Study on Multi-target Angle Tracking Algorithm of Bistatic MIMO Radar with Unknown Target Number
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摘要: 针对目标个数未知时双基地MIMO雷达角度跟踪问题，该文提出一种基于改进自适应非对称联合对角化(AAJD)的目标个数与角度联合跟踪算法。AAJD算法中无法得到特征值变量，因此改进AAJD算法引入主成分顺序估计思想，循环求出特征值，然后运用改进信息论准则估计出目标个数。其次提出目标个数防抖动算法，提高了稳健性。最后改进了ESPRIT算法，完成了目标参数的自动配对和关联。仿真结果表明改进AAJD算法能够成功跟踪目标个数和角度，验证了理论分析的有效性。Abstract: In order to solve the angle tracking problem of bistatic MIMO radar when the number of target is unknown, a joint tracking algorithm of the number of target and the angle is proposed. There is no variable in Adaptive Asymmetric Joint Diagonalization (AAJD) algorithm that can directly represent the eigenvalue. Therefore, the idea of principal component sequence estimation is introduced to the improved AAJD algorithm, and the eigenvalues are iteratively evaluated. Then, the number of target is estimated by using the improved information theory. Secondly, the anti-dithering algorithm of target number is proposed, which improves the robustness of the algorithm. Finally, the ESPRIT algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the improved AAJD algorithm can successfully track the number of target and angle trajectories. The efficiency of the proposed method is verified.
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表 1 改进AAJD算法流程
初始值： ${{P}}\left( 0 \right) = {{{I}}_{P \times P}}$, $0 < \beta \le 1$, $K$为稳定脉冲数 输入： ${{y}}\left( t \right)$ 输出： $φ \left( t \right),{θ} \left( t \right)$ For $t = 1,2, ·\!·\!· ,T\,$ 步骤 1 for $i = 1,2, ·\!·\!· ,L$ ${d_i}\left( t \right) = {{W}}\!_i\,^{ - 1}\left( {t - 1} \right){{{y}}_i}\left( t \right)$ ${g_i}\left( t \right)\; = \beta {g_i}\left( {t - 1} \right) + {\left| {{d_i}\left( t \right)} \right|^2}$ ${Q_i}\left( t \right) = {{d_i^{*} \left( t \right)} / {{g_i}\left( t \right)}}$ ${\eta _i}\left( t \right) = {{{{\left| {{d_i}\left( t \right)} \right|}^2}} \bigl/ {{g_i}\left( t \right)}}$ ${{{e}}_i}\left( t \right) = {{{y}}_i}\left( t \right) - {{{W}}_i}\left( {t - 1} \right){d_i}\left( t \right)$ ${\widehat{{W}}_i}\left( t \right) = {{{W}}_i}\left( {t - 1} \right) + {1 / {\left( {\beta + {\eta _i}\left( t \right)} \right)}}{{{e}}_i}\left( t \right)Q_i^{}\left( t \right)$ ${{{y}}_{i + 1}}\left( t \right) = {{{y}}_i}\left( t \right) - {\widehat{{W}}}_i^{ - 1}\left( t \right){d_i}\left( t \right)$ end if $t < K$ 对 ${{g}}\!\left( t \right)$进行降序排列，并取最大的 $P$个特征值对应的矢量 构成 ${{W}}\left( t \right)$ else
取前 $P$个特征矢量构成 ${{W}}\!\left( t \right)$end 步骤 2 if $t = = 1$ ${{{Ψ}}_r} = {{W}}\!_{r1}\,\!\!\!^{- 1}{{{W}}\!_{r2}}$, 对 ${{{Ψ}}_r}$进行特征值分解：
${{{Ψ}}_r} = {{T}}{{{Φ}}_r}{{T}}_{}^{ - 1}$，取 ${{{Φ}}_r}$的对角线元素组成 ${{{ω }}_r}$${{{Φ}}_t} = {{{T}}^{ - 1}}{{W}}\!_{t1}\,\!\!\!^{ - 1}{{{W}}\!_{t2}}{{T}}$，取 ${{{Φ}}_t}$的对角线元素组成 ${{{ω }}_t}$ else ${{{Ψ}}_r} = {{W}}\!_{r1}\,\!\!\!^{ - 1}{{{W}}\!_{r2}}$, ${{{Ψ }}_t} = {{W}}\!_{t1}\,^{ - 1}{{{W}}\!_{t2}}$，取 ${{{Ψ}}_r}$和 ${{{Ψ }}_t}$的对角线元 素组成 ${{{ω }}_r}$和 ${{{ω }}_t}$ end 利用 ${\theta _p} = \arcsin \left\{ {{\rm{angle}}\left[ {{{ω}_r}\left( p \right)} \right]/{π} } \right\},$
${\varphi _p} = \arcsin \left\{ {{\rm angle}\left[ {{ω}_r \left( p \right)} \right]/{π} } \right\}$，得到了 ${θ} \left( t \right),φ \left( t \right)$根据 ${{W}}\!\!\left( t \right) \!=\! \left[ {{{{a}}_r}\left( {{\theta _1}} \right) \otimes {{{a}}_t}\left( {{\varphi _1}} \right), ·\!·\!·, {{{a}}_r}\left( {{\theta _P}} \right) \otimes {{{a}}_t}\left( {{\varphi _P}} \right)} \right]$更新 $\widehat{{W}}\!\left( t \right)$ End 
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表 2 目标个数跟踪过程
输入： ${{y}}\left( t \right)$, ${{W}}\left( t \right)$, $P\left( {t - 1} \right)$，稳定脉冲数 $K$ 输出： $P\left( t \right)$ For $i = 1,2, ·\!·\!· ,L$ ${d_i}\left( t \right) = {{W}}_i^{ - 1}\left( t \right){{{y}}_i}\left( t \right)$ ${g_i}\left( t \right)\; = \beta {g_i}\left( {t - 1} \right) + {\left| {{d_i}\left( t \right)} \right|^2}$ ${{{y}}_{i + 1}}\left( t \right) = {{{y}}_i}\left( t \right) - {\widehat{{W}}}_i^{ - 1}\left( t \right){d_i}\left( t \right)$ End If $t < K$, $K$为稳定脉冲数 ${{g}}\!\left( t \right) = {\left[ {{g_1}\!\left( t \right),{g_2}\left( t \right), ·\!·\!· {g_L}\!\left( t \right)} \right]^{\rm{T}}}$ Else 取 ${{g}}\left( t \right) = \left[ {g_1}\!\left( t \right),{g_2}\!\left( t \right), ·\!·\!· ,{g_{P\left( {t - 1} \right)}}\left( t \right),{g_{P\left( {t - 1} \right) + 1}}\left( t \right),\right. $
$\left.{g_N}\left( {t - 1} \right), ·\!·\!· ,{g_N}\left( {t - 1} \right) \right]^{\rm{T}}$End 根据AIC准则估计出 $t$时刻的目标个数 $P\left( t \right)$，注意当 $t > K$只需求 出前 $P\left( {t - 1} \right) + 1$个AIC值，即可得到全局最小值。
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