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摘要:
舰载机飞行试验时,舰上常配备有光电经纬仪测量系统。针对光电经纬仪引导时所遇到引导信息频率低、存在干扰的问题,提出了数据预测的外推内插法和粗差剔除的三点截止法;为了平滑切换引导源,提出了渐进式跟踪算法。实际数据比对表明,上述方法有效地解决了舰载复杂环境下的数据滤波、插值和多源信息的引导问题。最后,基于舰载GPS/INS组合惯导信息,推导出动基座光电目标引导算法公式。
Abstract:The warship is generally equipped with photoelectric theodolite in carrier-borne aircraft flying test. Due to the low frequency of guidance source signal and disturbance from environment, the performance of the system is restricted. We proposed an extrapolation-interpolation method and a three points cut-off method to solve the problem, respectively. To smooth the switch of different guidance sources, we also recommended a gradually tracking algorithm. All the methods above resolve data filter, interpolation and multi-source problem effectively, which are usually encountered in the guiding photoelectric theodolite on the shipboard. At last, the guidance formulae of moving platform are established based on GPS/INS navigation information.
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Key words:
- flight test /
- photoelectric theodolite /
- moving base /
- outlier /
- guidance algorithm
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Abstract: In order to accurately measure the trajectory and characteristic points of the carrier borne aircraft during the flight test, the shipborne photoelectric theodolite is adopted. According to the target position information and the video image information measured by the observation system, the solution is obtained in the deck coordinate system for the accurate trajectory of the target. However, due to the influence of the weather, the distance is short and the field of view is small. When the aircraft enters its working area, it is often too late to be tracked. Related research report is relatively small. In order to solve this problem, according to the ship and aircraft equipped with infrared guide, mutual guide and guide work, when a target signal appears, primary mirror of theodolite is guided to aim target direction. Once the target runs into the test area, it will be timely captured. The warship is generally equipped with photoelectric theodolite in shipboard plane flying test. Flight test equipment configuration of the aircraft is equipped with a real-time GPS system, and the ship is equipped with telemetry system, and therefore the project uses an external guide work.
According to the environment caused by theodolite data source interference and low data sending rate, the guidance algorithm of moving optoelectronic target under complex environment is proposed to solve the problem of photoelectric theodolite stability guidance. The GPS with three organic loading error cutoff methods is adjusted by extrapolation prediction data interpolation method, incremental tracking algorithm source guide smooth switching and coordinate transformation algorithm. Several algorithms are successfully applied to the project, and achieve good results.
In flight test, there are two sources of guidance: airborne GPS data and telemetry data sent by the network. Airborne GPS positioning system through the wireless data chain under the plane cause the ship affected by the electromagnetic environment and the plane distance. Pose variation and occlusion of wireless data link bandwidth and limited data issued by the noise pollution and low frequency eliminate the coordinate transmission conversion error after using three points method of gross error on the received data of coordinate conversion for the first time. The remote sensing system sends the guide data. The frequency is high, and the data is stable. The threshold method is used to remove the outliers and then participates in the guidance calculation. Aiming at the problem of guidance source signal low frequency and interference, thesis puts forward an extrapolation-interpolation method and a three points cut-off method, respectively. Thesis also puts forward gradually tracking algorithm for the smooth transition of guidance sources. The methods all above resolve effectively data filter, interpolation and multi-source problem which are encountered in the guiding photoelectric theodolite on the shipboard. The last moving base photoelectric equipment guidance formulae are educed based on GPS/INS integrated navigation information.
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1. 引言
舰载机飞行试验时,为了精确测量舰载机进近段轨迹和特征点信息,一般采用舰载光电经纬仪。它采用自主方式工作,依据自身观测系统测得的目标位置信息和视频图像信息,在甲板坐标系下解算,获得目标精确的运动轨迹。但由于光电经纬仪易受天气影响,作用距离短且视场小,当飞机进入它的工作区域内时,经常来不及跟踪。国内外在该方面的论文资料较少,针对这个问题,业界常根据舰上和机上装备情况采用红外引导[1]、互引导和外引导等工作方式,当有目标信号时,引导经纬仪主镜朝向目标方向,一旦目标进入试验区域则及时捕获。
目前,国内外研究的视轴稳定技术主要有两种:一是采用机械稳定平台的反方向摇摆克服舰艇的纵摇、横摇和艏摇,为光电跟踪测量设备提供近似水平的安装基础,如我国远望号测量船上的718光电经纬仪的稳像平台。另一种是直接把光电经纬仪安装在甲板上,通过船姿测量仪测量出船体摆动[2],从而实时计算出视轴在大地坐标系中的偏离误差,并对俯仰轴和方位轴进行船摇姿态角的实时补偿。这种方法取消了笨重的机械稳定平台和中间测控环节,可以保证视轴的指向准确度。
飞行试验设备配置中,飞机上装备有GPS实时下发系统,舰上配备有遥测系统,因而项目采用了外引导工作方式。针对经纬仪舰载使用环境引起的数据源干扰大和数据下发速率低的问题,展开了复杂环境下动基座光电目标引导算法研究,旨在解决舰载光电经纬仪的稳定引导问题。本文涉及到的算法有机载GPS数据粗差剔除的三点截止法、数据预测的外推内插法、引导源平滑切换的渐进式跟踪算法、坐标变换算法等, 几种算法均成功应用到项目中,取得了很好的效果[3]。
2. 坐标系定义及数据源
2.1 坐标系定义
2.1.1 大地切平面坐标系GXgYgZg
以舰上GPS安装点G为原点,GXg指向大地东,GYg指向北,Xg, Yg, Zg构成右手系,在不引起误解时,也称为大地坐标系。
2.1.2 甲板坐标系OXYZ
设原点O为惯导的三轴交点,OY轴平行于原点处的甲板切平面,指向船艏;OZ轴垂直于甲板切平面,向上为正;OX轴按右手法则确定。
2.1.3 舰姿态角
1) 艏摇角Ψ:指艏艉线在水平面的投影与大地北之间的夹角。从正北开始到舰艏艉线在水平面的投影顺时针方向为正。
2) 纵摇角θ:指艏艉线与水平面之间的夹角。舰艏上翘时取正值。
3) 横摇角λ:指甲板绕已经纵倾的舰艏艉线的转角。甲板右舷下倾取正值。
2.2 目标源
在飞行试验中有两个引导源:机载GPS下发数据和遥测系统通过网络发送的数据。机载GPS定位系统通过无线数据链下发飞机的定位数据,受舰上电磁环境和飞机距离、姿态变化引起的遮挡及无线数据链带宽的影响和限制[4],下发的数据受到噪声污染且频率低,为了消除坐标转换中的误差传递,采用“三点截止法”对接收到的数据进行第一次粗差剔除之后,再进行坐标转换。对遥测系统送来的引导数据,频率较高,数据较稳定,采用门限法剔除野值后,再参与引导计算。
2.3 动基座环境数据
经纬仪外引导方式下工作时,需要将目标的大地坐标转换到经纬仪甲板坐标系。经纬仪舰载应用时,它的稳定跟踪除了定基座所面临的振动干扰,大气干扰,背景干扰外,由于舰的运动和海浪的影响,舰载经纬仪还存在包括舰的艏摇、横摇、纵摇的摇摆和舰的垂荡、横荡和纵荡等干扰运动和甲板扰曲变形的影响,为了隔离舰运动的干扰,在经纬仪的底座上安装环境姿态测量系统[5],该系统采用GPS与惯导组合方式,实时获取经纬仪底座的位置和舰平台的姿态,参与目标引导计算。
3. 算法及实现
3.1 三点截止法
机载下发的GPS数据经数据提取后以时间、大地纬度、经度、高程和东、北、天速度的形式参与计算,记为T, B, L, H, Ve, Vn, Vu。对实际接收数据分析发现有以下几个特点[6]:一是数据丢点较多且成片;二是含有偏离正常航迹不多的小野点且常以单点的形式存在;三是一组数据中的各变量T, B, L, H, Ve, Vn, Vu出错无相关性,即纬度B出错,经度L可能正确;四是东北天三向速度Ve, Vn, Vu相比大地坐标来说异值较少。下发数据率低,飞机又是大机动目标,关键时刻每个正确数据都非常珍贵。因此,三点截止法的出发点是在剔除掉粗差时用估计值替代的同时,尽量保留正确数据[7]。
在数据滤波的顺序上,通常是将大地极坐标系T, B, L, H转换到大地切平面坐标直角坐标系后再利用常规的滤波方法,如最小二乘滤波,Kalman滤波等,但是若用含有野值(即使是贴近正确数据的小野值)的数据直接进行坐标转换[8],转换后的数据野值量成几何级数增加。因此,该方法对大地极坐标系下的数据粗差进行剔除,再进行其它的数学计算。
1) 算法
设ˆTk−1,ˆBk−1为前一时刻的数据接收时刻和参数估计值,Tk, Bk为当前时间和数据实测值,算法分三步:
第一步:判断是否abs(Bk−ˆBk−1)>λ⋅Dt⋅abs(dB),如果是,则到第二步;如果不是,则到第三步;
第二步:ˆBk=ˆBk−1+Dt⋅dB;
第三步:ˆBk=Bk。
第二步连续只执行三次,第四次跳过第二步直接执行第三步。λ由试验确定,试验表明:对经度和纬度处理取5,高程处理取20。
2) Dt, dB的确定
Dt表示当前接收时刻与上次接收时刻之间所经过的时间周期数[9],可由接收数据的计算机时刻决定。dB表示Dt内目标的位置变化,可由目标的速度估计得到,采用五点中位数法估计,设Vx(k−4),Vx(k−3),Vx(k−2),Vx(k−1),Vx(k)表示Tk时刻已采集到的速度的前5个采样值,则:
ˆVx=median(Vx(k−4),Vx(k−3),Vx(k−2),Vx(k−1),Vx(k)), (1) dB=function(ˆVx), (2) 式中:median表示取中位数,速度估计ˆVx的下标x表示GPS的东、北、天三向速度,function表示大地切平面直角坐标到大地极坐标运算。
3.2 外推内插法
在光电目标引导时,光电经纬仪要求的引导速率为50 Hz。对飞机下发的1 Hz数据,通常的作法对已接收到的若干个数据[10],采用多项式拟合外推,由于下发的数据频率太低,飞机又是高速运动目标,下一个接收到的数据与上个时间点的第49个外推数据存在明显的“台阶”,用这样的数据引导光电经纬仪,导致光电经纬仪的主镜筒出现明显的抖动。外推内插法很好地解决了该问题。
3.2.1 1 Hz数据的外推
设tk时刻(k≥5)系统已接收到5组数据{tk−i,xk−i},(i=4,3,2,1,0),用二次多项式x=a+bt+ct2拟合,外推出tk+1时刻的估计值ˆxk+1。用滑窗最小二乘估计系数ak, bk, ck,则:
(akbkck)T=(ATkAk)−1ATkXk. (3) 其中:
Ak=[1tk−5t2k−51tk−4t2k−41tk−3t2k−31tk−2t2k−21tk−1t2k−1],Xk=[xk−5xk−4xk−3xk−2xk−1],k≥5. 则:
ˆxk+1=ak+bk(tk+1)+ck(tk+1)2. (4) 3.2.2 数据内插
根据在tk时刻的测量值xk与tk+1时刻的估计值ˆxk+1,用线性插值获取tk和tk+1之间的48个估计值,设xik为tk和tk+1之间的第i个估计,N为要内插的数据个数,则:
xik=xk+(ˆxk+1−xk)⋅iN, (5) 其中i=1, …, N-1。
从该公式可得出,当i=0时,估计值为tk时刻的测量值;当i=N时,估计值为ˆxk+1,这时下一个实时数据xk+1已接收到,下一个周期的估计循环开始。
3.3 渐进式跟踪算法
舰载机飞行试验时,不同的任务需求会配备各种测量系统,除了机载GPS外,一般舰上装备的遥测系统、雷达系统等均可用于光电经纬仪引导。在引导源切换时,由于各系统中系统误差、随机误差、测量误差、标校误差的存在,从各系统解算的飞机位置在空间并不重合[11],当外引导源切换时,引起经纬仪镜头的抖动。应用渐进式跟踪算法在不占用太多系统资源的情况下采用引导源的融合结果解决了该问题。
当外引导源切换时,以时间为基准分别取源1和源2数据,并在时间上有一定重叠(如2 s),在切换前,用源1数据作为引导源,切换后,用源2数据作为引导源,在切换的过程中用渐进式跟踪算法计算出引导数据。数学模型如下:
设有K个数据重叠,θ1为源1,θ2为源2,则切换过程中引导数据:
θ12(i)=K−iKθ1+iKθ2. (6) 3.4 引导解算
光电经纬仪与舰甲板紧固连接,经纬仪镜头的指向(方位角A和俯仰角E)解算要在甲板系下完成,目标坐标的解算在大地坐标系,甲板系与大地系之间的转换通过舰载GPS/INS组合惯导测量系统获得的舰姿态信息和舰位信息解算得到[12]。
3.4.1 甲板系下目标解算
设舰载GPS/INS系统测得的舰位大地坐标为(B0, L0, H0),飞机下发的GPS位置信息为B, L, H,根据文献[1]计算出飞机在以B0, L0, H0为原点的大地切平面坐标[13]为(Xg, Yg, Zg),则目标在以经纬仪三轴交点为圆心的甲板坐标系Oj-XjYjZj下的坐标(Xj, Yj, Zj)为
[XjYjZj]=[cosγ0−sinγ010sinγ0cosγ]⋅[1000cosθsinθ0−sinγcosθ]⋅[cosψ−sinψ0sinψcosψ0001]⋅[XgYgZg]−[ΔXΔYΔZ]. (7) 其中:Ψ, θ, γ为舰的姿态角,定义见2.1.3节,△X, △Y, △Z为GPS/INS系统舰位GPS点在Oj-XjYjZj的坐标,可静态标校得到。
3.4.2 引导解算
不失一般性,设经纬仪的方位与舰艏线平行并指向舰艏,则经纬仪的引导方位角A和俯仰角E可以表示为
A=argtan(Xj/Yj), (8) E=argtan(Zj√X2j+Y2j). (9) 方位角速度:
dA=YjX2j+Y2j(Yjdx−Xjdy). (10) 俯仰角速度:
dE=δ⋅{−XjZjdx−YjZjdy+(X2j+Y2j)dz}. (12) 其中:
δ=1(X2j+Y2j+Z2j)√X2j+Y2j, (13) 式中:dx, dy, dz为飞机在Og-XjYjZj坐标系下三向的瞬间位移变化率,可通过机载GPS下发数据中目标的东、北、天三向速度经过必要坐标旋转获得。
4. 试验分析
4.1 三点截止法
如图 1所示,某日实际接收的数据如星号,从上到下依次为接收到的时间、纬度、经度、高程数据,不但包含偏离真实数据较大的大野值点,也包含与真实数据很“贴近”的小野值点,圆点是剔除野值后的结果[13]。
4.2 外推内插法
如图 2,野值剔除后的飞机定位信息经坐标转换后,数据频率仍然很低(图中星号所示)。采用该算法将低频率数据处理成经纬仪引导所需的高频率数据[14]。图 2为采用最小二乘外推结果与本方法的结果比较,从图可看出,最小二乘外推结果呈“刺猬”状,本方法的外推结果平滑连续。
4.3 渐进式跟踪算法
如图 3,星号表示源1,圈表示源2,点表示切换过程的数据融合结果,从引导源1切换到引导源2,采用式(6)的算法[15],可平滑地完成引导源的切换。
5. 结束语
舰载机飞行试验中,根据光电设备的引导需求,分析了机载系统可提供数据特点,研究并实现了舰载环境下光电经纬仪的引导算法。通过飞行试验验证,方法有效可行,已应用到舰载环境的数据处理和目标跟踪中,文中的数据处理方法也可推广应用到其它目标,如导弹、舰艇和民用飞机的航迹和姿态解算中。
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