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1、各专业全套优秀毕业设计图纸课程编号: 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,1P第一次观测了图中 115 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 1620(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。图
2、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)1 1.4957 0.4 11 2.0416 0.82 1.7892 0.5 12 1.5355 0.73 5.2062 0.7 13 1.7450 0.84 2.0853 0.9 14 2.7434 0.45 3.4175 0.4 15 1.3785 0.56 1.2080 1.0 16 0.67 6.0373 0.6 17 0.68 4.3307 0.6 18 1.89 3.6510 0.6 19 0.810 2.5120 0.3 20 1.2已知点高程:、 、 、mHA564.1mHB568
3、4.1mHC3194.数学模型: 间接平差:函数模型: V = B x - l , l=L - L0;基础方程:V = B x - lBT P V = 0解向量: x=NBB-1 W ,L.0xX随机模型:D= 02 QQxx=NBB-1计算过程:(1).列误差方程 易得到矩阵 B 和矩阵 l:B=0 0 0 1 0 0 0 0 01 0 0 0 0 0 0 0 0-1 0 0 0 0 0 0 0 00 1 0 -1 0 0 0 0 00 -1 0 0 0 0 0 0 00 0 1 0 0 0 0 0 00 0 -1 0 0 0 0 0 00 0 0 0 1 0 0 0 00 0 0 0 1
4、-1 0 0 00 0 0 0 0 1 -1 0 00 0 0 0 0 0 -1 0 10 0 0 1 0 0 0 0 -10 0 0 1 0 0 0 0 00 0 0 0 1 0 0 -1 00 0 0 0 0 0 0 1 -1 l= (单位: 0.1mm)0-29030-17000200406(2).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=2 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 00 2 0 0 0 0 0 0 0 0 0 0 0 0 00 0 1 3/7 0 0 0 0 0 0 0 0 0 0 0 00 0 0 1 1
5、/9 0 0 0 0 0 0 0 0 0 0 00 0 0 0 2 1/2 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 2/3 0 0 0 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 0 0 0 02/30 0 0 0 0 0 0 0 1 2/3 0 0 0 0 0 00 0 0 0 0 0 0 0 0 3 1/3 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1/4 0 0 0 00 0 0 0 0 0 0 0 0 0 0 1 3/7 0 0 00 0 0 0 0 0 0 0 0
6、 0 0 0 1 1/4 0 00 0 0 0 0 0 0 0 0 0 0 0 0 2 1/2 00 0 0 0 0 0 0 0 0 0 0 0 0 0 2组成法方程:BTPBx - BTPl=0令:N BB=BTPB W=BTPl得: x =NBB-1 W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-
7、1.5767解:(1). 1 公里高差平差值中误差:= = 1.2422 mm6PV(2). 各待定点高程平差值及中误差:平差值:X = X 0 + x 因为 Qxx=NBB-1 ,所以 Dxx= Qxx 2144.6687148.2427144.8917146.0689148.7982145.1062142.3737146.1807144.3605DXX=0.45006 0 0 0 0 0 0 0 00 0.45624 0 0.09404 0. 0. 0. 0. 0.0 0 0.57865 0 0 0 0 0 00 0.09404 0 0.30563 0. 0.13072 0.14752 0
8、.13943 0.192340 0. 0 0. 0.66253 0.57139 0.52582 0.54776 0.404290 0. 0 0.13072 0.57139 1.1609 0.9927 0.55932 0.544240 0. 0 0.14752 0.52582 0.9927 1.2261 0.5651 0.614210 0. 0 0.13943 0.54776 0.55932 0.5651 0.90522 0.580520 0. 0 0.19234 0.40429 0.54424 0.61421 0.58052 0.80081则各点中误差为: 0.67090.67540.7607
9、0.55280.81391.07741.10730.95140.8949(3).最弱点为 P7 ,其精度为 1.1073(4).加测后的 B=0 0 0 1 0 0 0 0 01 0 0 0 0 0 0 0 0-1 0 0 0 0 0 0 0 00 1 0 -1 0 0 0 0 00 -1 0 0 0 0 0 0 00 0 1 0 0 0 0 0 00 0 -1 0 0 0 0 0 00 0 0 0 1 0 0 0 00 0 0 0 1 -1 0 0 00 0 0 0 0 1 -1 0 00 0 0 0 0 0 -1 0 10 0 0 1 0 0 0 0 -10 0 0 1 0 0 0 0 0
10、0 0 0 0 1 0 0 -1 00 0 0 0 0 0 0 1 -1-1 1 0 0 0 0 0 0 00 1 -1 0 0 0 0 0 00 0 -1 1 0 0 0 0 00 0 0 -1 1 0 0 0 00 0 0 0 0 0 -1 1 0加测后的权P= diag(5/2,2,10/7,10/9,5/2,1,5/3,5/3,5/3,10/3,5/4,10/7,5/4,5/2,2,5/3,5/3,5/9,5/4,5/6)所以加测后的 Qxx=(NBB)-1 Dxx= Qxx2DXX=0.33253 0.09076 0. 0. 0. 0. 0.01231 0. 0.014210.090
11、76 0.27747 0.10113 0. 0. 0.03562 0. 0. 0.0. 0.10113 0.35567 0. 0. 0. 0. 0. 0.0. 0. 0. 0.25812 0.14165 0.15971 0.16874 0.1658 0.194780. 0. 0. 0.14165 0.4955 0.44063 0.41319 0.42211 0.334090. 0.03562 0. 0.15971 0.44063 0.98643 0.79641 0.51098 0.479980.01231 0. 0. 0.16874 0.41319 0.79641 0.98801 0.5554
12、1 0.552920. 0. 0. 0.1658 0.42211 0.51098 0.55541 0.77243 0.529220.01421 0. 0. 0.19478 0.33409 0.47998 0.55292 0.52922 0.76325精度为: 0.57670.52680.59640.50800.70390.99320.99400.87890.8736(5).精度最弱的点没有改变,仍是 P7。(6).比较可知,P3 点的精度提高的最多。结果检核:h1= HP4 - HB =146.0640m - 144.5684m=1.4956m h2= HP1 - HB =146.3587m
13、- 144.5684m=1.7903mh3= HA - HP1 = 151.5664 - 146.3587 = 5.2077m h4= HP2 - HP4 = 148.1590m - 146.0640m = 2.0850mh5= HA - HP2 = 151.5664m - 148.1590m = 3.4175mh6= HP3 - HC =145.5286m-144.3194m = 1.2092mh7= HA - HP3 = 151.5664m - 145.5286m = 6.0378mh8= HP5 - HC = 148.6501m - 144.3194m = 4.3307mh9= HP5
14、- HP6 = 148.6501m - 144.9991m = 3.6510mh10= HP6 - HP7 = 142.9991m - 142.4869m = 2.5122mh11= HP9 - HP7 = 144.5283m - 142.4869m = 2.0414mh12= HP4 - HP9 = 146.0640m - 144.5283m = 1.5357mh13= HP4 - HC = 146.0640m - 144.3194m = 1.7446mh14= HP5 - HP8 = 148.6501m - 145.9067m = 2.7434mh15= HP8 - HP9 = 145.9
15、067m-144.5283m = 1.3784m经检核,由每个高程点平差后的高程得到的各点间的高差与已知高差平差后的结果相同。(二) (题目详见课程设计辅助系统)数学模型(1) 函数模型:测角网函数模型:测边网函数模型:(2)随机模型: nnnPQD12020(3)平差准则:VPV=min计算过程:根据题意可知:n=46 t=30 r=16现在选取待定点坐标平差值作为参数:X=X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X10 Y10 X11 Y11 X12 Y12 X13 Y13 X14 Y14 X15 Y15 T设单位权中误差为 =6 , 则角度观测的权为 ,导线边0120iP的权为 PSi = 02/s2 = 36/(k*1000*s)2,其 k 为边精度 1/2000。利用 Excel 表格计算已知方位角和各个待定点的近似坐标如下:坐标方位角() 坐标分量 坐标点号 观测角 0距离(m) x(m) y(m) X/m Y/m17 126.63535 73.431 181.148 230.5015 (17 5 6) 300. 246. 49.091 -19. -45. 137.33 289.4266 ( 5 6 7 ) 182. 249.0301 34.896 -