一种简易的雷达多目标参数提取方法

摘要

一种简易的雷达多目标参数提取方法，D＝3个目标，当目标数多于3个时，可仿照写出类似(3)和(4)的公式，只是表达式更冗长，具体包括以下步骤：步骤1)，估计信号方位初始参数，i从1到D，D代表信号序数，假设D＝3，对于i＝1，计算得到估计目标方位参数初始值i从1到3；步骤2)，主迭代循环，根据步骤1)获得的初始参数估计i从1到3；获得他们的精确估计；步骤3)，对于步骤2)得到的精确估计i从1到3，利用式(4)和式(8)计算和得到3个目标波形参数估计，为目标定位、波形辨识提供参数依据；当目标个数D≥3时，借助于已有表达式如和下面的矩阵求逆迭代运算关系就写出相应矩阵Q_i及投影矩阵算符的表达式；从根本上降低其运算复杂度且规避求逆时误差。

主权项

一种简易的雷达多目标参数提取方法，D＝3个目标，当目标数多于3个时，可仿照(3)、(4)式的推导原理写出类似(3)和(4)的公式，只是表达式更冗长，具体包括以下步骤：步骤1)，估计信号方位初始参数，i从1到D，D代表信号序数，假设D＝3，对于i＝1，计算$P_{a\left({\theta }_1^{\left(0\right)}\right)}=I,b=(\theta ,{\theta }_0^{\left(0\right)})=a\left(\theta \right),$利用公式：${\hat{\theta }}_1^{\left(0\right)}=\arg {\max }_{\theta }\left\{b^H(\theta ,{\theta }_0^{\left(0\right)}\hat{R}b(\theta ,{\theta }_0^{\left(0\right)}))\right\}---\left(5\right)$得对于i＝2，令$A\left({\Theta }_1^{\left(0\right)}\right)=a\left({\hat{\theta }}_1^{\left(0\right)}\right),P_{A\left({\Theta }_1\right)}=a\left({\hat{\theta }}_1^{\left(0\right)}\right)a^H\left({\hat{\theta }}_1^{\left(0\right)}\right),$$b(\theta ,{\theta }_1^{\left(0\right)})=P_{A\left({\Theta }_1\right)}a\left(\theta \right)/\left|\right|P_{A\left({\Theta }_1\right)}a\left(\theta \right)\left|\right|;$利用公式${\hat{\theta }}_2^{\left(0\right)}=\arg {\max }_{\theta }\left\{b^H(\theta ,{\theta }_1^{\left(0\right)})\hat{R}b(\theta ,{\theta }_1^{\left(0\right)})\right\}---\left(6\right)$得对于i＝3，令$a_1=a\left({\hat{\theta }}_1^{\left(0\right)}\right),a_2=a\left({\hat{\theta }}_2^{\left(0\right)}\right),b=(\theta ,{\Theta }_2^{\left(0\right)})=P_{A\left({\Theta }_2\right)}a\left(\theta \right)/\left|\right|P_{A\left({\Theta }_2\right)}a\left(\theta \right)\left|\right|,$原始信号方位参数搜索方法中采用公式(3)计算；常数利用公式：${\hat{\theta }}_3^{\left(0\right)}={\arg \max }_{\theta }\left\{b^H(\theta ,{\Theta }_2^{\left(0\right)})\hat{R}b(\theta ,{\Theta }_2^{\left(0\right)})\right\}---\left(7\right)$得得到估计目标方位参数初始值i从1到3；步骤2)，主迭代循环，根据步骤1)获得的初始参数估计i从1到3；为获得他们的精确估计，具体做法是，利用下列公式进行循环移位赋值变换获得新的目标方位参数i从1到3；循环直到对于所有i从1到3，式中：ε是预先设定的一个门限值，k是迭代次数；对于i＝1，令$A\left({\Theta }_1^{\left(k\right)}\right)=[a\left({\hat{\theta }}_2^{\left(k\right)}\right),a\left({\hat{\theta }}_3^{\left(k\right)}\right)],P_{A\left({\Theta }_1^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$原始信号方位参数搜索方法中用公式(3)计算，$b(\theta ,{\Theta }_1^{\left(k\right)})=P_{A\left({\Theta }_1^{\left(k\right)}\right)}a\left(\theta \right)/\left|\right|P_{A\left({\Theta }_1^{\left(k\right)}\right)}a\left(\theta \right)\left|\right|,$利用公式${\hat{\theta }}_1^{(k+1)}=\arg {\max }_{\theta }\left\{b^H(\theta ,{\Theta }_1^{\left(k\right)}\hat{R}b(\theta ,{\Theta }_1^{\left(k\right)}))\right\}---\left(5\right)$得目标1的方位较精确估计对于i＝2，令$A\left({\Theta }_2^{\left(k\right)}\right)=[a\left({\hat{\theta }}_1^{(k+1)}\right),a\left({\hat{\theta }}_3^{\left(k\right)}\right)],P_{A\left({\Theta }_2^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$即令$a_2=a\left({\hat{\theta }}_1^{(k+1)}\right),a_3=a\left({\hat{\theta }}_3^{\left(k\right)}\right)$代入公式(3)，$b(\theta ,{\Theta }_2^{\left(k\right)})=P_{A\left({\Theta }_2^{\left(k\right)}\right)}a\left(\theta \right)/\left|\right|P_{A\left({\Theta }_2^{\left(k\right)}\right)}a\left(\theta \right)\left|\right|,$利用公式${\hat{\theta }}_2^{(k+1)}={\arg \max }_{\theta }\left\{b^H(\theta ,{\Theta }_2^{\left(k\right)}\hat{R}b(\theta ,{\Theta }_2^{\left(k\right)}))\right\}---\left(6\right)$得目标2的方位较精确估计对于i＝3，令$A\left({\Theta }_3^{\left(k\right)}\right)=[a\left({\hat{\theta }}_1^{(k+1)}\right),a\left({\hat{\theta }}_2^{(k+1)}\right)],P_{A\left({\Theta }_3^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$即令$a_2=a\left({\hat{\theta }}_2^{(k+1)}\right),$$a_3=a\left({\hat{\theta }}_1^{(k+1)}\right)$代入公式(3)，$b(\theta ,{\Theta }_3^{\left(k\right)})=P_{A\left({\Theta }_3^{\left(k\right)}\right)}a\left(\theta \right)/\left|\right|P_{A\left({\Theta }_3^{\left(k\right)}\right)}a\left(\theta \right)\left|\right|,$利用公式${\hat{\theta }}_3^{(k+1)}=\arg {\max }_{\theta }\left\{b^H(\theta ,{\Theta }_3^{\left(k\right)})\hat{R}b(\theta ,{\Theta }_3^{\left(k\right)})\right\}---\left(7\right)$得目标3的方位较精确估计步骤3)，对于步骤2)得到的精确估计i从1到3，利用式(4)和式(8)计算${\left[A^H\left(\hat{\Theta }\right)A\right]\left(\hat{\Theta }\right)}^{-1}{A}^H\left(\hat{\Theta }\right),$和$\hat{s}\left(t\right)={\left[A^H\left(\hat{\Theta }\right)A\left(\hat{\Theta }\right)\right]}^{-1}{A}^H\left(\hat{\Theta }\right)y\left(t\right),$得到3个目标波形参数估计，为目标定位、波形辨识提供参数依据；当目标个数D≥3时，借助于已有表达式如和下面的矩阵求逆迭代运算关系$(H_{\left(D\right)}^{-1}=[A^H({\theta }_1,{\theta }_2,...,{\theta }_D)A({\theta }_1,{\theta }_2,...,{\theta }_D){]}^{-1}),$$H_{\left(D\right)}^{-1}{A}_D^H=\left[\begin{array}{c}{D}_{(D-1)}^{-1}{A}_{D-1}^H+{\beta }_D{H}_{(D-1)}^{-1}{A}_{D-1}^H{A}_D{a}_H^D{A}_{D-1}{A}_{(D-1)}^{-1}{A}_{D-1}^H-{\beta }_D{H}_{(D-1)}^{-1}{A}_{D-1}^H{a}_D{a}_H^D\\ {-\beta }_D{a}_D^H{A}_{D-1}{H}_{(D-1)}^H{A}_{D-1}^H+{\beta }_D{a}_D^H\end{array}\right]---\left(8\right)$就可以完整地写出相应矩阵Q_i及投影矩阵算符的表达式。