间接平差程序设计

P间接平差程序设计论文闭合导线网P目录编程任务……………………………………3间接平差原理………………………………4平差过程…………………………………9平差结果…………………………………10结论………………………………………27课程设计的体会及建议…………………28参考文献…………………………………29P编程任务导线网示意图：1）起算数据：T0=100°20′30″XB=100.208mYB=120.365m2）观测角、观测边长及其观测中误差：L1=90°24′02″±1.0″,S1=908.018m±3.4mmL2=220°30′55″±3.5″,S2=533.226m±6.2mmL3=286°35′56″±3.1″,S3=623.836m±4.6mmL4=227°05′38″±4.0″,S4=545.382m±6.8mmL5=230°28′10″±3.1″,S5=609.897m±8.8mmL6=295°19′18″±2.2″。要求：1）计算待定三角点Pi（i=1.....4）的坐标平差值（Xi,Yi）及其方差协方差阵DXX；2）计算待定三角点Pi的点位中误差；3）计算观测值的平差值及其方差协方差阵DLL；4）计算各导线边边长的相对中误差；5）绘出待定点的点位误差椭圆；6）验算平差结果的正确性。BP1P2P3P4T0S1S2S3S4S5L2L3L4L5L6L1P间接平差原理设某一平差问题中,有n个观测值L，已知其协因数阵,，必要观测数为t.选定t个独立量为参数X，其估量为观测值L与改正数V之和为:，称为观测值平差值。按具体平差问题,可列出n个平差值方程为:令1PQ,ˆˆ0xXXVLLˆntmtnnnttttdXbXbXbVLdXbXbXbVLdXbXbXbVLˆˆˆˆˆˆˆˆˆ2211122222121221121211111ntntnttnnnnbbbbbbbbbBddddXXXXVVVVLLLL1222211121121212121ˆˆˆˆP则平方值方程的矩阵形式为:令：得误差方程为:按最小二乘原理:按求函数自由极值的方法，得转置后得推得间接平差的基础方程:解此基础方程，得法方程:上式法方程式可简写成:其纯量形式为:dBXVLdBXLlxXXn01,0ˆˆ1,1,,1,ˆnttnnlxBVminPVVT0ˆ2ˆPBVxVPVxPVVTTT0PVBT1,1,,,1,1,,1,0nnnnTntnttnnVPBlxBV1,1,,,1,,,,0ˆnnnnntTttnnnTntlPBxBPBPlBWPBBNTtTttbb1,,,0ˆWxNbb0ˆˆˆ0ˆˆˆ0ˆˆˆ22112222212111212111ttttttttttWxNxNxNWxNxNxNWxNxNxNP解之，得或将求出的代入误差方程,即可求得观测值的改正数V:从而求得平差结果为:误差方程及其系数按角度坐标平差：按两点距离平差WNxbb1ˆPlBPBBxTT1ˆVLLxXXˆˆˆ000111ˆBBXLllxBVnttnnxˆ)()()()()(0000200200200200jkjkjkkjkkjkjjkjjkjkXXYYarctgxSXxSYySXxSYVjkjkjkjk20~~020~0~)()(jkjkkkkkjjjjjkjkYYXXxYfxXfyYfxXfVSP单位权中误差TbbTbbTbbTbbTXLLXTXXVVVXbbbbXLXXXVTLVTbbLXVLTXLTbbTbbLXbbbbTbbXXBBNQQBBNBBNBBNQBQBQBBQQQBNBNQBQQQQBBNQBQQQBNPQBNQNPQPBNBNQ1111ˆˆˆˆˆ11ˆˆˆˆ1ˆˆ11ˆ111ˆˆ000BBXlLPlBNxTbb1ˆlxBVˆVLLˆtnPVVT0ˆ,ˆˆPVlPVBxPVlxBPVVTTTTTxPBlPlllxBPlPVVTTTTˆˆxWPllxPlBPllPVVTTTTTˆˆˆˆ20ˆˆQDP误差椭圆三要素计算：点位误差椭圆形象的反映了控制点在不同方向上的位差，可称为点位精度曲线。根据这个图可以找出待定点坐标平差值在各个方向上的位差，进而进行精度评定。F2=0.5∗(σx2+σy2−√(σx2−σy2)2+4∗σxy2）tan2∗φ=4∗σxy2/(σx2−σy2)E2=0.5∗(σx2+σy2+√(σx2−σy2)2+4∗σxy2)P平差过程一，该平差问题中有11个观测量，8个必要观测值；二，所以要设8个未知参量，分别为四个待定点的X,Y坐标.三，将每一个观测量的平差值分别表达成所选参数的函数，若函数非线性要将其线性化，列出误差方程四，由误差方程系数B和自由项组成法方程五，法方程个数等于参数的个数8；六，解算法方程，求出参数x，y，计算参数的平差值七，由误差方程计算V，求出观测量平差值八，评定精度九，计算待定三角点Pi的点位中误差；a)计算观测值的平差值及其方差协方差阵DLL；b)计算各导线边边长的相对中误差；c)绘出待定点的点位误差椭圆；d)验算平差结果的正确性计算过程各待定点的近似坐标P1P2P3P4X0992.3141326.018748.195253.711Y0289.611705.509940.651710.592P边号方向∆X0/m∆Y0/m方位角近似值S0/m∆X0/S0(cosa)∆Y0/S0(sina)l=S-S0/mm1BP1892.106169.24610°44′32″908.0180.982480.1863902P1P2333.704415.89851°15′27″533.2260.625820.7799703P2P3-577.823235.142157°51′23″623.836-0.926240.3769304P3P4-494.484-230.059204°57′0.84″545.382-0.90667-0.4218305BP4153.503590.227255°25′18.4″609.86152730.251700.9678035.27297角度号观测值L近似值L0l=L-L0/″方向编号abL190°24′02″90°24′02″0BP110.04234-.223179L2220°30′55″220°30′55″0P1P220.30171-.242083L3286°35′56″286°35′56″0P2P330.1246270.306252L4227°05′38″227°05′38″0P3P44-0.15953790.34291L5230°28′10″230°28′17.45421″-7.45421BP450.327327-0.08513L6295°19′18″295°19′13.5479″4.45421权阵P1000000000000.082000000000000.104000000000000.0625000000000000.104000000000000.207000000000000.087000000000000.026000000000000.047000000000000.022000000000000.013P系数阵B-a1-b1000000a1+a2b1+b2-a1-b20000-a2-b2a3+a2b3+b2-a2-b20000--a3-b3a3+a4b3+b4-a4b40000-a4-b4a4-a5b4-b5-a1-b10000a5b5cosa1sina1000000−cosa2−sina2cosa2sina2000000−cosa3−sina3cosa3sina3000000−cosa4−sina4cosa4sina4000000cosa5sina5-0.042340.223180000000.344-0.465-0.3020.2420.0000.0000.0000.0000.0000.0000.4260.064-0.125-0.306-0.3020.2420.0000.000-0.125-0.306-0.0350.6490.160-0.3430.0000.0000.0000.0000.160-0.343-0.486860.42804-0.0420.2230.0000.0000.0000.0000.32733-0.085130.9820.1860.0000.0000.0000.0000.0000.000-0.626-0.7800.6260.7800.0000.0000.0000.0000.0000.0000.926-0.377-0.9260.3770.0000.0000.0000.0000.0000.0000.9070.422-0.907-0.4220.0000.0000.0000.0000.0000.0000.2520.968P观测量观测值改正数v=Bx-l观测值的平差值L190°24′02″0.07326/″90°24′02.07L2220°30′55″-2.50499220°30′52.5L3286°35′56″-2.80412286°35′53.2L4227°05′38″3.323435227°05′41.3L5230°28′10″4.51760230°28′14.5L6295°19′18″0.30314295°19′18.3S1908.018m2.00325/mm908.020S2533.226m6.16387533.23216S3623.836m-0.28447623.83572S4545.382m-5.95462545.3761S5609.897m-8.82192609.88818P源程序#includeiostream#includecmath#includeiomanip#includefstreamusingnamespacestd;constdoublePI=3.14159265358979312;constdoublen=3600*180/PI;constintv=8;#includewindows.h/*---------------矩阵相乘---------------------*/voidmult(double*m1,double*m2,double*result,inti_1,intj_12,intj_2){inti,j,k;for(i=0;ii_1;i++)for(j=0;jj_2;j++){result[i*j_2+j]=0.0;for(k=0;kj_12;k++)result[i*j_2+j]+=m1[i*j_12+k]*m2[j+k*j_2];}Preturn;}/*---------------矩阵求逆---------------------*/voidinverse(doublec[v][v]){inti,j,h,k;doublep;doubleq[v][16];for(i=0;iv;i++)for(j=0;jv;j++)q[i][j]=c[i][j];for(i=0;iv;i++)for(j=v;j16;j++){if(i+8==j)q[i][j]=1;elseq[i][j]=0;}for(h=k=0;kv-1;k++,h++)for(i=k+1;iv;i++){if(q[i][h]==0)co