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相干激光测风雷达的原理是激光信号经移频器和分束器后,一路作为本振光,另一路经过调制和放大后发射到大气中。激光与大气相互作用产生后向散射回波信号,由光学天线接收,与本振光混频后被光电探测器接收转换为电信号[16]:
$$ \begin{split} i(t) =& \alpha \left\{ {\frac{1}{2}{A_s}^2 + {A_s}{A_{Lo}}\cos [2\pi ({f_s} - {f_{Lo}})t + } \right. \\ &\left. { ({\varphi _s} - {\varphi _{Lo}})] + \frac{1}{2}{A_{Lo}}^2} \right\} \end{split} $$ (1) 式中:α为光电探测器的光电转换因子;As为回光幅度;ALo为本振光幅度;fs为信号光频率;fLo为本振光频率;φs为信号光相位;φLo为本振光相位。对光电探测器输出的电信号进行滤波和放大,使用满足奈奎斯特采样定理的采样率进行数据采样,得到回波信号的采样序列:
$$x\left( n \right) = x\left( {n \cdot \Delta T} \right) \;\;\;\;n = 0,1, \cdots ,N - 1$$ (2) 式中:N为总采样点数;ΔT为采样间隔。对采样序列x(n)进行区间划分,划分得到的区间称为距离门。对每一个距离门做FFT,获得频率估计结果。根据多普勒效应计算气溶胶粒子在激光径向上的速度v:
$${f_d} = \frac{{2\left| v \right|}}{\lambda }$$ (3) 式中:
${f_d} = {f_s} - {f_{Lo}}$ ,为回波信号的多普勒频移;λ为激光波长。 -
固定距离门划分方法的特点是划分出的所有距离门长度均相同,距离分辨率与距离门长度相等。对每个距离门做FFT得到频率估计值,再由多普勒频移公式计算得到径向风速。
取一段激光测风雷达回波信号,使用固定距离门方法进行处理,结果如图1所示。
图 1 固定距离门方法处理激光测风雷达信号。 (a)固定距离门划分时域信号;(b)风速计算结果
Figure 1. Fixed range-gate method processing wind lidar signal. (a) Time domain signal is divided with fixed range-gate; (b) Calculation result of wind speed
固定距离门划分信号的优点是方法简单,容易实现,缺点是划分距离门时会存在信号的非整周期截断,进行FFT计算时往往存在频谱泄露问题,造成频率测量误差。另外,固定距离门方法划分的距离门长度与风速大小无关,单个距离门出现的风速变化无法在计算结果体现,计算结果中会丢失部分风场细节信息。
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自适应距离门方法的特点是距离门长度与信号频率自适应,并且实现了信号的整周期截断,减少了频谱泄露产生的误差,提高了频率估计精度。该方法主要步骤是整周期搜索。整周期搜索算法的作用是提取出信号所有的整周期,依据整周期搜索结果获取频率突变点,根据频率突变点和整周期分界点进行距离门划分,划分出的距离门长度较短,提高了距离分辨率。
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整周期搜索算法的主要作用是搜索到回波信号中所有的整周期分界点。电力谐波分析中通常使用同步采样方法,令采样与信号频率同步变化以实现整周期采样,获得信号完整周期[17]。同步采样方法的缺点是对于频率变化的信号,采样率无法与信号频率同步。
浙江大学蔡忠法等提出一种与初始值比较的整周期搜索方法,用于提取电力谐波信号的整周期[17],实现对非同步采样数据中得到同步采样数据。激光测风雷达回波信号受激光器、大气波动等引起的低频噪声影响,整周期分割点处信号幅值不一定在初始值附近,因此与初始值比较的整周期搜索方法不适合用于处理激光测风雷达回波信号。
该整周期搜索方法是从信号采样序列x(n)的最后一个数值开始,以初始值x(0)做为阈值,每一个数值与x(0)进行比较,当x(0)<x(1)时,搜索到满足x(k−1)>x(0),x(k)≤x(0)的k值,认为x(k−1)是整周期采样点;x(0)>x(1)时,搜索到满足x(k−1)<x(0),x(k)≥x(0)的k值,同样认为x(k−1)是整周期采样点。使用参考文献[17]中提出的整周期搜索方法对部分风场回波信号进行整周期搜索,结果如图2(a)所示。
图 2 整周期搜索结果。(a) 未改进的整周期搜索算法的结果;(b) 改进后的整周期搜索算法的结果
Figure 2. Results of full cycle search. (a) Results of unimproved full cycle search algorithm; (b) Results of improved full cycle search algorithm
图2(a)中T1~T10是搜索出的整周期信号,其中T1、T4和T9区间内有多个整周期没有被搜索到。
为了解决与初始值比较的整周期搜索方法产生的整周期遗漏的问题,文中提出一种以极值点作为周期开始点的整周期搜索算法。第一步是对s(n)进行二值化,将激光测风雷达回波信号的离散采样序列记为s(n),定义离散序列b(n),初始值b(0)=0。
$$s\left( k \right) > s\left( {k - 1} \right) \wedge s\left( k \right) > s\left( {k + 1} \right)$$ (4) $$s\left( k \right) < s\left( {k - 1} \right) \wedge s\left( k \right) < s\left( {k + 1} \right)$$ (5) 从点s(1)开始搜索,符合公式(4)的点标记为1,即b(k)=1,符合公式(5)的点标记为−1,即b(k)=−1。符合公式(4)和(5)的条件点根据公式(6)赋值:
$$b\left( k \right) = b\left( {k - 1} \right)$$ (6) 整周期搜索算法的第二步是对信号进行整周期划分。搜索b(n)序列中所有的上升沿与下降沿,若s(0)<s(1),使用b(n)中的上升沿对s(n)进行划分;若s(0)>s(1),使用b(n)中的下降沿对s(n)进行划分。使用改进的整周期搜索方法重新对风场回波信号进行整周期搜索,结果如图2(b)所示。
与图2(a)中的整周期搜索结果相比,改进的整周期搜索算法能够提取出信号所有的整周期。
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信号单个周期采样点数Ns与采样率Fs的关系为:
$${N_s} = \left\lfloor {\frac{{{F_s}}}{f}} \right\rfloor $$ (7) 回波信号的频率与单个整周期内的采样点数成反比例关系。根据采样率和回波信号频率范围,得Ns的取值范围:
$$\frac{{{F_s}}}{{{f_{\min }}}} \leqslant {N_s} \leqslant \frac{{{F_s}}}{{{f_{\max }}}}$$ (8) 式中:fmin为回波信号最小频率;fmax为回波信号最大频率,依据Ns的值粗略判断信号频率范围,进一步找到频率突变点。对二值化离散序列b(n)进行处理,得到每个周期内的采样点个数的离散序列p(n):
$$p\left( n \right) = b\left( {n + 1} \right) - b\left( n \right), \;\; n = 0,1, \cdots ,N - 2$$ (9) 式中:p(n)为周期n中采样点的数量。使用相邻的整周期内采样点数发生突变的点初步划分距离门,再对超过距离分辨率要求的距离门进行等间隔的整周期划分,至此自适应距离门划分过程结束。
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实验使用的激光测风雷达系统[15]的工作波长1550 nm,采样率500 MHz,中频80 MHz,脉宽200 ns,频率测量范围40~120 MHz,对应风速范围−31~31 m/s (见表1)。
表 1 激光测风雷达系统参数
Table 1. Parameters of wind lidar system
Parameters Value Wavelength/nm 1550 Sample rate/MHz 500 Range resolution/m 30/50/75/100 Maximum detection range/km 10 Intermediate frequency/MHz 80 Pulse width/ns 200 Wind speed range/m·s−1 −31~31 Dimension/mm3 ≤φ420×700 Pointing precision/(°) 0.1 生成频率100、40、80、20、60 MHz,信噪比−1 dB的仿真变频信号,使用自适应距离门方法和固定距离门方法(距离分辨率设置30 m)进行距离门划分(见图3)。
图 3 距离门划分结果。(a)固定距离门划分结果;(b)自适应距离门划分结果
Figure 3. Results of range-gate division. (a) Results of fixed range-gate division; (b) Results of adaptive range-gate division
仿真信号距离门划分结果表明,固定距离门方法划分的距离门与信号频率变化无关;自适应距离门方法能够识别出频率突变点t1、t2、t3和t4,并对区间[0, t1]、[t1, t2]、[t2, t3]、[t3, t4]进行了等间隔整周期划分。
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为验证自适应距离门方法能够在提高距离分辨率的同时满足测量误差要求,使用自适应距离门方法和固定距离门方法处理范围信号频率40~120 MHz,信噪比−5~5 dB的仿真信号,进行5000次独立计算,对比分析频率计算结果的误差(见图4)。
结果表明,仿真信号信噪比大于1 dB时,自适应距离门方法与固定距离门方法的频率估计结果误差基本一致,约为0.2%。当信噪比小于1 dB时,随着信噪比的降低,两种方法的频率估计误差均增大,自适应距离门方法频率估计误差更小;信噪比小于−1 dB时,自适应距离门方法的频率误差是固定距离门方法频率误差的38%~62%。
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距离分辨率指相邻两个距离门中心的距离间隔,固定距离门方法的距离分辨率与距离门的长度相同;自适应距离门的距离门长度与信号频率相关,距离分辨率不固定。
单个自适应距离门内包含的整周期数量对频率估计误差和距离分辨率均会产生影响。通过仿真分析整周期的数量与频率估计误差的关系(见图5)以及自适应距离门长度与整周期数量、信号频率之间的关系(见图6)。
由仿真结果知,单个距离门内整周期数量取5以下时,频率估计误差开始明显增加,由0.5%以下增加到1%以上,最大增加到4.1%。整周期个数取5及以上时,频率估计误差基本保持不变,在0.2%左右。整周期数取5时,对应距离分辨率范围6.25~18.75 m。
在划分自适应距离门时,需要综合考虑距离分辨率和风速误差,选择合适的整周期数量,令距离分辨率和风速误差同时达到最优。
Research on high resolution range-gate adaptive technology of coherent wind lidar
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摘要: 脉冲相干激光测风雷达的信号处理通常采用固定长度距离门来划分时域信号,并对每个距离门做频谱计算得到风速度信息。固定距离门的时域信号划分存在中频信号的非整周期截断问题,导致频谱计算时出现频谱泄露而产生误差,使信噪比降低。文中提出一种基于整周期搜索的自适应距离门划分方法,距离门长度与中频信号频率自适应,可实现对信号的整周期分割,避免了频谱处理中的频谱泄漏问题,提高频率估计精度。采用加噪信号对两种处理方法进行仿真分析,结果表明:自适应距离门方法可实现距离门长度与中频信号的自适应,在信噪比小于1 dB时,该方法得到的中频估计误差是固定距离门方法的38%~62%。应用自适应距离门方法处理激光测风雷达系统获取的转盘和风场回波信号,与使用固定距离门方法的激光测风雷达测量结果进行对比。结果表明:自适应距离门划分方法对转盘速度测量的均方根误差为0.19 m/s,大气风速度测量的距离分辨率在7~11 m之间变化,均优于固定距离门方法,实现了激光测风雷达的距离分辨率和测量精度的提升。Abstract: The signal processing of pulse coherent wind lidar usually uses fixed range-gate to divide the time domain signal, and perform frequency spectrum calculation for each range-gate to obtain wind speed information. The time domain signal division of the fixed range-gate has the problem of non-periodic truncation of the intermediate frequency signal, which leads to spectrum leakage during spectrum calculation, resulting in errors and reduced signal-to-noise ratio. An adaptive range-gate division method based on full cycle search was proposed. The length of the range-gate was adaptive to the frequency of the intermediate frequency signal, which could realize the full cycle division of the signal, avoide the problem of spectrum leakage and improve frequency estimation accuracy. The two processing methods were simulated and analyzed by adding noise signal. The results show that the adaptive range-gate method can realize the adaptation of the range-gate length and the intermediate frequency signal. When the signal-to-noise ratio was less than 1 dB, the intermediate frequency estimation error obtained by this method was 38%-62% of the fixed range-gate method. The adaptive range-gate division method was used to process the turntable and wind field echo signals obtained by the laser wind measurement radar system, and the results were compared with the wind lidar equipped with the fixed range-gate method. The results show that the root mean square error of the adaptive range-gate method for the speed measurement of the turntable is 0.19 m/s, and the range resolution of atmospheric wind speed measurement varies from 7 to 11 m, which is better than that of fixed range-gate method, and improves the range resolution and measurement accuracy of the wind lidar.
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Key words:
- wind lidar /
- full cycle search /
- adaptive range-gate /
- signal processing
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图 8 目标回波信号距离门划分。(a)固定距离门划分旋转盘回波信号;(b)自适应距离门划分旋转盘回波信号;(c)固定距离门划分建筑物回波信号;(d)自适应距离门划分建筑物回波信号
Figure 8. Target echo signal range-gate division. (a) Fixed range-gate dividing the turntable echo signal; (b) Adaptive range-gate dividing the turntable echo signal; (c) Fixed range-gate dividing the building echo signal; (d) Adaptive range-gate dividing the building echo signal
表 1 激光测风雷达系统参数
Table 1. Parameters of wind lidar system
Parameters Value Wavelength/nm 1550 Sample rate/MHz 500 Range resolution/m 30/50/75/100 Maximum detection range/km 10 Intermediate frequency/MHz 80 Pulse width/ns 200 Wind speed range/m·s−1 −31~31 Dimension/mm3 ≤φ420×700 Pointing precision/(°) 0.1 -
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