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卫星激光测距在经过多年的发展之后,其定轨和预报的精度已经达到米级,而对于一些形状比较规整的目标定轨精度可以达到厘米级,这为提高距离门的精度提供了有利条件[14]。距离门控的计算实际上就是通过计算机对目标卫星的轨道进行预报,并根据预报结果计算出激光在观测站和卫星之间的飞行时间,从而确定单光子信号探测器的打开时刻,进而准确地接收回波。由于预报过程中需要不断地更新数据,导致数据传输以及计算本身都需要面对巨大压力。
为此,在官方预报的星历中通常按一定时间间隔给出在地固坐标系下的卫星坐标来减少数据量[15],例如,卫星ajisai的星历每30 s给出一组坐标,卫星lageos1的星历每60 s给出一组坐标,卫星glonass105的星历每900 s给出一组坐标,但是,按间隔给出的预报时刻数量无法满足测距的要求,所以在获得预报数据后,还需利用多项式拟合的方法,拟合出预报间隔内公的距离门长度,这样才能达到高频率激光测距所需要的预报数量,多项式的一般形式如公式(1)所示:
$$ {{y}} = {{{p}}_{{0}}}{{{x}}^{{n}}} + {{{p}}_{{1}}}{{{x}}^{{{n}- 1} }} + {{{p}}_{{2}}}{{{x}}^{{{n}- 2} }} + {{{p}}_{{3}}}{{{x}}^{{{n}- 3} }} + \cdots + {{{p}}_{{n}}} $$ (1) 考虑到拟合多项式阶数过大会增大计算量且拟合精度过高,而拟合多项式阶数越小虽计算量较小,但会导致拟合精度有限等问题,综上考虑,文中选用最高次数为二次的多项式进行拟合,即每次使用三个参数为一组进行拟合,每个式子形式如公式(2)所示:
$$ {R_i} = {p_{j2}}{({t_i} - {t_0})^2} + {p_{j1}}({t_i} - {t_0}) + {p_{j0}}$$ (2) 式中:
$ {{{t}}_0} $ 为每组计时零点;$ {t_i} $ 为星历给出的每组卫星坐标对应的时刻值;$ {R_i} $ 为星历给出的$ {t_i} $ 时刻卫星与测距台站之间的距离;经过计算求出每组数据对应的系数$ {p_{j0}} $ ,$ {p_{j1}} $ ,$ {p_{j2}} $ 。然后将求得的三个系数反代入公式(2),根据激光发射时刻值即可求得对应的台站与卫星之间的距离值$ {R_i} $ ,其中$ j $ 表示第$ j $ 组系数,$ i $ 表示星历提供的第$ i $ 个预报时刻。此外,考虑到开启延时和稳定性等因素,所以还需减去一个提前开启量[16]。 -
考虑到实际应用场景,对距离门控模块进行模拟测试,测试下位机平台为基于一片STM32 F4系列芯片(ARM核心)和一片CylconeIV系列芯片(FPGA核心)搭建的距离门控电路,使用逻辑分析仪对电路工作情况进行采样后在上位机计算机显示。
实验通过FPGA产生固定频率脉冲模拟激光发射,其中,FPGA和ARM之间采用FSMC通信,用于高速传输激光发射时刻和预期回波时刻,观测计算机通过串行总线与距离门控模块通信,用于星历坐标、台站坐标的输入和测试结果的显示。通过逻辑分析仪对信号进行采样,并对其验证分析。硬件测试连接图如图如图6所示。
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模块每三组参数拟合一次,多项式拟合的过程就是求
$ {p_0} $ ,$ {p_1} $ ,$ {p_2} $ 三个参数的过程,$ {p_0} $ ,$ {p_1} $ ,$ {p_2} $ 三个参数作为系数参与每次激光预期回波时刻的多项式计算,所以,$ {p_0} $ ,$ {p_1} $ ,$ {p_2} $ 三个参数的准确度是整个拟合过程的关键点,拟合的准确度直接影响着最后的距离门控信号输出时刻的准确度。为了验证拟合效果,选用了三颗不同轨道高度的ajisai卫星(1485.9~1503.7 km)、lageos1卫星(5860~5960 km)和compassi3地球同步卫星(37790.2 km)的实际星历数据进行拟合实验,拟合精度分析实验图如图7所示,拟合结果对比如表1所示。表 1 lageos1卫星、ajisai卫星和compassi3卫星拟合结果对比
Table 1. Comparison of fitting results of lageos1, ajisai and compassi3 satellites
Group Fitting
parameterslageos1 ajisai compassi3 Theoretical
fitting valueActual fitting
valueTheoretical
fitting valueActual fitting
valueTheoretical
fitting valueActual fitting
value
1p0 12246910.77 12246910.77 7866493.98 7866493.98 42388583.21 42388583.21 p1 −23.797102532 −23.797123 −4.807358846 −4.807383 −2.133913994 −2.133917 p2 0.002695052 0.002655 −0.000652222 −0.000652 −0.000601398 −0.000601
2p0 12242715.62 12242715.62 7866056.24 7866056.24 42386175.97 42386175.97 p1 −22.801517445 −22.801567 −4.914551171 −4.914567 −3.214461718 −3.214467 p2 0.003110283 0.003111 −0.000310122 −0.000310 −0.000593678 −0.000594
3p0 12238713.09 12238713.09 7865611.63 7865611.63 42382802.64 42382802.64 p1 −21.657421675 −21.657433 −4.959844197 −4.959833 −4.28035888 −4.280350 p2 0.003508974 0.003508 0.0000378668 0.000038 −0.000583463 −0.000584
4p0 12234929.37 12234929.37 7865165.76 7865165.76 42378478.42 42378478.42 p1 −20.37088313 −20.370850 −4.942574962 −4.942633 −5.327123541 −5.327133 p2 0.003888814 0.003828 0.000383503 0.000384 −0.000570796 −0.000571
5p0 12231389.49 12231389.49 7864724.24 7864724.24 42373222.52 42373222.52 p1 −18.948802236 −18.948832 −4.863308719 −4.863317 −6.350358818 −6.350400 p2 0.004248104 0.004250 0.000720587 0.000721 −0.000555738 −0.000556
6p0 12228117.17 12228117.17 7864292.57 7864292.57 42367058.04 42367058.04 p1 −17.39867698 −17.398653 −4.723849386 −4.723800 −7.345782716 −7.345750 p2 0.004584425 0.004585 0.001041787 0.001041 −0.000538352 −0.000538
7p0 12225134.71 12225134.71 7863876.05 7863876.05 42360011.91 42360011.91 p1 −15.728883909 −15.728876 −4.527048447 −4.527033 −8.309222925 −8.309267 p2 0.00489588 0.004897 0.001340325 0.001340 −0.000518728 −0.000519
8p0 12222462.84 12222462.84 7863479.64 7863479.64 42352114.7 42352114.70 p1 −13.948542867 −13.948517 −4.277132092 −4.277150 −9.236671378 −9.236650 p2 0.005180277 0.005179 0.001613631 0.001614 −0.000496926 −0.000497
9p0 12220120.58 12220120.58 7863107.93 7863107.93 42343400.58 42343400.58 p1 −12.067513153 −12.067517 −3.97890934 −3.978917 −10.12425534 −10.124233 p2 0.005435328 0.005435 0.001858081 0.001858 −0.000473061 −0.000473
10p0 12218125.1 12218125.10 7862765.01 7862765.01 42333907.08 42333907.08 p1 −10.096478712 −10.096483 −3.637756603 −3.637767 −10.96827452 −10.968250 p2 0.005658921 0.005660 0.002068647 0.002069 −0.000447229 −0.000447 由表1可知,在三颗卫星各选取的十组数据里,实测拟合值与理论拟合值十分接近,实测拟合值通过下位机芯片计算得到,理论拟合值由上位机计算机计算得到。每个参数的误差为对应的实测拟合值减去理论拟合值,再根据样本标准差的计算公式
$S = \left( {{{\displaystyle\sum\nolimits_{i = 1}^n {{{(x_i - \bar x)}^2}} }}/{{n - 1}}}\right)^{1/2}$ 分别求出三颗卫星的拟合误差样本标准差,即为拟合精度。其中,n为样本个数,${{{x}}_{{i}}}$ 为每个参数的误差,$ \overline x $ 为参数的误差平均值。经计算,lageos1拟合结果误差为0.001997%,ajisai拟合结果误差为0.001600%,com-passi3拟合结果误差为0.001303%。模块拟合精度误差小于0.01%,在下位机中拟合的目标可行,达到流动卫星激光测距的要求。 -
实时性一直是高频率激光测距的一项重要指标,在每秒发出千次甚至万次脉冲的情况下,对于计算用时的把握直接关系到激光测距能否成功。模块中ARM芯片用于参数拟合、上位机通信和计算预期回波时刻。计算预期回波时刻的计算时长是否能够满足高频率距离门控模块对于时序方面的要求,还需要进行验证分析。实验中ARM芯片开始进行预期回波时刻计算时拉高通用输入输出(General Purpose Input Output, GPIO)端口,结束预期回波时刻计算时拉低GPIO端口,利用FPGA的逻辑分析仪可以观察到一次完整的预期回波时刻计算时间,结果如图8所示。
可以看出:基准时刻开始于8C49h,结束于A722h,总共持续6874个时钟周期,约为34.365 μs。当前模拟激光发射频率为2 kHz,基准时钟频率为200 MHz,即每十万个基准时钟周期发射一次脉冲,所以不会与下一次激光发射相冲突,经过计算,激光来回于台站与卫星的时间达到百万个时钟周期以上,所以该模块可以实现2 kHz频率以上的激光测距,理论上可以满足20 kHz以上的观测频率。
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预期回波时刻与当前时刻在FPGA内部的比较器中进行比较,当预期回波时刻等于当前时刻时输出距离门控信号,距离门发生器(Range Gate Generator, RGG)输出门控信号时序如图9所示。
由于受到FSMC总线位数(16位)的限制,设计中的预期回波时刻与当前时刻分别由两组四个16位计数器组成的64位计数表示,其中,两个16位计数器组成的高32位计数代表“粗”计数,两个16位计数器组成的低32位计数代表“细”计数。图中,RGG为距离门控输出,rgg_moment1与rgg_moment_2组成预期回波时刻“细”计数,rgg_moment3与rgg_moment_组成预期回波时刻“粗”计数,accurate_moment_low与accurate_moment_high组成当前时刻 “细”计数,second_moment_low与second_moment_high组成当前时刻“粗”计数,当预期回波时刻与当前时刻一致时,输出距离门控信号。图中连续两个预期回波时刻“粗”计数都为1C72h,“细”计数分别为5645BEDh和565E28Bh,计算得到两次时刻相差499990 ns。以上实验结果满足2 kHz重复频率的距离门控间隔为500000 ns的要求,表明距离门控模块能够产生连续稳定的RGG信号。
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由于被测卫星离观测台站的距离太过遥远,卫星激光测距接收的信号十分微弱,仅有单光子数量级,这也导致单次激光的回波接收成功率较低。高重复频率激光测距的诞生就是为了通过增大激光发射次数来提高总体接收到的激光回波次数,这也说明激光发射(点火)频率对于高频率激光测距系统而言是十分重要的,点火频率的下降也会导致回波的接收数量下降。文中通过点火延迟法对后向散射干扰进行自动规避,由于部分点火信号需要规避后向散射的影响而被延迟,所以在单位时间内的实际激光发射次数会相较于原来激光发射次数有所下降。故需要对实际激光发射次数进行测量,以此判断经过后向散射规避延迟后,单位时间内系统的实际点火次数是否损失过多。单位时间(1 s)点火损失次数为不进行后向散射规避时的每秒点火次数(理论点火次数)与进行后向散射规避时的每秒实际点火次数(实际点火次数)之间的差值,点火频率损失率为每秒点火损失次数与每秒理论点火次数的比值。测试采用ajisai卫星星历在2 kHz重复率(每秒理论点火2 000次)下的模拟测试,在距离门控模块正常运行过程中按1 s为间隔对实测点火次数进行连续20 s采样,并计算每秒点火损失次数和点火频率损失率。后向散射规避点火频率测试结果如表2所示。
表 2 后向散射规避点火频率测试结果
Table 2. Test results of firing frequency of backscat-tering avoidance
Second Actual firing
timesNumber of firing
lossLoss rate of
firing1 1 984 16 0.80% 2 1 986 14 0.70% 3 1 985 15 0.75% 4 1 986 14 0.70% 5 1 984 16 0.80% 6 1 986 14 0.70% 7 1 985 15 0.75% 8 1 986 14 0.70% 9 1 985 15 0.75% 10 1 986 14 0.70% 11 1 984 16 0.80% 12 1 986 14 0.70% 13 1 985 15 0.75% 14 1 986 14 0.70% 15 1 985 15 0.75% 16 1 986 14 0.70% 17 1 984 16 0.80% 18 1 986 14 0.70% 19 1 985 15 0.75% 20 1 986 14 0.70% 表2中列举了系统在每秒内的实际点火次数、每秒点火损失次数和点火频率损失率,其中,每秒点火损失次数通过理论点火次数(2 kHz)减去实际点火次数得到,点火频率损失率通过每秒点火损失次数除以理论点火次数(2 kHz)得到。点火频率损失率反映了由点火延迟法造成的点火数量损失对系统总体回波接收数量的影响程度。结果表明,文中后向散射自动规避电路在模拟运行中起到了精确规避作用,在对ajisai卫星的测试中平均点火损失率仅不到1%,系统点火频率损失小,并不会对系统最后的回波数据量造成明显影响,所以文中后向散射规避功能满足预期要求。
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距离门信号分辨率测试采用AMS公司的GPX2评估板作为测量装置,评估板使用TDC-GPX2芯片作为测量核心,在双通道高分辨率工作模式下,可以在5 ns脉冲间距下达到10 ps均方根(Root Mean Square, RMS)的最大分辨率[23]。GPX2评估板计算距离门控信号产生时刻与距离门控信号输出时刻的差值,差值的变化范围反映了距离门控信号的抖动范围,即是距离门控信号的分辨率。图10为距离选通模块分辨率测量实验图,实验采用ajisai卫星轨道进行预报,在2 kHz频率下测试结果如表3所示。
图11是距离门信号抖动结果,X轴为测试选取的点数,Y轴为距离门信号输出时刻与产生时刻的差值。差值最大值为37.84 ns,差值最小值为35.36 ns,差值的峰峰值为2.48 ns。图11显示距离门的分辨率优于5 ns,说明新的距离选通模块硬件设计是可行的,能够实现高重复率激光测距的连续观测。
表 3 距离门信号抖动测试结果
Table 3. Test results of range-gate signal jitting
Points Range gating output epoch/s Range gate generation epoch/s Difference/s 1 20778.02314267039 20778.02314263426 0.00000003613 2 20778.02364278037 20778.02364274427 0.00000003610 3 20778.02414289025 20778.02414285416 0.00000003609 4 20778.02464300007 20778.02464296397 0.00000003610 5 20778.02514310989 20778.02514307378 0.00000003611 6 20778.02564322089 20778.02564318477 0.00000003612 $\vdots $ $\vdots $ $\vdots $ $\vdots $ 5745 20780.89577451081 20780.89577447433 0.00000003648 5746 20780.89627461940 20780.89627458289 0.00000003651 5747 20780.89677472837 20780.89677469187 0.00000003650 5748 20780.89727483847 20780.89727480185 0.00000003662 5749 20780.89777494398 20780.89777490776 0.00000003622 5750 20780.89827505415 20780.89827501757 0.00000003658
Implementation method of range gating for mobile satellite laser ranging system
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摘要: 现有流动卫星激光测距系统的距离选通模块因硬件架构问题,有稳定性不高、可靠性不强等不足。由于和固定站的设备互不兼容,因此需要研制新的距离选通模块,在兼顾高集成度的同时提升运行稳定性。在基于距离选通与后向散射规避的实现原理基础上,依靠ARM、FPGA嵌入式双核心架构设计全新的距离选通模块。采用人卫激光测距卫星lageos1、ajisai和地球同步卫星compassi3的星历进行距离门参数拟合等测试。经测试,该距离门控模块参数拟合误差小于0.01%,在2 kHz重复频率下单次预期回波时刻计算时间约为34.365 μs,平均后向散射规避点火频率损失率低于1%,在2 kHz重复频率下距离门分辨率优于5 ns,高频率门控信号输出平稳,并且能够满足20 kHz以上的重复频率应用需求,符合预期结果,具有实际应用价值。Abstract: Due to the problem of hardware architecture, the range gating module of the existing mobile satellite laser ranging system has some shortcomings, such as low stability and low reliability. Since it is incompatible with the equipment of the fixed station, it is necessary to develop a new range gating module to improve the operation stability while giving consideration to high integration. Based on the realization principle of range gating and backscattering avoidance, the new range gating module is designed with ARM and FPGA embedded dual core architecture. The module used the ephemeris of lageos1, ajisai and geosynchronous compassi3 satellites to fit the range gating parameters. The test results show that the parameter fitting error of the range gating module is less than 0.01%, and the calculation time of a single expected echo epoch is 34.365 μs at repetition rate of 2 kHz. The average firing frequency loss rate due to the backscattering avoidance is less than 1%. The resolution of range gating is lower than 5 ns at repetition rate of 2 kHz. The output of high frequency gating signal is stable and the module can meet the requirements of repetition frequency applications over 20 kHz. It conforms to the expected results and has practical application value.
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Key words:
- range gating /
- laser ranging /
- polynomial fitting /
- high repetition rate /
- mobile observation
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表 1 lageos1卫星、ajisai卫星和compassi3卫星拟合结果对比
Table 1. Comparison of fitting results of lageos1, ajisai and compassi3 satellites
Group Fitting
parameterslageos1 ajisai compassi3 Theoretical
fitting valueActual fitting
valueTheoretical
fitting valueActual fitting
valueTheoretical
fitting valueActual fitting
value
1p0 12246910.77 12246910.77 7866493.98 7866493.98 42388583.21 42388583.21 p1 −23.797102532 −23.797123 −4.807358846 −4.807383 −2.133913994 −2.133917 p2 0.002695052 0.002655 −0.000652222 −0.000652 −0.000601398 −0.000601
2p0 12242715.62 12242715.62 7866056.24 7866056.24 42386175.97 42386175.97 p1 −22.801517445 −22.801567 −4.914551171 −4.914567 −3.214461718 −3.214467 p2 0.003110283 0.003111 −0.000310122 −0.000310 −0.000593678 −0.000594
3p0 12238713.09 12238713.09 7865611.63 7865611.63 42382802.64 42382802.64 p1 −21.657421675 −21.657433 −4.959844197 −4.959833 −4.28035888 −4.280350 p2 0.003508974 0.003508 0.0000378668 0.000038 −0.000583463 −0.000584
4p0 12234929.37 12234929.37 7865165.76 7865165.76 42378478.42 42378478.42 p1 −20.37088313 −20.370850 −4.942574962 −4.942633 −5.327123541 −5.327133 p2 0.003888814 0.003828 0.000383503 0.000384 −0.000570796 −0.000571
5p0 12231389.49 12231389.49 7864724.24 7864724.24 42373222.52 42373222.52 p1 −18.948802236 −18.948832 −4.863308719 −4.863317 −6.350358818 −6.350400 p2 0.004248104 0.004250 0.000720587 0.000721 −0.000555738 −0.000556
6p0 12228117.17 12228117.17 7864292.57 7864292.57 42367058.04 42367058.04 p1 −17.39867698 −17.398653 −4.723849386 −4.723800 −7.345782716 −7.345750 p2 0.004584425 0.004585 0.001041787 0.001041 −0.000538352 −0.000538
7p0 12225134.71 12225134.71 7863876.05 7863876.05 42360011.91 42360011.91 p1 −15.728883909 −15.728876 −4.527048447 −4.527033 −8.309222925 −8.309267 p2 0.00489588 0.004897 0.001340325 0.001340 −0.000518728 −0.000519
8p0 12222462.84 12222462.84 7863479.64 7863479.64 42352114.7 42352114.70 p1 −13.948542867 −13.948517 −4.277132092 −4.277150 −9.236671378 −9.236650 p2 0.005180277 0.005179 0.001613631 0.001614 −0.000496926 −0.000497
9p0 12220120.58 12220120.58 7863107.93 7863107.93 42343400.58 42343400.58 p1 −12.067513153 −12.067517 −3.97890934 −3.978917 −10.12425534 −10.124233 p2 0.005435328 0.005435 0.001858081 0.001858 −0.000473061 −0.000473
10p0 12218125.1 12218125.10 7862765.01 7862765.01 42333907.08 42333907.08 p1 −10.096478712 −10.096483 −3.637756603 −3.637767 −10.96827452 −10.968250 p2 0.005658921 0.005660 0.002068647 0.002069 −0.000447229 −0.000447 表 2 后向散射规避点火频率测试结果
Table 2. Test results of firing frequency of backscat-tering avoidance
Second Actual firing
timesNumber of firing
lossLoss rate of
firing1 1 984 16 0.80% 2 1 986 14 0.70% 3 1 985 15 0.75% 4 1 986 14 0.70% 5 1 984 16 0.80% 6 1 986 14 0.70% 7 1 985 15 0.75% 8 1 986 14 0.70% 9 1 985 15 0.75% 10 1 986 14 0.70% 11 1 984 16 0.80% 12 1 986 14 0.70% 13 1 985 15 0.75% 14 1 986 14 0.70% 15 1 985 15 0.75% 16 1 986 14 0.70% 17 1 984 16 0.80% 18 1 986 14 0.70% 19 1 985 15 0.75% 20 1 986 14 0.70% 表 3 距离门信号抖动测试结果
Table 3. Test results of range-gate signal jitting
Points Range gating output epoch/s Range gate generation epoch/s Difference/s 1 20778.02314267039 20778.02314263426 0.00000003613 2 20778.02364278037 20778.02364274427 0.00000003610 3 20778.02414289025 20778.02414285416 0.00000003609 4 20778.02464300007 20778.02464296397 0.00000003610 5 20778.02514310989 20778.02514307378 0.00000003611 6 20778.02564322089 20778.02564318477 0.00000003612 $\vdots $ $\vdots $ $\vdots $ $\vdots $ 5745 20780.89577451081 20780.89577447433 0.00000003648 5746 20780.89627461940 20780.89627458289 0.00000003651 5747 20780.89677472837 20780.89677469187 0.00000003650 5748 20780.89727483847 20780.89727480185 0.00000003662 5749 20780.89777494398 20780.89777490776 0.00000003622 5750 20780.89827505415 20780.89827501757 0.00000003658 -
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