High Frequency Surface Wave Radar Detector Based on Log-determinant Divergence and Symmetrized Log-determinant Divergence
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摘要: 高频地波雷达(HFSWR)利用电磁波绕射原理进行目标探测，具有超视距的特性。然而，探测距离的增加会使得雷达目标回波能量减弱，进而使得雷达探测能力下降。为了改善高频地波雷达的探测性能，该文提出了一种基于信息几何理论的局域联合矩阵恒虚警率(CFAR)检测器，利用信号在角度、多普勒速度和距离的多维信息进行检测；并使用对数行列式散度(LDD)和对称对数行列式散度(SLDD)代替黎曼距离(RD)作为距离度量。最后，实验结果验证了该文提出的检测器能够有效地改善雷达对目标的检测性能。Abstract: High Frequency Surface Wave Radar (HFSWR) utilizes electromagnetic wave diffracting along the earth to detect targets over the horizon. However, the increase of target distance decreases the received echo energy, and this degrades the detection capability. A joint domain matrix Constant False Alarm Rate (CFAR) detector is proposed to improve the detection performance. It employs the multi-dimensional information of signal in azimuth, Doppler velocity and range domain to detect target, and Log-Determinant Divergence (LDD) and Symmetrized Log-Determinant Divergence (SLDD) are used to replace the Riemannian Distance (RD) as the measure of distance. Finally, the experiment results show that the detector presented by the paper can improve the detection performance effectively.
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表 1 不同距离度量方法及其几何均值
度量方法 距离计算 几何均值 RD ${{{D}}_R}^2({{{R}}_1},{{{R}}_2}) = {\rm{tr}}[{\lg ^2}({{{R}}_1}^{ - 1/2}{{{R}}_2}{{{R}}_1}^{ - 1/2})] $ ${\bar {{R}}_{t + 1}} = \bar {{R}}_t^{1/2}\exp \left[{\rm{ds}} \cdot \frac{1}{N}\mathop \displaystyle\sum \limits_{i = 1}^N \lg (\bar {{R}}_t^{ - 1/2}{{{R}}_i}\bar {{R}}_t^{ - 1/2})\right]\bar {{R}}_t^{1/2}$ LDD ${{{D}}_{\rm{LD}}}({{{R}}_1},{{{R}}_2}) = {\rm{tr}}({{R}}_2^{ - 1}({{{R}}_1} - {{{R}}_2})) - \ln \det({{R}}_2^{ - 1}{{{R}}_1})$ $\bar {{R}} = {\left( {\frac{1}{N}\mathop \sum \limits_{k = 1}^N {{R}}_k^{ - 1}} \right)^{ - 1}}$ SLDD $\begin{aligned} {{{D}}_{{\rm{SLD}}}}({{{R}}_1},{{{R}}_2}) =& \frac{1}{2}({\rm{tr}}({{R}}_2^{ - 1}({{{R}}_1} - {{{R}}_2})) - \ln \det({{R}}_2^{ - 1}{{{R}}_1}) \\ & + {\rm{tr}}({{R}}_1^{ - 1}({{{R}}_2} - {{{R}}_1})) - \ln \det({{R}}_1^{ - 1}{{{R}}_2})) \\ \end{aligned} $ $\bar {{R}} = {\left( {\frac{1}{N}\mathop \sum \limits_{k = 1}^N {{R}}_k^{ - 1}} \right)^{ - 1}}$ 
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表 2 基本矩阵运算的复杂度
矩阵运算 表达式 浮点数计算次数 矩阵运算 表达式 浮点数计算次数 矩阵乘法 ${{{R}}_1}{{{R}}_2}$ $8{n^3} - 2{n^2}$ 矩阵求逆 ${{R}}_1^{ - 1}$ $8{n^3} - 2{n^2}$ 矩阵加法 ${{{R}}_1}{{ + }}{{{R}}_2}$ $2{n^2}$ 矩阵开方 ${{R}}_1^{1/2}$ $24{n^3} + 2{n^2} - 8n$ 矩阵的迹 ${\rm{tr}}({{{R}}_1})$ $8{n^2} - 6n - 2$ 矩阵指数 $\exp ({{{R}}_1})$ ${n^4}/2 + 24{n^3} + 1.5{n^2} - n$ 矩阵行列式 $\det ({{{R}}_1})$ $8{n^2} - 2n - 6$ 矩阵对数 $\lg ({{{R}}_1})$ ${n^4}/2 + 25{n^3} + {n^2} - 1.5n$
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表 3 不同距离度量方法的复杂度
度量方法 距离计算复杂度 几何均值计算复杂度 RD ${n^4}/2 + 73{n^3} + 5{n^2} - 15.5n - 1$ $(N + 1){n^4}/2 + (41N + 88){n^3} - (N + 6.5){n^2} - (1.5N + 9)n$ LDD $16{n^3} + 14{n^2} - 8n - 6$ $8(N + 1){n^3} - 2{n^2}$ SLDD $32{n^3} + 28{n^2} - 15n - 11$ $8(N + 1){n^3} - 2{n^2}$
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