研究生数学建模竞赛B题Word格式文档下载.docx
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目标跟踪处理流程[4,5]通常可分为航迹起始、点迹航迹关联(数据关联)[6-8]、航迹滤波[9-18]等步骤。
如果某个时刻某雷达站(可以是运动的)接收到空间某点反射回来的电磁波,它将记录下有关的数据,并进行计算,得到包括目标相对于雷达站的距离、方位角和俯仰角等信息。
航迹即雷达站在接收到某一检测目标陆续反射回来的电磁波后记录、计算检测目标所处的一系列空中位置而形成的离散点列.航迹起始即通过一定的逻辑快速确定单个或者多个离散点序列是某一目标在某段时间内首先被检测到的位置.点迹航迹关联也称同一性识别,即依据一定的准则确定雷达站多个回波数据(点迹)中哪几部分数据是来自同一个检测目标(航迹).航迹滤波是指利用关联上的点迹测量信息采用线性或者非线性估计方法(如卡尔曼滤波、拟合等)提取所需目标状态信息,通常包括预测和更新两个步骤。
预测步骤主要采用目标的状态方程获得对应时刻(被该目标关联上的点迹时间)目标状态和协方差预测信息;
更新步骤则利用关联点迹的测量信息修正目标的预测状态和预测协方差。
现有3组机动目标的测量数据,数据分别包含在Data1.txt,Data2.txt,Data3.txt文件中,其中Data1.txt为多个雷达站在不完全相同时刻获得的单个机动目标的测量数据,Data2.txt为某个雷达站获得的两个机动目标的测量数据,Data3.txt为某个雷达站获得的空间目标的测量数据。
数据文件中观测数据的数据结构如下:
目标
距离
(m)
目标方位
(°
)
俯仰
测量
时间
(s)
传感器
标号
其中Data1.txt和Data2.txt数据的坐标系表示如下:
原点O为传感器中心,传感器中心点与当地纬度切线方向指向东为x轴,传感器中心点与当地经度切线方向指向北为y轴,地心与传感器中心连线指向天向的为z轴,目标方位指北向顺时针夹角(从y轴正向向x轴正向的夹角,范围为0~360°
),目标俯仰指传感器中心点与目标连线和地平面的夹角(即与xOy平面的夹角,通常范围-90°
到90°
)。
Data1.txt中的雷达坐标和测量误差如下:
雷达标号
经度(°
纬度(°
高度(m)
测距误差(m)
方位角误差(°
俯仰角误差(°
1
122.1
40.5
50
0.4
2
122.4
41.5
40
0.3
3
122.7
41.9
60
0.5
Data2.txt雷达坐标为[0,0,0]。
对应两个目标的测量误差如下:
100
0.6
Data3.txt的雷达坐标和测量误差为:
118
39.5
其余格式与Data1.txt和Data2.txt相同。
请完成以下问题:
1.根据附件中的Data1.txt数据,分析目标机动发生的时间范围,并统计目标加速度的大小和方向。
建立对该目标的跟踪模型,并利用多个雷达的测量数据估计出目标的航迹。
鼓励在线跟踪。
2.附件中的Data2.txt数据对应两个目标的实际检飞考核的飞行包线(检飞:
军队根据国家军标规则设定特定的飞行路线用于考核雷达的各项性能指标,因此包线是有实战意义的)。
请完成各目标的数据关联,形成相应的航迹,并阐明你们所采用或制定的准则(鼓励创新)。
如果用序贯实时的方法实现更具有意义。
若出现雷达一段时间只有一个回波点迹的状况,怎样使得航迹不丢失?
请给出处理结果。
3.根据附件中Data3.txt的数据,分析空间目标的机动变化规律(目标加速度随时间变化)。
若采用第1问的跟踪模型进行处理,结果会有哪些变化?
4.请对第3问的目标轨迹进行实时预测,估计该目标的着落点的坐标,给出详细结果,并分析算法复杂度。
5.Data2.txt数据中的两个目标已被雷达锁定跟踪。
在目标能够及时了解是否被跟踪,并已知雷达的测量精度为雷达波束宽度为3°
,即在以雷达为锥顶,雷达与目标连线为轴,半顶角为1.5°
的圆锥内的目标均能被探测到;
雷达前后两次扫描时间间隔最小为0.5s。
为应对你们的跟踪模型,目标应该采用怎样的有利于逃逸的策略与方案?
反之为了保持对目标的跟踪,跟踪策略又应该如何相应地变换?
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距离(m)方位(度)俯仰(度)时间(s)传感器标号
6.1709257e+0042.9025749e+0012.8113635e-0013.6620400e+0041
6.1566089e+0042.9298999e+0011.8411389e-0013.6621400e+0041
6.1556807e+0043.0005196e+0013.9184353e-0013.6622400e+0041
6.1363009e+0043.0240173e+0013.4887902e-0013.6623400e+0041
6.1365556e+0042.9778269e+0011.6884355e-0013.6624400e+0041
6.1151310e+0042.9455560e+0011.4172489e+0003.6625400e+0041
6.0924038e+0042.9627955e+0013.4168897e-0013.6627400e+0041
6.0817721e+0042.9077318e+001-1.6447141e-0013.6628400e+0041
6.0801700e+0043.0225009e+0013.6579707e-0013.6629400e+0041
6.0656470e+0043.0424156e+001-1.2408057e-0013.6630400e+0041
6.0536258e+0042.9980347e+0016.4441987e-0013.6631400e+0041
6.0421505e+0043.0653464e+0016.9032162e-0013.6632400e+0041
6.0366631e+0043.0096935e+0013.0829764e-0013.6633400e+0041
6.0278270e+0043.0549093e+0011.0437633e+0003.6634400e+0041
6.0164889e+0043.0503457e+0015.0976442e-0013.6635400e+0041
6.0122813e+0043.0411065e+0014.9408007e-0013.6636400e+0041
5.9988535e+0042.9946802e+0013.7855374e-0013.6637400e+0041
5.9848930e+0043.1031853e+0019.6555559e-0023.6638400e+0041
5.9739829e+0042.9925441e+0013.7306364e-0013.6639400e+0041
5.9751579e+0043.0332015e+0012.7023885e-0023.6640400e+0041
5.9297356e+0043.0364824e+0013.9771819e-0013.6643400e+0041
5.9258401e+0043.0757517e+0016.1911631e-0013.6644400e+0041
5.9122627e+0043.0321449e+0012.6125193e-0013.6645400e+0041
5.9068973e+0042.9444259e+0012.8332541e-0013.6646400e+0041
5.8913075e+0043.1067773e+0016.0779740e-0013.6647400e+0041
5.8873316e+0043.0106920e+0014.3514043e-0013.6648400e+0041
5.8660861e+0043.0517587e+0014.5842339e-0013.6650400e+0041
5.8576880e+0043.0701812e+0013.7672340e-0013.6651400e+0041
5.8459402e+0043.1066373e+0018.7206445e-0013.6653400e+0041
5.8213995e+0043.0860865e+0016.4123824e-0013.6654400e+0041
5.8162204e+0043.0528061e+0014.9847207e-0013.6655400e+0041
5.8049635e+0043.1487721e+0018.7414341e-0013.6656400e+0041
5.7940315e+0043.0718662e+001-5.7413434e-0023.6657400e+0041
5.7821136e+0043.1116464e+0018.3526055e-0013.6658400e+0041
5.7731826e+0043.1680866e+0018.4228061e-0013.6659400e+0041
5.7572462e+0043.0962798e+0019.4677418e-0013.6660400e+0041
5.7497896e+0043.0486905e+0018.7768291e-0013.6661400e+0041
5.7390837e+0043.1281488e+001-5.2542695e-0013.6662400e+0041
5.7172348e+0043.0425882e+0015.0071775e-0013.6663400e+0041
5.7193391e+0043.1668548e+0018.1163401e-0013.6664400e+0041
5.7085909e+0043.1482436e+0017.9890647e-0013.6665400e+0041
5.6998808e+0043.1434053e+0014.0979542e-0013.6666400e+0041
5.6738121e+0043.1329860e+001-3.8868989e-0023.6667400e+0041
5.6767076e+0043.1907055e+0016.4494877e-0023.6668400e+0041
5.6631847e+0043.1505313e+0015.9262719e-0013.6669400e+0041
5.6468937e+0043.1596825e+001-3.7922458e-0013.6670400e+0041
5.6236523e+0043.1657421e+001-9.3214248e-0023.6672400e+0041
5.6159602e+0043.2676037e+0019.3651090e-0013.6673400e+0041
5.6100817e+0043.1291699e+0013.8219826e-0013.6674400e+0041
5.6007456e+0043.1787861e+0011.1179070e+0003.6675400e+0041
5.5877982e+0043.2209221e+0015.2470939e-0013.6676400e+0041
5.5769525e+0043.1676044e+001-2.2820915e-0013.6677400e+0041
5.5507604e+0043.2123844e+0017.2584971e-0013.6679400e+0041
5.5385465e+0043.1941532e+0014.5400915e-0013.6680400e+0041
5.5257046e+0043.2343699e+0014.1697737e-0013.6682400e+0041
5.5097623e+0043.2231277e+001-7.6124448e-0023.6683400e+0041
5.4964826e+0043.2274033e+0016.4506077e-0013.6684400e+0041
5.4885721e+0043.2497680e+001-2.2602684e-0013.6685400e+0041
5.4915599e+0043.2787655e+0013.7851746e-0013.6686400e+0041
5.4636731e+0043.3201642e+0018.7596808e-0013.6687400e+0041
5.4538694e+0043.2625427e+0012.6903407e-0013.6688400e+0041
5.4448035e+0043.2135272e+0011.2026577e-0013.6689400e+0041
5.4286157e+0043.2838746e+0014.2755294e-0