平差-课程设计本科学位论文.doc

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1、课程编号：课程性质：必修误差理论与测量平差基础课程设计报告学院：测绘学院专业：测绘工程班级：2011级学号：姓名：2013-2-25至2013-3-8（一）图1为一水准网，A、B、C为已知高程点，为9个待定高程点，第一次观测了图中1~15条水准路线的高差，各水准路线的观测高差、距离及已知点高程均列于表1，试求（1）1公里高差平差值中误差；（2）各待定点高程平差值及中误差；如果准备加测5段高差16~20（图中用虚线表示），（3）试估算平差后各待定点的精度；（4）精度最弱的点发生改变没有；（5）哪一点精度提高得最多。

2、图1表1水准网观测数据线路号观测高差(m)距离(km)线路号观测高差(m)距离(km)11.49570.4112.04160.821.78920.5121.53550.735.20620.7131.74500.842.08530.9142.74340.453.41750.4151.37850.561.20801.0160.676.03730.6170.684.33070.6181.893.65100.6190.8102.51200.3201.2已知点高程：、、、数学模型：间接平差：函数模型：V=Bx-l,l=L-

3、L0;基础方程：V=Bx-lBTPV=0解向量：x=NBB-1W随机模型：D=σ02QQxx=NBB-1计算过程：(1).列误差方程易得到矩阵B和矩阵l：B=000100000100000000-100000000010-1000000-1000000000100000000-100000000001000000001-1000000001-100000000-10100010000-10001000000000100-1000000001-1l=（单位：0.1mm）0-29030-17000200406(2).

4、组成法方程取1公里的观测高差为单位权观测，即按P=1/S定权，得观测值的权阵：P=21/2000000000000000200000000000000013/700000000000000011/900000000000000021/2000000000000000100000000000000012/300000000000000012/300000000000000012/300000000000000031/300000000000000011/400000000000000013/700000000000

5、000011/400000000000000021/20000000000000002组成法方程：BTPBx-BTPl=0令：NBB=BTPBW=BTPl得：x=NBB-1W解法方程x=-16.9170.93821-6.3750.049181.4821.072-1.13312.7434-1.6798改正数为：v=（单位：0.1mm）0.0491812.08316.917-2.111-0.938210.6256.3751.4820.410070.20503-0.54681.729-3.9508-1.2614-1.5

6、767解：(1).1公里高差平差值中误差：==1.2422mm(2).各待定点高程平差值及中误差：平差值：X=X0+x144.6687148.2427144.8917146.0689148.7982145.1062142.3737146.1807144.3605因为Qxx=NBB-1，所以Dxx=QxxDXX=0.450060000000000.4562400.094040.0298780.0402210.0453920.0429020.059182000.5786500000000.0940400.305630

7、.0971050.130720.147520.139430.1923400.02987800.0971050.662530.571390.525820.547760.4042900.04022100.130720.571391.16090.99270.559320.5442400.04539200.147520.525820.99271.22610.56510.6142100.04290200.139430.547760.559320.56510.905220.5805200.05918200.192340.40

8、4290.544240.614210.580520.80081则各点中误差为：0.67090.67540.76070.55280.81391.07741.10730.95140.8949(3).最弱点为P7，其精度为1.1073(4).加测后的B=000100000100000000-100000000010-1000000-1000000000100000000-100