Distribution of Zero-effort Miss Distance Estimation Errors in Continuous-time Controlled System With Mode Mismatch
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摘要: 针对大机动目标拦截中零控脱靶量（Zero-effort miss distance，ZEM）估计误差分布的求解问题，在线性估计器与独立模式辨识器的配置下，提出了一种解析求解方法.在存在固定的模式辨识延迟下，ZEM的估计误差服从有偏的高斯分布.最后，通过与蒙特卡洛仿真的比较，验证了本文方法的正确性.Abstract: For the problem of solving the error distribution of zero-effort miss distance (ZEM) in highly maneuvering target interception, an analytical approach is proposed for the configuration of a linear estimator and a separate mode decision-maker. In the case of a fixed mode decision delay, the error of ZEM follows a biased Gaussian distribution. Finally, the correctness of the proposed method is verified by comparison with Monte Carlo simulation.1) 本文责任编委 倪茂林
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表 1 仿真参数
Table 1 Simulation parameters
参数类型 参数名称 单位 值(范围) 弹目参数 ${V_p}$ m/s 2 300 ${V_e}$ m/s 2 700 $a_p^{\max}$ g 30 $a_e^{\max}$ g 12, 15 ${\tau _p}$ s 0.2 ${\tau _e}$ s 0.2 观测参数 T s 0.01 ${\sigma _\theta }$ mrad 5 ${\sigma _a }$ $\rm m/{\rm s}^2$ 1 场景参数 $r_0$ m 15 000 ${\phi_p}(0)$ rad 均匀分布($-\pi /18, \pi /18$) ${\phi_e}(0)$ rad $ > \pi /2$且满足碰撞三角形 ${u _p}(0)$ g 0 ${a_p}(0)$ g 0 ${a_e}(0)$ g $a_e^{\max}$ 目标机动方式 - 随机乒乓 估计器参数 $s_w$ $\rm g^2\rm{/Hz}$ 1 $t_{sw}$ s 2 $\Delta t$ s 0.1 初始状态 - ${{\hat {\pmb x}}_0} = {[0, 0, 0, 0]^{\rm T}}$ 初始估计误差 - ${{\tilde {\pmb x}}_0} = {[0, 0, a_e^{\max}, 0]^{\rm T}}$ 初始估计协方差 - ${{{\tilde P}}_0} = \left[{\begin{array}{*{20}{c}} 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 &{{{(a_e^{\max})}^2}}& 0\\ 0 & 0 & 0 & 0 \end{array}} \right]$ 
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符号说明 $P$ 导弹 $E$ 目标 $\tau_p$, $\tau_e$ 导弹和目标控制系统的时间常数 $a_p^{\max}, a_e^{\max}$ 导弹和目标最大横向加速度 ${V_p}, {V_e}$ 导弹和目标的飞行速度 ${u_p}, {u_e}$ 导弹和目标的横向加速度指令 $r$ 弹目相对距离 ${t_{sw}}$ 目标模式切换时刻 $t$ 仿真时间 ${t_f}$ 终止时刻 g 重力加速度, $9.8\rm m/{\rm{s}^2}$ $m$ 目标的运动模式 ${m_1}, {m_2}$ 目标在模式切换时刻前后的运动模式 $\Delta m$ 目标运动模式改变量, $\Delta m = {m_2} - {m_1}$ $T$ 离散采样时间间隔 ${\sigma _\theta }$ 测角精度 ${\sigma _a}$ 导弹加速度测量精度 ${s_w}$ 目标指令加速度误差的功率谱密度 $\Delta t$ 目标运动模式辨识延迟 ${\tilde {\pmb x}}$ 状态估计误差 ${\pmb \xi }, {\Sigma}$ 状态估计误差的均值和方差 $\eta (t)$ ZEM估计误差 $\mu, {\sigma ^2}$ ZEM估计误差的均值和方差
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