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文中以64位Windows 10系统,Intel(R) Core(TM) I7-7500U CPU@2.70 GHz处理器,16 GB内存为实验环境验证文中方法运动估计的有效性。实验源数据来自上海宇航系统工程研究院,采用尼康激光扫描仪获取卫星模型的三维点云,整体尺寸14400 mm×4800 mm×4400 mm。根据空间失稳目标的实际运动情况,实验分别对
${\omega _s} =$ 15~37 (°)/s,${\omega _p} = $ 3~14 (°)/s的空间失稳目标进行运动估计。实验数据采集条件(线阵激光成像雷达参数)如表1所示。Detection distance Imaging Resolution View angle Ranging Precision Angle precision Updating rate Scanning time (once) 50 m 512×512 10°×10° 2 cm 36″ 1 frame/s 500 ms Table 1. Parameters of linear laser imaging radar
这里,采用向量2范数(
$\left\| \cdot \right\|_2$ )计算初始自旋轴、进动轴的估计误差,采用绝对误差($\left| \cdot \right|$ )计算自旋角速度${\omega _s}$ 和进动角速度${\omega _p}$ 的估计误差。 -
当自旋运动较进动显著且帧数选取满足自旋轴绕进动轴旋转一周时,参考文献[15]能够估算出精度较高的运动参数,以这些运动参数为求解初值,能够快速地(平时运行时间<0.25s)收敛到高精度的运动参数。这里,选取实验对象为自旋角速度
${\omega _s} = $ 15~37 (°)/s,进动角速度${\omega _p} = $ 3~10 (°)/s的空间失稳目标,图5给出了文中方法与其他两种解决文中问题方法的运动估计比较结果。Figure 5. Comparisons results of motion estimation among RPM, LGME and our proposed method with initial values close to global solutions. (a), (b), (c) and (d) are the comparisons of estimation errors of initial spin axis, spin angular velocity, precession axis and precession angular velocity under a variety of motion states
RPM方法仅考虑空间失稳目标的自旋运动,这里只给出该方法自旋参数的实验比较结果。如图5所示,RPM方法的运动估计误差是很大的。同时发现,当进动比较剧烈时,LGME方法的运动估计精度仍会受到影响,很难获得高精度的运动估计,而文中方法在该组实验中针对不同运动状态的运动估计均能够达到高精度(<10−4)的估计结果。
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在一般情况下,LGME方法不能保证运动估计的精度,甚至存在远远偏离真实解的情况。为检验文中方法在一般情况下运动估计的有效性,文中对
${\omega _s} = $ 15~37 (°)/s,${\omega _p} =$ 3~14 (°)/s的空间失稳目标采用固定帧数(15帧)给出与RPM、LGME方法的实验比较结果。从图6可以看出,在固定帧数选取方案下,LGME方法的运动估计也出现了严重偏离真实解的情况,充分说明了LGME方法的局限性。而文中方法在固定帧数(15帧)选取方案下对研究背景下所有运动状态均能够达到高精度(<10−5)的运动估计,其平均运行时间<2.62s。
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最后,笔者数值分析了所提方法在线阵成像畸变矫正中的有效性。动态目标线阵成像的畸变是由测量目标与采集设备的相对运动引起的,笔者通过将其他时刻
${t_i}$ 获取的线阵数据归一化到同一时刻,这里称其为基准时刻$T$ ,完成对测量目标的成像畸变矫正。不失一般性,这里设初始采集时刻${t_0}$ 为基准时刻,以点云在基准时刻空间位置的平均估计误差评价畸变矫正效果。图7给出了一般情况固定帧数选取方案下文中方法与RPM、LGME方法在畸变矫正方面的比较结果。Figure 7. Comparisons results of restoration among RPM, LGME and our proposed method under a variety of cases
容易发现,畸变矫正的准确度与运动估计的精度是正相关的,文中方法较其他两种方法在不同运动状态下均获取了最好畸变矫正结果,实现了固定帧数选取方案一般情况下的精准(<10−6)畸变校正。
High-precision motion estimation for instability space targets
doi: 10.3788/IRLA20200104
- Received Date: 2020-04-07
- Rev Recd Date: 2020-06-09
- Available Online: 2021-01-22
- Publish Date: 2021-01-22
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Key words:
- linear measurement /
- instability space targets /
- motion estimation /
- distortion rectification /
- similarity comparison under different selections of frame number
Abstract: Motion estimation is an effective way to rectify the distortion of linear array images of moving target in linear measurement system. However, the non-cooperation and motion complexity of instability space targets make it difficult to precisely estimate their motion parameters. In order to improve the estimation accuracy, a feature-driven high-precision motion estimation for instability space targets was presented. Firstly, a self-constrained motion model of instability space targets by means of the spherical coordinate was established, which transformed the motion estimation into an unconstrained nonlinear optimization problem in high dimensional space. Then, according to the existence and uniqueness of global solutions, an effective way was devised to judge the validity of obtained solutions via comparing the similarity of two solutions calculated via two solving processes under different selections of frame number, which evidently improved the effectiveness and robustness of our method. Finally, the solving efficiency among different non-linear solution methods in the view of our problem was numerically analyzed and an efficient solution scheme in terms of the accuracy of initial values was presented to improve the efficiency of our method. Experimental results illustrate that only needing a maximum of 15 frames of linear array images the estimation accuracy of motion parameters all reach (<10−5) and thus achieve the high performance of rectification for distorted linear array images in our research background.