测量平差技术报告

测量平差课程设计实习报告姓名： 邹建鑫学号： 631101040124班级：测绘 2011级1班指导老师： 曹智翔2013/7/4一、 控制网概况及测量数据的整理和检验我们的测区包括学校的德园小区、 A01教学楼、B01教学楼、食堂和学生活动中心，控制点基本都在学校的公路边上， 测区整体来说比较平整，自南向北整体是一个上升的缓坡的区域， 在测区中主要是楼房和绿化带，在整个外业过程中基本都是35度以上高温天气。在测区中已知两个控制点（B,C）的坐标，其标石保存完好。（一）、光电测距导线的主要技术要求：闭合或符测距中误测角中误全长相对等级合导线全平均边长差差（m）闭合差长（km）（mm）（″）二级2．4200≤±15≤±8≤1/100001、测距中误差计算：测距单位权中误差：p d d2ns——单位权中误差；——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；1pi 2sisi——测距先验中误差，根据测距仪的标称精度估算。任一边的实测距离中误差估值：mDi

1pi注：索佳SET510全站仪测距标称精度为±（2+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均为1，求出的单位权中误差可视为各边的测距中误差。2、 测角中误差的计算：m

1 f fN n——符合导线或闭合导线环的方位角闭合差；——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。（二）、水准测量的主要技术要求：每千米高差闭合差等级全中误差往返各一次（mm）（mm）二等≤±2≤4L平差前计算每千米水准测量高差全中误差：Mw

1 WWN LMw——高差全中误差（ mm）；——闭合差；——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。若进行往返观测，计算每千米水准测量的高差偶然中误差：1MD4n LMD——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）下图为控制网简图测量数据如下：角度 ( °' ")BCD=1662950，∠CDE=167217，∠DEF=854022EFG=1562437，∠FGH=144621，∠GHI=1521432HIA=195569，∠IAB=1012616，∠ABC=903936DECH5=1004143，∠ECH5CH4=82249，∠CH5CH4CH3=16400CH4CH3CH2=1643213，∠CH3CH2CH1=1724410，∠CH2CH1B=89430CH1BC=99272，∠BCD=1933010，∠CDE=1925744距离（m）CD=170.617ECH5=136.333DE=161.181CH5CH4=171.754EF=108.361CH4CH3=189.328FG=111.698CH3CH2=121.741GH=124.967CH2CH1=218.272HI=151.589CH1B=88.261IA=174.935AB=161.473BC=263.584水准测量数据记录测站目标点前视读数后视读数高差1A1.192-0.562B1.7541.80221.435C0.3673.38332.96D0.4232.83742.072E0.7651.92551.336F0.5590.7496-0.187G0.9360.0807-3.756H-3.6760.3188-2.576I2.8941.067-0.7199A1.786表格二测站目标点前视读数后视读数高程1E1.6980.471CH51.2180.8412-4.86CH45.7011.0643-0.356CH31.4261.0744-0.907CH21.9810.8685-1.226CH1-2.0941.396B0.9730.423二、 水准网、导线网的条件平差及间接平差（一）水准网条件平差如图为路线号已知B,C两点高程HB=385.2968、HC=386.7212系数矩阵1 1 1 1 1 1 1 1 0 0 0 0 0 0A0 1 1 0 0 0 0 0 1 1 1 1 1 1常数阵l=-7.6-1.4协因数阵Q为单位阵所以Naa=A*Q*AT82=82所以联系数k1=0.967；k2=-0.067所以V=Q*AT*K=[-0.9667-0.9000-0.9000-0.9667-0.9667-0.9667-0.9667-0.96670.06670.06670.06670.06670.06670.0667] Tmm-0.96672.959-0.90002.071-0.90001.335-0.96670.188-0.96673.757-0.96672.577VQ*AT-0.96670.720*K；所以h-0.96670.5630.06670.4710.06674.8600.06670.3560.06670.9070.06671.2260.06670.423（二）水准网间接平差^^^^^^设D、F、G、H、I、A、CH5、CH4、CH3、CH2、CH1点高程X1、X2、X3、X4、X5、X6、^^^^^^X7、X8、X9、X10、X11、X12作为参数取^

^X x HC

h11^XxHCh1h222^^XxHCh1h2h333^^XxHCh1h2h3h444^^XxHBh6h7h855^^XxHBh7h866^^XxHBh877^^XxHCh1h2h988^^XxHCh1h2h9h1099^^XxHBh12h13h141010^^XxHCh13h141111^^XxHCh141212所以得到误差方程，其系数矩阵100000000000-1100000000000-1100000000000-1100000000000-1100000000000-11000000B00000-1100000000000-1000000-100000100000000000-1100000000000-1100000000000-1100000000000-11000000000001常数矩阵l0000-7.6000001.4000T权阵P为单位阵所以2-10000000000-13-10000-100000-12-10000000000-12-10000000000-12-1000000NBBBT*P*B0000-12-10000000000-12000000-1000002-10000000000-12-10000000000-12-10000000000-12-10000000000-12所以W BT*P*l 0007.6-7.6000-1.41.400T所以0.62000.62000.62001.24001.06002.30001.06003.3600-14.1400-3.18001.0600^-2.1200^1.0600xNbb1VB*xl*W-1.06001.06000.8000-0.44000.3600-0.44001.32002.36000.8800-0.44000.4400-0.44000.4400-1.0960-2.00300.8790-4.42700.0660-0.4880^-0.8130LLV0.85200.56000.71902.58203.76600.19503.1110NBB10.80000.60000.50000.40000.30000.20000.10000.50000.40000.30000.20000.10000.60001.20001.00000.80000.60000.40000.20001.00000.80000.60000.40000.20000.50001.00001.66671.33331.00000.66670.33330.83330.66670.50000.33330.16670.40000.80001.33331.86671.40000.93330.46670.66670.53330.40000.26670.13330.30000.60001.00001.40001.80001.20000.60000.50000.40000.30000.20000.10000.20000.40000.66670.93331.20001.46670.73330.33330.26670.20000.13330.06670.10000.20000.33330.46670.60000.73330.86670.16670.13330.10000.06670.03330.50001.00000.83330.66670.50000.33330.16671.66671.33331.00000.66670.33330.40000.80000.66670.53330.40000.26670.13331.33331.86671.40000.93330.46670.30000.60000.50000.40000.30000.20000.10001.00001.40001.80001.20000.60000.20000.40000.33330.26670.20000.13330.06670.66670.93331.20001.46670.73330.10000.20000.16670.13330.10000.06670.03330.33330.46670.60000.73330.8667各点高程中误差：^D^E^CH5^CH4^CH3^CH2

^4.3106CH14.79494.0285^5.2008L5.8146^7.3546M6.5785^9.0080N6.6805^10.4015O6.1536^11.6293P（三）导线网条件平差下表为各点的近似坐标，各边的方位角、方位角的正余弦及各边的长度第一个闭合环点改正后之增量号方位角cosaxy坐标值B观测角改正角174352距离sina+-+-xyC166295000.855153384.691039397.026031142170.6170.5185145.9388.471D16721700.717053530.62139485.530441145161.1810.6971115.604112.361E8540220-0.749253646.22439597.9251383123108.3610.662381.22971.77F15624370-0.951753565.08039669.728162646111.6980.3071106.34234.307G1446210-0.951053458.82439704.069198025124.967-0.3091118.88938.631H15214320-0.697653340.02139665.4662254553151.589-0.7165105.749108.611I1955690-0.867553234.31439556.8882094944174.935-0.4974151.75987.015A101261600.315553082.59839469.9062882328161.473-0.948950.945153.226B90393600.952553133.58639316.713C16629500174352263.5840.3046251.06380.27553384.691039397.0260第二个闭合环点改正后之增量号方位角cosaxy坐标值B观测角改正角174352距离sina+-+-xyC1933080.855153384.691039397.026031140170.6170.5185145.88888.469D19257420.717053530.56839485.520441142161.1810.6971115.562112.360E10041420.818053646.11939597.9053245324136.333-0.5751111.52778.412CH582248-0.678353757.63539519.5182271732171.754-0.7348116.494126.209CH41645958-0.854553641.13039393.3342111730189.328-0.5194161.78798.336CH31643213-0.962153479.33239295.0231954943121.741-0.2728117.12533.206CH2172449-0.988853362.19639261.8421883352218.272-0.1489215.83832.505CH1894259-0.144053146.34739229.36298165188.2580.989612.71187.338B992710.952553133.62539316.725C1933010174352263.60.3046251.07880.27953384.691039397.0260因为n=32，t=24，故r=8，可列出八个条件方程，其系数矩阵 A为8*32的矩阵A=接上表改正数依次为VS1、VS2、VS3、VS4、VS5、VS6、VS7、VS8、VS9、VS10、VS11、VS12、VS13、VS14、Vb1、Vb2、Vb3、Vb4、Vb5、Vb6、Vb7、Vb8、Vb9、Vb10、Vb11、Vb12、Vb13、Vb14Vb15、Vb16、Vb17、Vb18常数矩阵为W 1 0 0 11-99 -83-22 10协因数阵 Q=接上由此可计算的2.000001.00001.0000-1.26790.9714-1.26740.973902.00001.00001.0000-0.70750.4291-0.70720.42901.00001.00009.000000.41826.251600NaaA*Q*AT1.00001.000009.000000-3.0033-0.3732-1.2679-0.70750.4182011.8146-0.24171.24191.56210.97140.42916.25160-0.241714.70361.56212.0762-1.2674-0.70720-3.00331.24191.562114.0958-0.71490.97390.42900-0.37321.56212.0762-0.714911.4122所以可以组成法方程Naa*KW0解得K11.59309.9676-9.6768-3.891011.52929.7110-0.1078-5.7190所以计算的改正数V15.927917.44630.3904-6.3683-15.9943-22.7914-24.7688-12.7180-6.29346.79889.35836.734312.37830.6327-9.6768-3.6992-3.2689-6.92080.63525.45826.254910.63990.5776-7.0923-3.6546-1.0133-0.15450.6332-1.7957-3.89103.69922.2689TmmVS1V S 2V S 3V S 4V S 5V S 6V S 7V S8V S 9VS10V S11V S12V S13V S14V b1V b 2V b3V b 4Vb5V b6V b7V b8V b9V b10V b11V b12V b13Vb14V b15V b16V b17V b18111111

15.9279170.633m17.4463161.198m0.3904108.361m-6.3683111.692m-15.9943124.950m-22.7914151.568m-24.7688174.911m-12.7180161.462m-6.2934136.328m6.7988171.760m9.3583189.338m6.7343121.747m12.3783218.284m0.632788.259m-9.67689039'26"-3.6992^16629'46"mm-LLV1672'14"3.2689-6.92088540'15"0.635215624'38"5.45821446'26"6.254915214'38"10.63991955619"0.577610126'17"-7.092310041'36"-3.65468224'6"-1.013316359'59"-0.154516432'13"0.633217244'11"-1.79578942'58"-3.89109926'58"3.699219330'14"2.268919257'46"1（四）导线网间接平差（四）导线网间接平差坐标方位角改正数方程的系数计算表（第一个闭合环）a（"/mm）b（"/mm）点号近似坐标S-S°"sin"cosBxy近似边长S°（m）cossin(mm)S*1000S*1000C53384.691039397.0260170.6710.85510.5185-540.6266-1.0334D53530.62139485.530161.2350.71700.6971-540.8918-0.9172E53646.22439597.925108.351-0.74920.6623101.26081.4262F53565.08039669.728111.668-0.95170.3071300.56731.7579G53458.82439704.069124.917-0.9510-0.309150-0.51041.5703H53340.02139665.466151.536-0.6976-0.716553-0.97530.9495I53234.31439556.888174.882-0.8675-0.497453-0.58671.0232A53082.59839469.906161.4550.3155-0.948918-1.2123-0.4031B53133.58639316.713C 53384.6910 39397.0260 263.636 0.9525 0.3046 -52 0.2383 -0.7452点号坐标值BxyC53384.691039397.0260D53530.56839485.520E53646.11939597.905CH553757.63539519.518CH453641.13039393.334CH353479.33239295.023CH253362.19639261.842CH153146.34739229.362B53133.62539316.725C53384.691039397.0260

坐标方位角改正数方程的系数计算表（第二个闭合环）a（"/mm）b（"/mm）近似边长S°"sin"cos（m）cossinS-S°(mm)S*1000S*1000170.62030.85510.5185-30.6268-1.0337161.19060.71700.6971-100.8920-0.9175136.30970.8180-0.575123-0.8703-1.2378171.7435-0.6783-0.734811-0.88250.8146189.3242-0.8545-0.51944-0.56590.9310121.7449-0.9621-0.2728-4-0.46221.6300218.279-0.9888-0.1489-7-0.14070.934488.28444-0.14400.9896-262.31210.3364263.595 0.9525 0.3046 5 0.2384 -0.7453^^由题意，选取A、D、E、F、G、H、I、CH1、CH2、CH3、CH4、CH5等12个点坐标x,y，AA^^^^^^^^^^^^^^x,y，x,y，x,y，x,y，x,y，x,y，x,y，DDEEFFGGHHIICH1CH1^^^^^^^^xCH2,y，xCH3,y，xCH4,y，xCH5,y作为参数。CH2CH3CH4CH5根据以上数据结合以下公式列出了 30个条件方程误差方程系数计算表一方向 y x S^2 xa ya xb ybCD-88.494-145.87729111.28762.702-115.80689.218-91.732DE-112.385-115,55125982.422-89.21891.73287.021123.799ECH578.387-111.51618580870.20961237.9897-870.21-1237.99CH5CH4126.184116.50529496.0015-882.402814.717882.402-814.717CH4CH398.311161.79835843.577-565.739931.081565.739-931.081CH3CH233.181117.13614821.845-461.7561630.098461.756-1630.1CH2CH132.48215.84947645.7218140.611934.441140.6105-934.441CH1B-87.36312.7227794.06466-2312.01-336.6797BC-80.301-251.06669484.96CD-88.504-145.9329128.5902626.713-1033.358DE-112.395-115.60325996.7252-891.772917.22525891.772-917.225EF-71.80381.14411739.9392-1261.54-1425.661261.5441425.661FG-34.341106.25612469.7422-568.043-1757.606568.0431757.606GH38.603118.80315604.2569510.2741-1570.398-510.2741570.398HI108.578105.70722963.1593975.2944-949.5059-975.294949.506IA86.982151.71630583.7139-586.6311023.215586.6306-1023.21AB153.193-50.988260681212.151403.44636误差方程系数计算表二方向 y x S a bECH578.387-111.516136.310.81810579-0.5750642CH5CH4126.184116.505171.744-0.6783643-0.7347214CH4CH398.311161.798189.324-0.854609-0.5192738CH3CH233.181117.136121.745-0.9621422-0.2725451CH2CH132.48215.849218.279-0.9888675-0.1488004CH1B-87.36312.72288.284-0.14410310.98956776BC-80.301-251.066263.60.952450680.30463202CD-88.504-145.93170.6710.855036880.51856496DE-112.395-115.603161.2350.716984530.6970881EF-71.80381.144108.351-0.74889940.66268885FG-34.341106.256111.668-0.95153490.30752767GH38.603118.803124.917-0.9510555-0.3090292HI108.578105.707151.536-0.6975702-0.7165162IA86.982151.716174.882-0.8675335-0.4973754AB153.193-50.988161.4550.31580316-0.9488278以下为条件方程的系数矩阵 B常数项矩阵32.4000-18.7000-42.800033.600052.9000111.4000-41.0000-34.900063.7000-56.8000-131.60001.27678.30000.719342.20001.2765-6.9000-1.725824.30000.6147l2.0395116.9000-63.3012-1.7126-49.6381-2.019523.27910.2652110.5376-0.5184113.8190-0.2829-23.9024*P*L0.5962WBT-47.04430.2094-26.4440-0.1828-54.00000.7534110.0000-0.265930.0000-0.457050.00002.199553.00000.212055.0000*10^6-1.32400.0009-0.22050.67200.2561由公式NBB BT*P*B 10000*通过计算得1ffm=3"Nn11.16个 .1P0.360.36.^xA^yA^xD^yD^xE^yE^xF^yF^xG

14个 .0.361.21183.49130.89450.51275.23714.724035.388140.681529.029038.626233.171637.2800

^xI^yI^xCH1^yCH1^xCH2^yCH2^xCH3^yCH3^xCH4

4.61961.53740.46853.21623.91263.73401.85124.311010.503411.82744.94574.9235所以

^yG

^yCH4^xH^yH

^xCH5^yCH5于是计算的到各点坐标的平差值53082.599239469.9025D53530.621939485.530553646.229239597.929753565.044639669.768753458.79539704.107653234.318639556.8865CH153146.347539229.3588CH2 53362.1999 39261.8383CH3 53479.3339 39295.0187CH4 53641.1195 39393.3222CH5 53757.6399 39519.5229VTPVr

VTPVn t

=6.3"由Q^^NBB1得xx点号QxxQyyQxy点号QxxQyyQxyA8.91041.43521.3397I3.08975.5183-0.9831D2.13322.73551.4508CH12.62463.6481-1.7729E2.37739.9624-2.5124CH22.93145.82041.1765F4.59252.97111.2885CH32.66366.3074-1.3169G6.38476.54844.7776CH47.60982.00660.6598H2.88134.08142.9558CH58.32123.6493-0.4061点号EF点号EFA6.62．4I6．62．9D9．26.1CH13．41．7E8.45．