), so as to realize spoofing attacks detection in the tracking phase by Beidou receiver. Simulations were implemented on the platform of Beidou software receiver, proving effectiveness of the proposed algorithm.
Keywords: Beidou satellite navigation system    spoofing attacks    Doppler shift    power threshold detection    carrier-to-noise ratio    detection probability    detection statistics    mobile variance

1 跟踪阶段系统模型分析

1.1 正常接收信号模型

 ${S_{{\rm{IF}}}}(t) = A(t)C(t)D(t)\sin ({\omega _{{\rm{IF}}}}t + {\theta _{{\rm{IF}}}}) + {n_{{\rm{IF}}}}$

 ${S_{{\rm{IF}}}}(t) = A(t)D(t){\rm{sin}}({\omega _{{\rm{IF}}}}t + {\theta _{{\rm{IF}}}}) + {n_{{\rm{IF}}}}$

 ${S_{{L_I}}}(t) = {\rm{sin}}({\omega _L}t + {\theta _L}){\kern 1pt} {\kern 1pt} {\kern 1pt}$
 ${S_{{L_Q}}}(t) = \cos ({\omega _L}t + {\theta _L}){\kern 1pt} {\kern 1pt}$

 \begin{aligned} \;\; {\varepsilon _I} = & A(t)D(t)\frac{{\cos \; {\varphi _1} - \cos {\varphi _2}}}{2} + {n_c}(t)\frac{{\sin \;{\varphi _1} + \sin \;{\varphi _2}}}{2} + \\ \;\; & {n_s}(t)\frac{{\cos \; {\varphi _1} - \cos \; {\varphi _2}}}{2} \end{aligned}
 \begin{aligned} \;\;\;\; {\varepsilon _Q} = & A(t)D(t)\frac{{\sin \; {\varphi _1} - \sin \; {\varphi _2}}}{2} + {n_c}(t)\frac{{\cos \; {\varphi _1} + \cos \; {\varphi _2}}}{2} + \\ \;\;\;\; & {n_s}(t)\frac{{\sin \; {\varphi _1} - \sin \; {\varphi _2}}}{2} \end{aligned}

${\varepsilon _I}$ ${\varepsilon _Q}$ 进行积分，积分时间的长度设置为 $T$ ，假设在积分时间内幅度和数据均不变，则积分后的信号为

 ${S_I}(t) = \frac{{ADT\cos \;{\varphi _1}}}{2} + \frac{{{N_c}\sin \; {\varphi _1}}}{2} + \frac{{{N_s}\cos \; {\varphi _1}}}{2}$
 ${S_Q}(t) = \frac{{ADT\sin \;{\varphi _1}}}{2} + \frac{{{N_c}\cos \; {\varphi _1}}}{2} + \frac{{{N_s}\sin \; {\varphi _1}}}{2}$

1.2 欺骗信号入侵后的接收信号模型

 ${S_S}(t) = {A_S}(t){C_S}(t){D_S}(t){\rm sin}({\omega _S}t + {\theta _S})$

 $S(t) = {S_{{\rm{IF}}}}(t) + {S_S}(t)$

 $S(t) = C(t)D(t){A_M}(t){\rm cos}({\omega _{IF}}t + {\theta _M}) + n(t)$

2 跟踪阶段欺骗检测方法设计

2.1 信号功率异常检测算法设计

 \begin{aligned} \sigma _{MV}^2 =& \frac{1}{W}\sum\nolimits_{k = n - W + 1}^n {{{[x(k) - \overline {x(n)} ]}^2}} - \overline {x(n)} = \\ & \overline {{x^2}(n)} - \overline {x(n)} \end{aligned}

2.2 多普勒频移异常检测算法设计

 ${f_r} = {f_c}(1 - \frac{{a{v_r}}}{c})$

3 仿真实验

 ${p_{\rm df}}(x) = \frac{1}{{x\sigma \sqrt {2{\rm{{\text{π} }}}} }}\exp ( - \left( {\log (x) - \mu } \right)/2{\sigma ^2})$
 $c_{\rm df}(x) = \frac{1}{2} + \frac{1}{2}{\rm erf}\left[ {\frac{{\ln (x) - \mu }}{{\sqrt {2{\sigma ^2}} }}} \right]$

 ${P_{\rm fa}} = P_{\rm fa}^{\rm PTD} \cdot P_{\rm fa}^{\rm DOD} = 2.271\;3 \times {10^{ - 8}}$