《测量平差》课程设计实习报告 - 图文

目录

第1部分实习概述 ....................................................................................................... 1

1.1课程设计名称及目的 ...................................................................................... 1 1.2课程设计要求 .................................................................................................. 1 第2部分控制测量技术要求 ....................................................................................... 2

2.1高程控制的技术要求 ...................................................................................... 2 2.2平面控制的技术要求 ...................................................................................... 2 第3部分控制网概况 ................................................................................................... 4

3.1测区概况 .......................................................................................................... 4 第4部分条件平差 ....................................................................................................... 5

4.1条件平差公式汇编 .......................................................................................... 5 4.2水准网条件平差 .............................................................................................. 5 4.3 平面控制网条件平差 ..................................................................................... 8 第5部分间接平差 ..................................................................................................... 14

5.1间接平差公式汇编 ........................................................................................ 14 5.2水准网间接平差 ............................................................................................ 14 5.2平面控制网间接平差 .................................................................................... 18 第6部分精度评定及误差椭圆 ................................................................................. 26

6.1高程间接平差的精度评定 ............................................................................ 26 6.2平面间接平差的精度评定 ............................................................................ 26 6.3平面间接平差的误差椭圆 ............................................................................ 27 第7部分技术总结 ..................................................................................................... 29 第8部分实习心得 ..................................................................................................... 30

第1部分 实习概述

1.1课程设计名称及目的

1.课程设计名称：

测量平差基础课程设计

2.课程设计目的：

通过控制测量外业工作采集的数据，应用测量平差基础课程中所学的知识对数据进行处理，通过数据处理更好的理解测量平差的两个基本任务：

i.对带有观测误差的观测值，列出误差方程，求出改正数，求出未知量的最可靠值；

ii.对测量成果进行精度评定。

通过平差课程设计进一步掌握平差的函数模型和随机模型的建立，掌握测量平差最常用的两种基础方法：条件平差和间接平差，并能对间接平差的成果进行评定精度。

1.2课程设计要求

1.课程设计要求：

Ⅰ.控制网概况及测量数据的整理和检验；

Ⅱ.列出条件平差和间接平差的函数模型并进行线形化，将线形化后的系数阵和常数向量列表；

Ⅲ.采用条件平差和间接平差的方法求控制点的高程和坐标平差值； Ⅳ.对控制点的坐标平差值进行精度评定，求出各点的点位中误差；对水准测量求各点高程平差值的高程中误差；

Ⅵ.对平面控制网间接平差法计算的点位，计算并绘制点位误差椭圆； Ⅶ.了解课程设计技术总结； Ⅷ.个人课程设计小结。

第2部分 控制测量技术要求

2.1高程控制的技术要求

1.水准测量的主要技术要求： 每千米高差 等级 全中误差 （mm） 二等 ≤±2 闭合差 （mm） ≤?4L 往返各一次 2.平差前计算每千米水准测量高差全中误差：

Mw??1N?WW??L? ??； Mw——高差全中误差（mm）

W——闭合差；

L——计算W时，相应的路线长度（km）； N——符合路线或闭合路线环的个数。

3.若进行往返观测，计算每千米水准测量的高差偶然中误差：

MD??1???? ??4n?L?MD——高差偶然中误差(ｍｍ)；

?——水准路线往、返高差不符值(ｍｍ)；

L——水准路线的测段长度；

n——往、返测的水准路线测段数。 (二等要求MD??1mm)

2.2平面控制的技术要求

1.光电测距导线的主要技术要求： 闭合或符平均边长 等级 合导线全(m) 长(km) 二级 2.4 200 2.测距中误差计算： 测距单位权中误差：

测距中误差 (mm) ≤±15 测角中误差 全长相对闭(″) 合差 ≤±8 ≤1/10000 ????p?d?d?

2ns误差理论与测量平差基础课程设计报告

?——单位权中误差；

?d——各边往、返测距离较差； ns——测距的边数；

pi——各边距离测量的先验权；

pi?

1?2si

?s——测距先验中误差，根据测距仪的标称精度估算。

i任一边的实测距离中误差估值：

mDi???1 pi注：宾得全站仪测距标称精度为±（2MM+2PPM），因距离较短，影响测距精

度的主要是固定误差，故可以认为各边为等精度观测，即可取pi均相等，求出的单位权中误差即可求出各边的测距中误差。

3.测角中误差的计算：

m???1?f?f???? N?n?f?——符合导线或闭合导线环的方位角闭合差；

n——计算f?时的测站数； N——f?的个数。

如控制为单一的闭合或符合导线，N为1。

3

误差理论与测量平差基础课程设计报告

第3部分 控制网概况

3.1测区概况

1.测区环境叙述

本测区位于重庆市南岸区重庆交通大学校园内从学生雅园小区到菁园操场整个片区，交通便利，人口密集，气候炎热潮湿。很多测站上的工作都会受到不同程度的人为干扰。测区中H6为已知点(H=200.000m X=10000.000m

Y=10000.000m),H6到H7的方位角已经给出(T=150o00′00″)，要求根据实习数据及已知点算出各点高程和坐标。（注：在平面控制网间接平差中认定H6、H7都为已知） 该地形中局部坡度起伏较大，其中H3-H4-H5-H6、H7-H8-H9-H10、H12-H13-H14等的坡度较缓，其余路段的坡度都相对较陡，其中H17-H18-H19坡度最陡，测量难度也比较大，水准测量时水准路线要分为很多段。 2.测区概况图

4

误差理论与测量平差基础课程设计报告

第4部分 条件平差

4.1条件平差公式汇编

条件平差的函数模型为：AL?A??0

或AV?W?0

22?1条件平差的随机模型：D???Q???P

条件方程：AV?W?0 法方程：NaaK?W?0 法方程的解：K??NaaW 改正数方程：V?QATK?PA?1K

?1??L?V 观测量平差值：L

4.2水准网条件平差

1.外业高差观测数据及其初步处理

5

误差理论与测量平差基础课程设计报告

2.水准网中有18个待定点，高差观测值个数n=21，必要观测数t=18，多余观测r=3。列出3个条件方程：

V1100V2100V3100V4100V5100V6100V7110V8011V8'100V9001V9'010V10001V11001V12001V13001V14001V15001V16001V17100V18100V19100W0.254-0.002-0.5253.定权并组成法方程。

令C=50,于是Pi=C/Si ，Qii=1/Pi，则

?1.86???1.58????0.76??1.44????0.88??1.74????0.49??1.08????1.80????1.19????0.93???2.97??4.45????2.85??2.14????1.10????1.59??1.23????3.63??1.26???1.06???Q2121

4.由条件方程知系数阵为

?111111101000000000111??000000110010000000000? ?A??321??000000010101111111000??W31?w1??0.254?????0.002?

??w?2?????w3?????0.525??5.根据Naa?AQAT?AP?1AT的

Naa?16.50.490??0.061?0.01230.0007??而N?1???0.01230.4128?0.024?

??0.492.51.08aa??????1.0818.6??0??0.0007?0.0240.0552??6

误差理论与测量平差基础课程设计报告

6.由此组成法方程NaaK?W?0为

?16.50.490??k1??0.254? ??????0.492.51.08k??0.002?0???2????0????1.0818.6????k3???0.525?7.解算法方程K??NaaW为

?1?-0.0151??

K??-0.0086????0.0287????L?V求得： 8.计算改正数和平差值。利用改正数方程V?QATK和L?v1??-0.0282???L??v??-0.0239??-238.0182?1??????2???L-360.5949?2????v3??-0.0115??L?3??-67.9815?????v-0.0218?????4????L-39.0748?4????v5??-0.0133??L?10.6457??5??????????v6??-0.0263???L6??-674.6563??v??-0.0117?????-6.2157??7???L7?????v8??0.0217??8??L?10.5377??v??-0.0272???????8????L-51.5912?8?????v9??0.0342??9??L?-220.2438????????V??v9????-0.0080?L??L?V??L??-4.3220?9?????v10??0.0853??L??-601.2377??10?????????v11??0.1278???L11??-62.6492??v??0.0819??L??-95.7081???12??12?????v0.0615?13?????L13??438.5705??v??0.0316?????333.7916?14L?????14????v15??0.0457???L??250.3127?15?????????v0.035316L-53.3737?????16??? ?v17??-0.0549??L???830.4001?17?????????v-0.0191L333.7269?18??18??????L????-0.0160???v19????263.3600??19???9. 条件平差后各点高条高程

条件平差后的高程H1H2H3H4H5H6H7H8H9H1020695.023820457.005620096.410720028.429219989.354420000.000019325.343719319.128019329.665719109.4219 7

误差理论与测量平差基础课程设计报告

H11H12H13H14H15H16H17H18H1918508.184218445.535018349.826918788.397419122.189019372.501719267.536820097.936920431.6638

4.3 平面控制网条件平差

1.外业角度距离观测数据及其初步处理 雅园闭合圈导线坐标计算表点号H1H2H3H4H5H6H7H8H17H18H19H1Σ1619 59 35+251620 00 00823.786角度观测值°′″167 38 10183 05 36114 22 37160 03 02193 52 21108 08 56204 47 10125 11 40106 14 57173 34 2983 00 37改正数″+02+02+02+03+02+02+03+03+02+02+02改正后角度°′″167 38 12183 05 38292 32 55114 22 39227 55 34160 03 05207 58 39193 52 23221 51 02108 08 58150 00 00204 47 13174 47 13125 11 43119 58 56106 14 5946 13 59173 34 3139 48 2683 00 39302 49 0552.10663.056-10.95181.318-118.26289.76491.55424.32365.44187.116-62.79343.75343.36372.162-28.40937.89134.27179.141-41.25方位角°′″290 27 17水平距离m93.156-14.015视距差m坐标增量△X/m△Y/m32.555-87.2820.13930.3480.118-25.3900.057-63.7290.108-32.5910.065-75.4450.130-24.2220.036-44.8580.134125.4220.27148.4400.09428.2400.078-1.2300.057-73.0910.048-28.1260.023-33.8530.044-29.1920.02743.5580.0532.2100.01577.7520.055130.9410.11140.3690.039-43.7900.032-0.504改正后坐标增量△X/m△Y/m32.69430.466-25.333-63.621-32.526-75.315-24.186-44.724125.69348.53428.318-87.225-73.04310121.480-28.10310096.147-33.80910032.526-29.16510000.00043.6119924.6852.2259900.49977.8079855.775131.0529981.46840.40810030.002-43.75810058.3200.0000.00010251.34510295.10310254.69510123.64310045.83610043.61110000.00010029.16510062.97410091.077坐标X/m10058.32010091.014Y/m10251.34510164.120一教门前小三角形闭合圈导线坐标计算表点号H7H8H9H7Σ179 59 45+15180 00 00124.774角度观测值°′″94 28 2758 52 0226 39 16改正数″+05+05+05改正后角度°′″94 28 3258 52 07295 55 0626 39 2189 15 4546.40754.044-7.637方位角°′″174 47 13水平距离m24.32329.721视距差m坐标增量△X/m△Y/m-24.2222.2100.001-0.00123.622-48.6080.001-0.0020.59746.4030.001-0.002-0.0030.005改正后坐标增量△X/m△Y/m-24.22123.6230.5982.209-48.6109924.12246.4019924.72010043.6279997.226坐标X/m9924.7209900.499Y/m10043.62710045.836菁园及足球场闭合圈导线坐标计算表点号H8H9H10H11H12H13角度观测值°′″ 83 09 30138 55 45222 37 5190 49 2288 40 0194 37 42改正数″-09-08-08-08-08-08-08-09-09改正后角度°′″83 09 21138 55 37254 50 43222 37 43297 28 2690 49 14208 17 40 88 39 53116 57 3394 37 3431 35 07H14211 35 50 H15H16H8Σ1260 01 15-751260 00 00929.776Σ194 55 32134 39 42211 35 42 63 10 49194 55 2378 06 12134 39 3332 45 4561.34579.322-17.97755.23724.085106.974-51.737142.490-35.516222.506-80.016148.48174.02559.37789.104方位角°′″295 55 06水平距离m54.0445.333视距差m坐标增量△X/m△Y/m23.622-48.6080.014-0.034-15.522-57.3120.015-0.03868.501-131.7350.038-0.095-196.228-104.8980.057-0.142-64.599127.0060.037-0.09191.12756.0290.027-0.06824.92249.2950.014-0.03516.35277.6180.020-0.05151.58633.1970.017-0.038-0.2390.592改正后坐标增量△X/m△Y/m23.636-15.50768.539-196.171-64.56291.15424.93616.37251.603-48.642-57.3509908.628-131.8309977.167-105.0409780.996126.9159716.43455.9619807.58849.2609832.52477.5679848.89633.1599900.4990.0000.00010045.83610012.6779935.1109885.8509829.8899702.9749808.0149939.844坐标X/m9900.4999924.135Y/m10045.8369997.194，

8

2.平面控制中有18个带定点，高差观测值个数n=44，必要观测数t=35，多余观测r=9。 3.由

n?1[v?i]1?wT?0

n[cosTi?vSi]1?1n[(yn?1?yi)v?i]1?wx?02062.65

n[sinTi?vSi]1?1n[(xn?1?xi)v?i]1?wy?02062.65

列出9个条件方程：

平面控制网条件方程Vβ11Vβ12Vβ13Vβ14Vβ15Vβ16Vβ17Vβ17'Vβ18Vβ18'Vβ8''Vβ19Vβ19'Vβ110Vβ111Vβ112Vβ113Vβ114Vβ115Vβ116Vβ117Vβ118Vβ119VS11-0.1071.174-2.827-4.412-5.89-4.661-12.186-7.957-4.416-3.053-1.577-1.4143.651-2.1144.824-2.222-1.1462.358-2.3571.1456.9920.8981.4550.3945-5.994-12.348-14.307-0.9369-0.3945.139-3.7175.7948.92411.5316.62210.4694.5047.7563.2965.3682.5021.608 VS17VS18VS19W-25-1575-0.30.5-123.0-50.4-23.959.2VS2VS3VS4VS5VS6VS7VS8VS8'VS9VS9'VS10VS11VS12VS13VS14VS15VS160.3835-0.6701-0.8831-0.7449-0.8660-0.9236-0.7423-0.4691-0.66720.5-0.99590.0909-0.99590.09090.4371-0.0899-0.49970.8660.4371-0.8994-0.2614-0.96520.01290.99990.69170.76860.54200.72220.6402-0.84040.4613-0.8872-0.8805-0.474-0.45340.89130.85190.52380.45120.89240.20610.8410.97850.5412 4.定权并组成法方程。

知测角中误差σβ= ±2.5″，测边所用测距仪的标称精度公式σS= 2mm+2ppm2Dk m，由于D较小，可认为σS=2mm。令σ0=σβ，于是Pβ=1，又PS=σ0/σs，则PS=25/16。可得协因素阵

2

2

Q4444?1??????????????23个?????????????????11....1110.640.640.64....0.640.6421个??????????????????????????????0.64?

5.由条件方程知系数阵A和W，根据Naa?AQAT?AP?1AT得

?w1??-25?????w-152?????w3??75?????w-0.34??????w5???0.5?????w?6??-123.0??w??-50.4?7???? ?w8??-23.9??????59.2??w9?W91Naa?11?0000-1.547-66.01100??030-2.4642.3190000???009000019.76360.85???0-2.46406.324-2.89920.4950.184300?????02.3190?2.89923.3396?0.0292?0.044500??000.495?0.0292178.256119.943300?-1.547???66.011? 000.1843?0.044519.9433648.710900??0019.763o000167.907199.4184????0060.850000199.4184646.1133??

而

误差理论与测量平差基础课程设计报告

?0.2336??-0.0008?0??-0.009??0.0001??-0.0006?0.0238?0??0?-0.0008Naa?1??0.74830.0887?00.30670000-0.0028-0.0028??0.088700.27330.1756-0.0007-0.000100??-0.442700.17560.7593-0.0004000?-0.00030-0.0007-0.00040.0056-0.000200??-0.00010-0.00010-0.00020.00400?0-0.002800000.0094-0.0026??0-0.00280000-0.00260.005?000000-0.00090.0001-0.00060.0238-0.4427-0.0003-0.0001

?16.由此组成法方程NaaK?W?0 ，解算法方程K??NaaW为

?6.9475??11.4077?-21.4142??1.2049K??-7.0091??0.6604?0.7635??0.5942??1.7417??????????? ?????L?V求得： 7.计算改正数和平差值。利用改正数方程V?QATK和L11

误差理论与测量平差基础课程设计报告

??V?1?167.6349?V????4.2238??2?2.0415???183.0928?V???3???0.3139??V??114.3769?41.5384?????160.0510?V?5??4.8265??V???193.8738?6??6.9475??108.1508?V?7??7.7445??V???204.7883??7??94.4750?V??3.0501?8?????8.4367??125.1968?V?8??83.1524?V????21.4142??8??11.4077?????58.8704?V?9???17.9882?138.9122?V??0.5422???9????26.6546?V?10?222.6273?V????12.6976????11???3.5409?90.8218?V?12??10.9798?88.6700?V?????13??2.1229?94.6289?V??14??5.2289?211.5958??V????15???10.106?194.9255?V????16134.6569???V??17.1268??17??6.9884?106.2511V??V???173.5742??18????1.8875??V?19???3.0154?83.0094?V????S1???0.2911?92.8649?V?S278.8518?????0.2892??V?S3???037.2450?V??.6460??S4?71.5595?V??0.6025??S5???0.6409?43.1121?V??S686.9943????0.1217???VS7???22.7707?V??1.5523?54.9963?S8??0.9523??S8??0.8363?V???88.9277?V???S9???1.175358.2017???V?S9???4.4754?41.9316????0.8135?147.6675?VS10??V????S?221.642811???0.8632?143.3111?VS12?0.8211??V????0.9079?107.8819?S13???56.4034?VS14??V??1.1664??80.4911?S15??1.1691?62.2681?S16??V?0.9231????0.6453?181.9633?VS17???63.6937?VS18?????0.6377??V51.9244S19????0.1816??

L??L?V?12

8.条件平差后各点坐标 条件平差后坐标X1Y1X2Y2X3Y3X4Y4X5Y5X6已知Y6已知X7Y7X8Y8X9Y910057.81510251.11410090.39510163.82410120.73210090.71710095.32010062.55210031.49610028.67110000.00010000.0009924.66110043.4979900.43810045.7079924.0619997.094 X10Y10X11Y11X12Y12X13Y13X14Y14X15Y15X16Y16X17Y17X189908.5539939.7769976.9699808.0689780.8059703.0679716.2259830.1489807.3419886.1979832.2719935.4839848.61210013.1149855.57510123.4619981.211Y1810254.586X19Y1910029.58210294.909

第5部分 间接平差

5.1间接平差公式汇编

间接平差的函数模型为：L??BX??d

或V?Bx??l

22?1间接平差的随机模型：D???Q???P

条件方程：V?Bx??l

l?L-L0?L?(BX0?d)

法方程：(BTPB)?1x??BTPl?0 法方程的解：x??(BTPB)?1BTPl?N?1BBW

??L?V，X??X0?x观测量和参数的平差值：L?

单位权中误差：

?0VTPVVTPV??rn-t

22?1??Q??N00BB ???平差参数X?的协方差阵：DX?XXX

5.2水准网间接平差

1.水准网中有18个待定点，高差观测值个数n=21，必要观测数t=18，多余观测r=3，选取18个待定点的高程为参数。其中参数近似值如下：

X10参数的近似值X50X6已知X70X80X9020695.17920457.18920096.61820028.64819989.5952000019325.3719319.16619329.682 X20X30X40X100X110X120X130X140X150X160X170X180X19019109.40418508.08118445.30418349.51418788.02319121.78319372.0519267.60220098.05720431.803 2.列出21个误差方程：

误差理论与测量平差基础课程设计报告

水准网间接平差方程Vx1x2x3x4x5x7x8x9x10x11x12x13x14x15x16x17x18x19v1-11v2-11v3-11v4-11v5-1v61v7-11v8-11v8’-11v9-11v9’1-1v10-11v11-11v12-11v13-11v14-11v15-11v161-1v17-11v18-11v191-1l0.254-0.002-0.525 3.定权并组成法方程。

令C=50,于是Pi=C/Si ，Qii=1/Pi，则

?1.86???1.58????0.76??1.44????0.88??1.74????0.49??1.08????1.80????1.19????0.93???2.97??4.45????2.85??2.14????1.10????1.59??1.23????3.63??1.26???1.06???Q21214.由条件方程可得矩阵B和Q可得：

Nbb?BTQ-1B?15

误差理论与测量平差基础课程设计报告

Nbb=1.48103-0.537630-0.53761.170546-0.63290-0.632911.948700-1.3158000000000000000000000000000000000000000-0.94340000000000000000-0.94340000000000000000000000000000000-0.6944000000000000001.830810000000000000003.6908-2.0408-1.0753000000000000-2.04084.33531-0.9259000000-0.813-0.55560000-1.0753-0.92592.84153-0.84030000000000000-0.84031.17704-0.33670000000000000-0.33670.56142-0.22470000000000000-0.22470.5756-0.35090000000000000-0.35090.81817-0.46730000000000000-0.46731.37638-0.90910000000000000-0.90911.53802-0.6289000000-0.813000000-0.62891.44194000000-0.5556000000000.83104-0.27550000000000000-0.27551.06913-0.79370000000000000-0.79371.73705 Nbb-1?

Nbb-1=3.928142.807531.855621.397740.530180.691690.847320.766020.771540.785320.805970.81920.829130.834230.841611.562863.005883.506762.8075343.3359982.2049091.660840.6299740.494370.60560.5474920.5514390.5612890.5760480.5855010.5925980.5962470.601521.1170172.1483742.5063661.855622.204912.501611.884330.714750.326750.400270.361860.364470.370980.380740.386980.391670.394090.397570.738291.419961.656571.397741.660841.884331.991830.755520.246120.30150.272570.274540.279440.286790.291490.295030.296840.299470.556111.069581.24780.530180.629970.714750.755520.832780.093360.114360.103390.104130.105990.108780.110570.111910.11260.113590.210940.40570.473310.691690.494370.326750.246120.093361.555411.513871.535571.53411.530421.524911.521381.518731.517371.51541.322920.937820.804150.847320.60560.400270.30150.114361.513871.854491.676551.688631.71881.763991.792941.814671.825851.841991.620561.148820.985070.766020.547490.361860.272570.103391.535571.676552.088742.060751.990871.886171.819121.768771.742891.705491.465071.038590.890560.771540.551440.364470.274540.104131.53411.688632.060753.144642.879832.483062.228952.038151.940071.79831.475631.046080.896980.785320.561290.370980.279440.105991.530421.71881.990872.879835.098513.972783.251812.710452.432182.029951.501991.064760.9130.805970.576050.380740.286790.108781.524911.763991.886172.483063.972786.204854.784373.717773.169522.377041.541491.092760.937010.81920.58550.386980.291490.110571.521381.792941.819122.228953.251814.784375.76594.362913.641742.599331.566781.110690.952380.829130.59260.391670.295030.111911.518731.814671.768772.038152.710453.717774.362914.847333.996332.766251.585771.124160.963930.834230.596250.394090.296840.11261.517371.825851.742891.940072.432183.169523.641743.996334.178592.852041.595541.131080.969860.841610.601520.397570.299470.113591.51541.841991.705491.79832.029952.377042.599332.766252.852042.976061.609651.141080.978441.562861.117020.738290.556110.210941.322921.620561.465071.475631.501991.541491.566781.585771.595541.609652.98912.118981.816953.005882.148371.419961.069580.40570.937821.148821.038591.046081.064761.092761.110691.124161.131081.141082.118984.075463.494573.506762.506371.656571.24780.473310.804150.985070.890560.896980.9130.937010.952380.963930.969860.978441.816953.494574.07688 W=BTQ-1l =

[0 0 0 -1.1764 -1.1764 -0.0022 -0.4268 0.0022 0 0 0 0 0 0 0.4268 0 0 0]T

5.由此组成法方程Nbbx??W?0，并解算法方程x??NbbW得参数改正数和参数平差值：

?1??X0?xx??X??16

误差理论与测量平差基础课程设计报告

-0.15531-0.18346-0.20738-0.218880.013321-0.02634-0.03799-0.01630.0178860.1032070.2310450.3129190.3743960.4059970.451674-0.06524-0.12019-0.1392620695.0220457.0120096.4120028.4319989.6119325.3419319.1319329.6719109.4218508.1818445.5418349.8318788.419122.1919372.519267.5420097.9420431.66 6.计算改正数和观测值的平差值。由V?Bx??L?V得： ??l和L

??L?V?V?L-0.02816-0.02392-0.0115-0.0218-0.01332-0.02634-0.011650.021691-0.027250.034186-0.008040.0853210.1278380.0818740.0614770.03160.0456770.035335-0.05495-0.01907-0.01605-238.018-360.595-67.9815-39.074810.64568-674.656-6.2156510.53769-51.5912-220.244-4.32204-601.238-62.6492-95.7081438.5705333.7916250.3127-53.3737830.4001333.7269263.36 7.间接平差后各点高条件程 条件平差后的高程H1H2H3H4H5H6H7H8H9H1020695.023820457.005620096.410720028.429219989.354420000.000019325.343719319.128019329.665719109.4219H11H12H13H14H15H16H17H18H1918508.184218445.535018349.826918788.397419122.189019372.501719267.536820097.936920431.6638

17

误差理论与测量平差基础课程设计报告

5.2平面控制网间接平差

1.平面控制网中有17个待定点，高差观测值个数n=43，必要观测数t=34，多余观测r=9，选取17个待定点的X，Y为参数。其中起算数据和参数近似值如下：

起算数据点号H6H7坐标（m）X10000.0009924.6607Y10000.00010043.4972边长（m）86.9943方位角150 00 00 2.定权并组成法方程。

知测角中误差σβ= ±2.5″，测边所用测距仪的标称精度公式σS= 2mm+2ppm2Dk m，由于D较小，可认为σS=2mm。令σ0=σβ，于是Pβ=1，又PS=σ0/σs，则PS=25/16。可得协因素阵

?1??????????????23个???????????????????????????????????????????????0.64?2

2

11....1110.640.640.64....0.640.6420个44Q44

18

坐标方位角改正数方程的系数计算表点号H1H2H3H4H5H6H7H8H17H18H19H1H8H9H10H11H12H13H14H15H16H8H7H8H9H7角度观测值°′″167 38 10183 05 36292 32 39114 22 37227 55 16160 03 02207 58 18193 52 21221 50 39108 08 56150 00 0086.9943204 47 10174 47 10125 11 40119 58 50106 14 5746 13 47173 34 2939 48 1683 00 37-25.00 83 09 30138 55 45254 50 53222 37 51297 28 4490 49 22208 18 06 88 40 01116 58 0794 37 4231 35 49211 35 50 63 11 39194 55 3278 07 11134 39 4275.0094 28 2758 52 02295 55 0826 39 16-15.0089 15 5246.4070.59746.40354.04423.622-48.60832 46 53174 47 2561.34524.32351.586-24.22233.1972.21079.32216.35277.61855.23724.92249.295106.97491.12756.029142.490-64.599127.006222.506-196.228-104.898148.48168.501-131.73559.377-15.522-57.312302 48 53295 55 0852.10654.04428.24023.622-43.790-48.60863.05648.44040.369181.318125.422130.94189.764-44.85877.75224.323-24.2222.210-75.44543.55843.753-32.591-29.19272.162-63.729-33.85337.891-25.390-28.12679.14130.348-73.091方位角α°′″0水平距离Sm93.156近似坐标增量△X/m32.555△Y/m-87.282X0(m)10057.68310090.23810120.58610095.19610031.467近似坐标Y0(m)10250.97910163.69710090.60610062.48010028.62710000.00010043.49710045.70710123.45910254.40010294.76910045.7079997.0999939.7879808.0529703.1549830.1609886.1899935.48410013.10210043.50210045.7079997.099近似边长S0(m)93.15679.14137.89172.16242.5486.994324.32389.764181.31863.05652.10654.04459.377148.481222.506142.490106.97455.23779.32261.22824.31954.04446.407S-S0(mm)0000121300000000000000117400l-l0(″)00007500000000000000-25-1500a(″/mm)b(″/mm)ρ″△Y/S02ρ″△X/S02△X/S0△Y/S0290 27 03-2.07457230.77378730.3494676-0.936944-2.4070570.99943040.3834675-0.923554-0.67008-0.742287-4.0407444-3.647675-1.3409284-2.524326-0.883138-0.469125-3.3273188-3.714739-0.766126-0.6862251.18716716-2.056243-0.8672410.50069950.77051932-8.445031-0.9958480.09086051.99036495-1.148315-0.4997330.86618240.82152230.78689620.69172390.72216220.7682060.640208710000.0009924.6619900.4399855.5819981.00310029.4439900.4399924.0619908.5399977.0409780.8129716.2139807.3409832.2629848.6149924.6589900.4399924.0612.094212262.5129095-3.32678722.1454320.5419721-0.840402-3.43271951.66819660.4370883-0.899415-3.3530081-0.908106-0.261414-0.965222-1.23249440.64088590.4613452-0.887218-0.4370281.290271211.0099083-0.817529-0.65627-0.8819-0.471439-0.4533580.89133271.64254070.85186120.52376283.332485321.68479970.45118310.89242722.544489580.53605470.20614710.97851791.826519162.83829310.77077282-8.447810.8425230.5421866-0.9960110.0908754-3.43271951.66819660.4370883-0.8994154.444312740.05717850.01286440.9999138

3.列出43个误差方程：

平面间接平差的误差方程x1y1x2y2x3y3x4y4x5y5x8y8x9y9x10y10x11y11x12y12x13y13x14y14x15y15x16y16x17y17x18y18x19y19lVβ11.25221.37162.07460.7738Vβ2-2.0746-0.7738-0.3325-0.22562.40710.9994Vβ3-2.4071-0.9994-1.63374.64714.0407-3.6477Vβ4-4.04073.64772.6998-1.12331.3409-2.5243Vβ5-1.34092.5243-1.98641.1904Vβ6-3.32733.7147Vβ7-0.7705Vβ7′0.7708Vβ81.2198Vβ8′-5.2594Vβ8″4.2035Vβ9-3.4327Vβ9′3.4327Vβ10Vβ11Vβ12Vβ13Vβ14Vβ15Vβ16-1.8265Vβ171.9904Vβ18Vβ193.32682.1454VS1-0.34950.93690.3495-0.9369VS2-0.38350.92360.3835-0.9236VS30.67010.7423-0.6701-0.7423VS40.88310.4691-0.8831-0.4691VS50.76610.6862VS7-0.9958VS8-0.4371VS8′0.4997VS9VS9′VS10VS11VS12VS13VS14VS15VS160.8425VS17VS18VS190.5420-0.8404-3.3268-2.145475.0000-8.44508.4478-4.4443-7.29671.7010-1.66823.43270.0797-3.35301.66822.57630.90083.3530-0.90812.1205-1.5490-1.2325-0.64091.23250.7955-0.43700.64091.45840.81750.4370-0.81751.7273-0.1661-1.2903-0.65631.29030.6563-0.2804-2.2988-1.00991.0099-1.64252.83831.14831.64251.68481.1487-2.54450.5361-1.1688-1.9352-0.82150.8215-0.78690.78692.51290.36755.1-155.3115.666.20.09090.8994-0.86620.26140.9652-0.2614-0.9652-0.46130.88720.4613-0.88720.88190.4714-0.8819-0.47140.4534-0.8913-0.45340.89130.85190.52380.45120.89240.20610.9785-0.6917-0.72220.69170.72220.7682-0.54200.64020.8404-0.8425-0.5422-0.7682-0.6402-0.2061-0.97850.5422-0.4512-0.8924-0.8519-0.5238-0.0129-0.99910.4371-0.8994-0.49970.866234.9-36.519.0-32.52.1-101.4-16.997.312.925.1466.7267.7-97.4-15.7 2.3226-0.0423-3.33253.3325-1.6848-0.78801.8265-2.838310.1160-3.4327-1.66821.6682-7.8770-1.61100.0572-1.9904-1.1483-25.0000-15.00002.5445-0.5361-0.7180-2.30221.2727-1.7260-2.09422.0942-2.5129-5.42104.由条件方程可得矩阵B和Q可得：

Nbb?BTQ-1B? Nbb=17.5894349.23681073.09675891.9486174-4.99377-2.0733550000000000000000000000006.9669846-8.359916-22.65941-0.7521579.23681079.55787823.6144451-0.13562-1.862614-0.7733360000000000000000000000004.4928967-5.391176-15.48154-3.2577463.09675893.614445110.6293123.02091952.9023181-10.9649-9.7263698.7803787000000000000000000000000-6.901779-4.4508471.9486174-0.135623.02091954.35286621.6431165-6.202647-4.0382763.6455114000000000000000000000000-2.574278-1.660111-4.99377-1.8626142.90231811.643116525.721779-19.7018-18.211999.7209545-5.41817510.199939000000000000000000000000-2.073355-0.773336-10.9649-6.202647-19.701838.09387627.848386-21.909644.8912009-9.20788900000000000000000000000000-9.726369-4.038276-18.2119927.84838627.334345-19.732285.0651856-9.058597000000000000000000000000008.78037873.64551149.7209545-21.90964-19.7322822.144396-7.1677875.49663730000000000000000000000000000-5.4181754.89120095.0651856-7.16778718.950309-16.64068000000000000000000000000000010.199939-9.207889-9.0585975.4966373-16.6406822.667709000000000000000000000000000000000082.2182345.53032-63.5205-29.5014-11.50983.11723500000000-4.647530.979187-9.4039418.41897-5.14443-4.57621-1.635111.56624600000000000045.53032319.0009-79.0898-21.8039-5.593471.514892000000007.222054-1.521610.355222-11.821613.857534.984263-0.943330.903597000000000000-63.5205-79.0898117.020320.87354-6.949574.727198-4.13257-2.14894000000006.269827-9.743030000000000000000-29.5014-21.803920.8735419.8924110.15426-5.190521.1102360.577323000000003.046967-4.734850000000000000000-11.5098-5.59347-6.9495710.1542617.69745-5.784861.3005660.201028-0.53861.0075690000000000000000000000003.1172351.5148924.727198-5.19052-5.784866.320323-1.7795-3.15732-0.280070.52393600000000000000000000000000-4.132571.1102361.300566-1.77953.8905731.602916-1.62243-1.227310.5638610.286803000000000000000000000000-2.148940.5773230.201028-3.157321.6029164.7830861.399814-1.67524-1.05482-0.5365300000000000000000000000000-0.5386-0.28007-1.622431.3998146.3758450.220816-2.91174-3.46834-1.303072.1193180000000000000000000000001.0075690.523936-1.22731-1.675240.2208162.7151150.661723-2.64097-0.66281.077973000000000000000000000000000.563861-1.05482-2.911740.6617234.218561-0.101561.494811-1.2005-3.365491.701480000000000000000000000000.286803-0.53653-3.46834-2.64097-0.1015610.08299-2.19054-4.1355.473631-2.7672800000000000000000000000000-1.30307-0.66281.494811-2.1905418.97198-6.04523-10.68427.112017-8.479551.7865530000000000000000000000002.1193181.077973-1.2005-4.135-6.045237.2111840.839445-3.250944.286974-0.903220000000000000000-4.647537.22205400000000-3.365495.473631-10.68420.83944518.58545-6.939630.111744-6.595500000000000000000.979187-1.52161000000001.70148-2.767287.112017-3.25094-6.939637.185841-2.853050.3539930000000000000000-9.403940.3552226.2698273.04696700000000-8.479554.2869740.111744-2.8530511.50155-3.86642000000000000000018.41897-11.8216-9.74303-4.73485000000001.786553-0.90322-6.59550.353993-3.8664215.598850000000000000000-5.1444313.8575300000000000000007.1403814.0052271.258116-3.11818-1.720392.0643470000000000-4.576214.98426300000000000000004.0052277.670109-0.19226-0.979581.647926-1.97746.96698464.492896700000000-1.635114-0.94332800000000000000001.2581159-0.1922618.3499576-6.556653-14.940033.1993463-8.359916-5.391176000000001.56624580.90359730000000000000000-3.118178-0.979577-6.55665311.36831216.46858-5.901156-22.65941-15.48154-6.901779-2.574278000000000000000000000000-1.7203851.647926-14.9400316.4685846.221599-0.06069-0.752157-3.257746-4.450847-1.6601110000000000000000000000002.0643474-1.9774013.1993463-5.901156-0.0606912.796414

误差理论与测量平差基础课程设计报告

0.74180.16140.52060.22670.53850.39540.38530.27620.16340.12520.0661-0.01140.01530.04150.03580.03500.00190.00900.0330-0.03530.0541-0.03300.0592-0.02970.0544-0.02620.0722-0.03160.1943-0.09400.31520.12820.57510.23230.16141.03250.11830.63710.35660.35360.18420.22430.13620.10240.0096-0.0119-0.0053-0.00110.0022-0.0026-0.0092-0.0100-0.0004-0.02180.0039-0.02110.0068-0.02170.0042-0.01930.0128-0.02070.04330.2530-0.09950.74890.17270.79940.52060.11830.77990.21450.47390.34080.42160.16460.12470.14530.0558-0.00290.01780.03970.03220.03450.00780.01490.0312-0.01890.0481-0.01720.0511-0.01370.0483-0.01200.0594-0.01610.0642-0.05530.4182-0.02480.57190.22760.22670.63710.21450.79770.34970.37390.20150.19120.13260.12600.0216-0.00670.00280.01150.01080.0092-0.0022-0.00040.0093-0.01640.0165-0.01560.0188-0.01480.0167-0.01310.0243-0.01510.02760.13660.08610.41090.27930.53950.53850.35660.47390.34970.56530.39440.41300.28790.16680.12350.0493-0.00920.01080.03040.02640.02550.00080.00590.0242-0.02750.0400-0.02570.0440-0.02340.0403-0.02060.0539-0.02470.1228-0.00020.23920.23590.47200.36400.39540.35360.34080.37390.39440.42900.19380.24610.15790.13050.0361-0.00740.00740.02180.01920.0181-0.00010.00350.0174-0.02130.0290-0.02000.0321-0.01830.0292-0.01620.0396-0.01920.08760.02530.16740.23510.35710.33840.38530.18420.42160.20150.41300.19380.54550.31640.20240.18280.0373-0.00500.00970.02450.02060.02080.00240.00670.0194-0.01760.0311-0.01630.0337-0.01430.0312-0.01260.0404-0.01560.0745-0.01790.21960.09560.36540.21840.27620.22430.16460.19120.28790.24610.31640.37880.23050.17420.0233-0.00610.00380.01310.01200.0107-0.00130.00080.0106-0.01580.0182-0.01490.0205-0.01400.0184-0.01240.0259-0.01440.07690.00950.07770.17370.21180.20610.16340.13620.12470.13260.16680.15790.20240.23050.29590.23130.0145-0.00320.00280.00860.00760.0071-0.00030.00110.0069-0.00900.0115-0.00840.0128-0.00780.0116-0.00690.0160-0.00810.03990.00730.06080.09600.13850.12930.12520.10240.14530.12600.12350.13050.18280.17420.23130.24220.0124-0.00180.00310.00800.00680.00680.00070.00210.0064-0.00600.0103-0.00560.0111-0.00490.0103-0.00440.0134-0.00530.02070.00630.07390.05600.12900.10590.06610.00960.05580.02160.04930.03610.03730.02330.01450.01240.1262-0.01150.03660.08630.07130.07430.01310.02830.0682-0.05090.1070-0.04680.1147-0.03950.1074-0.03470.1355-0.04430.11800.00590.09010.00730.0759-0.0084-0.0114-0.0119-0.0029-0.0067-0.0092-0.0074-0.0050-0.0061-0.0032-0.0018-0.01150.00650.0007-0.0041-0.0049-0.00270.00390.0035-0.00340.0136-0.00770.0130-0.00950.0129-0.00780.0114-0.01360.0126-0.0269-0.0008-0.0025-0.0189-0.0054-0.00950.0153-0.00530.01780.00280.01080.00740.00970.00380.00280.00310.03660.00070.0309-0.00750.0380-0.00660.0284-0.00880.0319-0.01260.0311-0.01020.0337-0.01160.0318-0.00790.0397-0.00670.02230.00150.0303-0.01130.0231-0.01000.0415-0.00110.03970.01150.03040.02180.02450.01310.00860.00800.0863-0.0041-0.00750.2334-0.01680.2055-0.02370.14980.03460.05420.10780.03960.09500.06730.10200.03970.07160.01410.06950.00380.0656-0.00770.0529-0.01290.03580.00220.03220.01080.02640.01920.02060.01200.00760.00680.0713-0.00490.0380-0.01680.17320.12510.00240.06320.0653-0.09310.1169-0.04040.0844-0.01970.0868-0.02230.0992-0.01820.06190.00330.0526-0.00120.0433-0.00770.0350-0.00260.03450.00920.02550.01810.02080.01070.00710.00680.0743-0.0027-0.00660.20550.12510.69290.09390.55640.14820.34440.25080.27610.19180.26040.16010.16000.11030.05300.05740.00330.0573-0.00930.0458-0.01260.0019-0.00920.0078-0.00220.0008-0.00010.0024-0.0013-0.00030.00070.01310.00390.0284-0.02370.00240.09390.58810.00530.28890.49730.00990.29510.09330.0926-0.00390.07830.05620.0033-0.00270.00040.0146-0.01610.0092-0.0103

Nbb-1=0.0090-0.01000.0149-0.00040.00590.00350.00670.00080.00110.00210.02830.0035-0.00880.14980.06320.55640.00530.87720.06240.70840.19440.48710.17890.42670.10490.27200.04880.06370.00870.00100.0265-0.01840.0186-0.01310.0330-0.00040.03120.00930.02420.01740.01940.01060.00690.00640.0682-0.00340.03190.03460.06530.14820.28890.06240.59550.26830.44630.32020.30260.19170.24160.11750.23510.08150.05560.00310.0516-0.00520.0417-0.0097-0.0353-0.0218-0.0189-0.0164-0.0275-0.0213-0.0176-0.0158-0.0090-0.0060-0.05090.0136-0.01260.0542-0.09310.34440.49730.70840.26831.8332-0.11821.05660.15700.5999-0.11740.4299-0.04080.0262-0.0738-0.0028-0.0271-0.0325-0.0282-0.01320.05410.00390.04810.01650.04000.02900.03110.01820.01150.01030.1070-0.00770.03110.10780.11690.25080.00990.19440.4463-0.11820.88830.10910.42640.27270.50120.12790.34260.18080.09390.00490.0786-0.00070.0649-0.0110-0.03300.0592-0.02970.0544-0.02620.0722-0.02110.0068-0.02170.0042-0.01930.0128-0.01720.0511-0.01370.0483-0.01200.0594-0.01560.0188-0.01480.0167-0.01310.0243-0.02570.0440-0.02340.0403-0.02060.0539-0.02000.0321-0.01830.0292-0.01620.0396-0.01630.0337-0.01430.0312-0.01260.0404-0.01490.0205-0.01400.0184-0.01240.0259-0.00840.0128-0.00780.0116-0.00690.0160-0.00560.0111-0.00490.0103-0.00440.0134-0.04680.1147-0.03950.1074-0.03470.13550.0130-0.00950.0129-0.00780.0114-0.0136-0.01020.0337-0.01160.0318-0.00790.03970.03960.09500.06730.10200.03970.0716-0.04040.0844-0.01970.0868-0.02230.09920.27610.19180.26040.16010.16000.11030.29510.09330.0926-0.00390.07830.05620.48710.17890.42670.10490.27200.04880.32020.30260.19170.24160.11750.23511.05660.15700.5999-0.11740.4299-0.04080.10910.42640.27270.50120.12790.34260.98900.20450.75130.00820.4962-0.02390.20450.55070.33260.48060.19330.43290.75130.33260.98780.25380.60410.04530.00820.48060.25380.62570.27790.44950.49620.19330.60410.27790.69510.1197-0.02390.43290.04530.44950.11970.53530.07710.16950.19350.24740.20100.1493-0.06940.1044-0.06430.0947-0.05670.1302-0.00260.0053-0.00230.0049-0.00200.0064-0.02440.0829-0.01860.0787-0.01620.0955-0.03160.0035-0.0331-0.0003-0.02940.0119-0.02580.0692-0.02130.0651-0.01860.0811-0.0131-0.0094-0.0147-0.0108-0.0131-0.0067-0.0316-0.0207-0.0161-0.0151-0.0247-0.0192-0.0156-0.0144-0.0081-0.0053-0.04430.0126-0.00670.0141-0.01820.05300.00330.06370.08150.02620.18080.07710.16950.19350.24740.20100.14930.2549-0.0668-0.0025-0.0227-0.0311-0.0243-0.01310.19430.04330.06420.02760.12280.08760.07450.07690.03990.02070.1180-0.02690.02230.06950.06190.0574-0.00270.00870.0556-0.07380.0939-0.06940.1044-0.06430.0947-0.05670.1302-0.06680.4340-0.16710.11260.08260.1499-0.0368-0.09400.2530-0.05530.1366-0.00020.0253-0.01790.00950.00730.00630.0059-0.00080.00150.00380.00330.00330.00040.00100.0031-0.00280.0049-0.00260.0053-0.00230.0049-0.00200.0064-0.0025-0.16710.3927-0.17090.3688-0.16840.35700.3152-0.09950.41820.08610.23920.16740.21960.07770.06080.07390.0901-0.00250.03030.06560.05260.05730.01460.02650.0516-0.02710.0786-0.02440.0829-0.01860.0787-0.01620.0955-0.02270.1126-0.17090.6982-0.23710.5086-0.17630.12820.7489-0.02480.41090.23590.23510.09560.17370.09600.05600.0073-0.0189-0.0113-0.0077-0.0012-0.0093-0.0161-0.0184-0.0052-0.0325-0.0007-0.03160.0035-0.0331-0.0003-0.02940.0119-0.03110.08260.3688-0.23711.1309-0.15560.86660.57510.17270.57190.27930.47200.35710.36540.21180.13850.12900.0759-0.00540.02310.05290.04330.04580.00920.01860.0417-0.02820.0649-0.02580.0692-0.02130.0651-0.01860.0811-0.02430.1499-0.16840.5086-0.15560.69390.06710.23230.79940.22760.53950.36400.33840.21840.20610.12930.1059-0.0084-0.0095-0.0100-0.0129-0.0077-0.0126-0.0103-0.0131-0.0097-0.0132-0.0110-0.0131-0.0094-0.0147-0.0108-0.0131-0.0067-0.0131-0.03680.3570-0.17630.86660.06710.9496

?15.由此组成法方程Nbbx??W?0，并解算法方程x??NbbW得参数改正数和参数平差值：

22

??X0?xW?x??X??-16.0810228.0819843.3842969-8.90904757.30160965.582484101.6091120.591828-329.814264.8501362.713406-260.6412-72.57191-17.6804586.361438-91.55169-96.37489128.1178492.218641-123.0575-86.10208124.94761-0.524391-24.440972.8820625-35.33088-39.66898135.61103-304.16-276.3674406.23558399.51316-103.6145-118.0465131.75814135.4415156.63696127.16982145.55425110.5915124.0185272.22157828.62789444.175854-0.703234-0.315624-0.161385-5.44425913.546168-11.04884-70.8409616.003281-7.077961-87.2216411.644671-11.90360.78285018.07467649.3394821-1.496884-1.50630611.518898-5.8809181.9205469207.75869185.90815138.99791139.67414100578151025111410090395101638241012073210090717100953201006255210031496100286719900438.3100457079924060.89997093.69908552.599397769976969.298080689780804.99703066.89716224.69830148.19807340.89886197.19832271.39935482.59848612.5100131149855575.1101234619981210.8102545861002958210294909 6.计算改正数和观测值的平差值。由V?Bx??L?V得： ??l和L??L?V V?Bx??lL误差理论与测量平差基础课程设计报告

12.0470121.96739949.6823782-4.16372711.73299-6.1535443.2072852-2.80254810.945222-16.9197418.48720444.3553647.1014164-35.5787425.5813739.089149-29.80537-0.857469-10.06627-0.481865-22.98782-2.907689-5.34856311.34488612.061523-12.38692-18.20429-13.9547-34.2284141.349536-14.4757434.3263893.341440538.4715749.3276355-38.65787-11.68856-29.78091-35.49937-12.4400912.95036514.97895615.333157

167.6349183.0928114.3769160.0510193.8738108.1508204.788394.4750125.196883.152458.8704138.912226.6546222.627390.821888.670094.6289211.5958194.9255134.6569106.2511173.574283.009492864.978851.837245.071559.543112.122770.754996.388927.758201.741931.6147667.5221642.8143311.1107881.956403.480491.162268.1181963.363693.751924.4 24

7.间接平差后各点的坐标

间接平差后坐标X1Y1X2Y2X3Y3X4Y4X5Y5X6已知Y6已知X7已知Y7已知X8Y8X9Y910057.81510251.11410090.39510163.82410120.73210090.71710095.32010062.55210031.49610028.67110000.00010000.0009924.66110043.4979900.43810045.7079924.0619997.094 X10Y10X11Y11X12Y12X13Y13X14Y14X15Y15X16Y16X17Y17X18Y18X19Y199908.5539939.7769976.9699808.0689780.8059703.0679716.2259830.1489807.3419886.1979832.2719935.4839848.61210013.1149855.57510123.4619981.21110254.58610029.58210294.909第6部分 精度评定及误差椭圆、

6.1高程间接平差的精度评定

1.水准网的单位权中误差

VTPVVTPV=0.102mm ????rn?t?2.待定点高程中误差

由Nbb-1中可得未知数的协因数

Q1=3.92814 Q2=3.335998Q3=2.50161Q4=1.99183Q5=0.83278

Q7=1.55541 Q8=1.85449 Q9=2.08874 Q10=3.14464 Q11=5.09851 Q12=6.2049 Q13=5.7659 Q14=4.8473 Q15=4.17859 Q16=2.97606 Q17=2.9891 Q18=4.07546 Q19=4.07688 有Dii???2Qii可得（单位：mm） σ1=0.20215 σ2=0.1863 σ3=0.16133 σ4=0.14395 σ5=0.09474 σ7=0.12721 σ8=0.138903 σ9=0.14741 σ10=0.18088 σ11=0.23031 σ12=0.25408 σ13=0.24493σ14=0.22457 σ15=0.18088σ16=0.17596 σ17=0.17635 σ18=0..20591 σ19=0.20595

6.2平面间接平差的精度评定

1.平面控制网的单位权中误差

VTPVVTPV=8.74″ ????rn?t?2.待定点坐标中误差

由Nbb-1中可得未知数的协因数

QX10.7418QX80.1262QX140.5507QY11.0325QY80.0065QY140.9878QX20.7799QY20.7977QX100.1732QX160.5353QX30.5653QY100.6929QY160.2549QY30.4290QX110.5881QX170.4340QX40.5455QY110.8772QY170.3927QY40.3788QX50.2959QX130.8883QX190.6939QY50.2422 QY130.9890QY190.9496QX90.0309QX150.6257QY90.2334QY150.6951QX120.5955QX180.6982QY121.8332QY181.1309 各点点位中误差为

误差理论与测量平差基础课程设计报告

σ111.1120σ119.2303

σ29.7503σ36.2019σ45.8051σ53.3422σ81.1056σ175.1155σ92.0574σ106.2421 σ12σ1316.847211.6181σ149.8841σ158.1736σ165.1819σ18σ1911.616310.2782

6.3平面间接平差的误差椭圆

1.误差椭圆中E、F、φ的求解方法：

12E2??0Q?x?x?Q?y?y?(Q?x?x?Q?y?y)2?4Q2?x?y2??

12F2??0Q?x?x?Q?y?y?(Q?x?x?Q?y?y)2?4Q2?x?y2

??

K?(Q?x?x?Q?y?y)2?4(Q?x?y)2tg2?0?，

2Q?x?yQ?x?x?Q?y?y2.每个未知点的协因数阵 H1QHiH2H3H4H5H8H9H100.74180.16140.77990.21450.56530.39440.54550.31640.29590.23130.1262-0.01150.0309-0.00750.17320.12510.16141.03250.21450.79770.39440.42900.31640.37880.23130.2422-0.01150.0065-0.00750.23340.12510.6929 H11H12H13H14H15H16 H17H18H190.58810.00530.59550.26830.88830.10910.55070.33260.62570.27790.53530.14930.4340-0.16710.6982-0.23710.69390.06710.00530.87720.26831.83320.10910.98900.33260.98780.27790.69510.14930.2549-0.16710.3927-0.23711.13090.06710.9496 3. 误差椭圆中E、F、φ的表格

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误差理论与测量平差基础课程设计报告

QxxH1H2H3H4H5H8H9H10H11H12H13H14H15H16H17H18H190.74180.77990.56530.54550.29590.12620.03090.17320.58810.59550.88830.55070.62570.53530.43400.69820.6939Qyy1.03250.79770.42900.37880.24220.00650.23340.69290.87721.83320.98900.98780.69510.25490.39271.13090.9496Qxy0.16140.21450.39440.31640.2313-0.0115-0.00750.12510.00530.26830.10910.33260.27790.1493-0.1671-0.23710.0671K0.43440.42930.80040.65440.46570.12190.20300.57680.28931.34900.24030.79600.56000.40960.33670.64190.2888QEE1.10441.00340.89730.78940.50190.12730.23360.72140.87731.88881.05881.16720.94040.59990.58171.23550.9661QFF0.67000.57410.09690.13500.03620.00540.03060.14460.58800.53980.81850.37130.38040.19030.24500.59360.6774E9.18478.75508.27937.76526.19173.11894.22457.42358.186412.01178.99329.44258.47566.76956.66589.71498.5907F7.15406.62242.72103.21071.66200.64511.52983.32386.70216.42177.90725.32545.39043.81304.32626.73377.1933φ6646.1940.137.6241.69-5.44-87.8977.1488.9578.2857.3861.6548.5623.4-41.48-66.1876.164. 误差椭圆的绘制图

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误差理论与测量平差基础课程设计报告

第7部分 技术总结

1. 高程网的技术鉴定

实习高程测量为单向观测，每个测站为2个测回，三个环的闭合差分别为W1=2.45mm，W2=0.02mm，W3=-3.25mm。它们对应的路线总长分别为S1=0.823km， S2=0.124km，S3=0.929km，根据技术要求闭合差W0≤?4L它们都满足要求。

同时每千米Mw??1N?WW??L?≤±2mm。 ??故高程网的测量合格。 2.平面控制网的技术鉴定

闭合导线网中技术要求测角中误差mβ≤±8\，实习测量得到方位角闭合差发fβ1=25″，fβ2=15″ fβ3=75″则测角中误差m度测量不合格。

坐标增量

f?????1?f?f????N?n?=15.8\，mβ>8\则角

?ffyx2?0.994m,

?0.995m?fy?0.083m，则闭合长增量

fx2??，总的距离L=1.896km，则全长相对闭合差

T?fL=1/1885，而技术要求全长相对闭合差T0≤1/10000，T≥1/10000则长

度测量不合格。 3.平差后的技术鉴定

高程网的单位权中误差为σ0=0.102mm,满足平差精度要求。

平面控制网的单位权中误差为σ0=8.74″，小于10″同样满足平差精度要求。

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误差理论与测量平差基础课程设计报告

第8部分 实习心得

通过本次误差理论与测量平差基础的课程设计实习，我获得很多很多的收获。

把在平时学习理论课中遇到的很多问题和盲点都搞清楚了，比如说导线网的条件平差方程的列法，间接平差方程的建立等。同时自己也和庞大的数据打了一回交到，是我不在像从前那样畏惧那些庞大的数据了。尤其是再平面控制网的间接平差44个方程的成功建立和完美求解，让我信心倍增。

说实话，这次的课程设计我过的的确很辛苦，天天要处理数据，还要面对多门考试，那是我真的很矛盾。但是现在好了，一切都过去了。我既没有落下课程设计，同时有没有耽误考试，我此时有种鱼与熊掌两者兼得的喜悦感。这次的成功我不仅要好好表扬自己，同时我还要感谢我的老师，我的同学。他们的确给了我不少的帮助，没有他们我很难想像我会顺利完成任务。

经过这次实习，我对测量平差有了深刻的认识，学到了课堂上学不到的知识。巩固了课堂教学内容，加深了对测量平差基本理论的理解和具体的实际操作。学习是为了应用！这次实习真正做到了理论与实际相结合！我感到很有意义。这次实习完全从测量平差的工程实际出发，加深我对书本知识的进一步理解、掌握与综合应用。这次实习培养了我理论联系实际的能力、独立工作能力、综合分析问题和解决问题的能力、组织协调能力和交际能力。所学的知识不再仅仅局限于理论上的计算，而是测量的一次全面综合实践过程。通过实习，我掌握了对四等导线测量和二等精密水准测量数据的处理方法和matlab软件的应用。经过对户外观测成果的整理、计算和检查，我也了解了用两种平差理论处理测量成果的基本技能，条件平差和间接平差。在这次实习中，我们遇到了不少问题，不过都在老师的指导和同学间的讨论下一一地解决了！

这次实习使我深刻的认识到学习测量平差的重要性。作为一个大学生最终是要走上社会的，我们要重视培养分析问题和解决问题的能力！我深刻地认识到，无论什么工作，特别是作为一个测绘工作者，更要有不怕苦、不怕累的精神，只有这样才能适应工作，并把工作做好。我们的工作大多都是和数据打交道的，从烈日下的观测到平差处理都离不开数据。通过实习，锻炼了我们吃苦耐劳、持之以恒的精神，为以后就业做准备。

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误差理论与测量平差基础课程设计报告

通过这次实习，我对测量平差有了进一步的认识。掌握了条件平差和间接平差法。通过实习，更好的巩固了两种平差方法的具体应用。这次实习难度大，数据很多，是一件很令人恼火的事情，虽然由于考试原因，在考试后时间紧迫，整整熬了两个通宵才完成任务，但是看到自己三十多页的实习报告，看到自己的成果，心里还是很开心的。

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