高速铁路CPIII轨道精调控制网数据处理

1、测绘工程1101自由网平差约束网平差置平平差观测值权确定近似坐标推算误差方程推导平差与精度评定lxBV0PlBxPBBTTPlBPBBxTT11PBBQTxx NNNNNNNN)()(PlBNxTNQxx XYXYSmmT000101101000010100PlBSSNxTT100YXKYXYXcossinsincosdKcKbYaXsincos，YXdcbaXYYXVVyx00001001 本次工程实例截取了一段CPIII控制网两相邻测站的观测数据，仪器测角中误差0.5，测距精度1+1ppm。两个测站(Z16705、Z16706)共观测16个CPIII点（167317168302）和一个加密

2、点（167JMP22），共25个方向值和斜距，观测示意图如下： 近似坐标推算（1）以单个测站为单位定义假定坐标系，具体的定义方法是：假设CPIII自由测站边角交会网第一个测站点的站心坐标为(0，0)，第一个测站点至观测的第一个CPIII点的坐标方位角为000000；（2）按极坐标法计算各点的坐标。当计算的坐标中，有一定数量的CPII点，暂且计算出在假定坐标系下的坐标，用于之后的置平；（3）令下一个测站的测站点坐标为(0，0)，该测站点到其观测的第一个CPIII点的方位角为0，先用极坐标法求出该测站下所有点的坐标，然后依据相邻两测站公共观测点解算出转换参数完成向前一测站所有点的坐标转换。将重复上

3、述（2）、（3）过程，则可完成全部CPIII点和测站点近似坐标的推算。推算后的近似坐标如下：目标点号XY加密点号XY测站点号XY167317-152.525-21.1989167JMP22-74.6295-3.63703Z1670500167318-153.529-12.0379Z16706129.732816.1452167319-87.412-14.334167320-88.4255-5.1697167321-30.2959-7.85875167322-31.36751.2650716732334.74875016732433.548029.1644716732599.71148.4132

4、5316732698.4557217.50156167327164.589717.302167328163.310226.43206167329229.398726.7736167330228.026135.8922168301294.183836.7409168302292.740245.8557 误差方程推导 （1）水平方向误差方程：已知坐标反算方位角公式：将上式用泰勒公式展开取常数项和一次项得：令误差方程可简写为：测站定向角：)()()()(arctanjjkkjjkkjkxXxXyYyY00002002002002000jkjkkjkjkjjkjkjjkjkjkjkSYxSYySXxS

5、Y 00200jkjkjkjkSSYasin 00200jkjkjkjkSSXbcos 000jkjkjjkjkjkjkkkijjjkLLZLllybxaybxazv)(nLZnjkjkj100)(方向编号方向观测值XY近似边长近似方位角（rad） 近似方位角（）系数(左a右b)常数（-l）Z16705167323136.53825 34.74875034.74875 00.00000 0-5935.92.558E-11167325241.36122 99.7114 8.413253100.06571 0.0841766644.82297 173.3082-2054-1.1E-06167327

6、342.53925 164.589717.302165.49664 0.1047372896.00100 130.2997-1239.513.995E-06167328445.73195 163.3102 26.43206165.43536 0.16046049.19370 199.2048-1230.78-3.38E-06167326546.61790 98.45572 17.5015699.99917 007965 361.0018-2030.83-5.38E-06167324651.81723 33.548029.1644734.77725 0.26666845

7、215.27898 1562.94-5721.42.961E-061673227214.22873 -31.36751.2650731.39297 3.10128387177.69048 264.77396565.083-1.71E-06167JMP228219.32832 -74.6295-3.6370374.71809 3.190288633182.79007 -134.3762757.304-1.39E-061673209219.88418 -88.4255-5.169788.57645 3.199990158183.34593 -135.9112324.697-8.11E-091673

8、1810221.02153 -153.529-12.0379154.00001 3.219840693184.48328 -104.6971335.285-1.23E-0616731711224.45090 -152.525-21.1989153.99108 3.279694416187.91265 -184.3941326.708-1.04E-0616731912225.85084 -87.412-14.33488.57945 3.304127975189.31259 -376.8132297.897-6.84E-0616732113231.08023 -30.2959-7.8587531.

9、29861 3.395398029194.54198 -1654.746379.1033.019E-06方向编号方向观测值XY近似边长近似方位角（rad） 近似方位角（）系数(左a右b)常数（-l）Z167061673271122.03940 34.85693 1.15679234.87612 0.0331746681.90077 196.1662-5910.96-4.8662481673292126.22431 99.6659110.6284100.23101 0.1062387366.08703 218.2172-2046.29-0.0036031683013127.27581 164.4

10、5120.5957165.73568 0.1245904127.13850 154.6571-1234.9-0.0821381683024130.46688 163.007429.7105165.69287 032961 223.2173-1224.690.02872741673305131.49670 98.2933119.747100.25726 0.19825953611.35943 405.2238-2017.060.03222471673286137.16968 33.57736 10.2868535.11778 0.2972839417.03312 172

11、0.497-5615.882.5815921673267297.65531 -31.2771 1.35635331.30647 3.098254092177.51688 285.456582.389-4.1527271673248304.28873 -96.1848-6.9807396.43776 3.214041909184.15104 -154.8222133.23-1.5011041673229305.41456 -161.1-14.8801161.78601 3.233696991185.27719 -117.261269.521-0.33259416732110308.66769 -

12、160.029-24.0039161.81898 3.290480401188.53064 -189.0821260.5630.819793316732311309.78396 -94.984-16.145296.34644 3.309961493189.64682 -358.7552110.5950.51678316732512314.57971 -30.0214-7.7319531.00109 3.393662574194.44254 -1659.446443.2150.4040617 200200jjkkjjkkjkjkyYyYxXxXvLjkjkjkjkjkjkjkjkjkyySYxx

13、SXSvL0000000jkjkSXa00jkjkSXbjkkkjjjklybxaybxav方向编号观测边长XY近似边长系数(左a右b)常数Z16705167323134.7488 34.74875034.7488 104.61E-051673252100.0657 99.7114 8.413253100.0657 0.996459 0.084077-5.3E-061673273165.4966 164.589717.302165.4966 0.99452 0.104546-3.8E-051673284165.4354 163.3102 26.43206165.4354 0.987154 0.

14、1597733.75E-05167326599.9992 98.45572 17.5015699.9992 0.984565 0.1750172.89E-05167324634.7773 33.548029.1644734.7773 0.964654 0.2635194.87E-05167322731.3930 -31.36751.2650731.3930 -0.99919 0.0402983.17E-05167JMP22874.7181 -74.6295-3.6370374.7181 -0.99881-0.048685.44E-06167320988.5764 -88.4255-5.1697

15、88.5764 -0.9983-0.05836-4.6E-0516731810154.0000 -153.529-12.0379154.0000 -0.99694-0.07817-9.2E-0616731711153.9911 -152.525-21.1989153.9911 -0.99048-0.137661.92E-051673191288.5795 -87.412-14.33488.5795 -0.98682-0.161824.56E-051673211331.2986 -30.2959-7.8587531.2986 -0.96796-0.25109-1.5E-05方向编号观测边长XY近

16、似边长系数(左a右b)常数Z16706167327134.8762 34.85693 1.15679234.8761 0.99945 0.0331696.17E-051673292100.2308 99.6659110.6284100.2310 0.994362 0.106039-0.000181683013165.7353 164.45120.5957165.7357 0.992249 0.124268-0.000361683024165.6925 163.007429.7105165.6929 0.983793 0.179311-0.000351673305100.2570 98.2933

17、119.747100.2573 0.980411 0.196963-0.00024167328635.1174 33.57736 10.2868535.1178 0.956136 0.292924-0.00033167326731.3065 -31.2771 1.35635331.3065 -0.99906 0.0433256.55E-05167324896.4387 -96.1848-6.9807396.4378 -0.99738-0.07239 0.0009711673229161.7855 -161.1-14.8801161.7860 -0.99576-0.09197-0.0005216

18、732110161.8181 -160.029-24.0039161.8190 -0.98894-0.14834-0.000881673231196.3464 -94.984-16.145296.3464 -0.98586-0.16757-8.1E-051673251231.0000 -30.0214-7.7319531.0011 -0.9684-0.24941-0.00109)(251，1 ，1SSPPdiagP 自由网平差计算与精度评定：（1）平差计算系数矩阵（表达通式）自由网平差.xlsxbbabababababababababaabababababababababaB000000000

19、00000000000000000000000000000000000000000000010000001000000100000000100000001-方向值距离基准条件：坐标改正数：常数项按先方向后距离的顺序依次罗列：0170170202010100002211101010101010010101010101XYXYXYXYXYSjjjjTTJMPJMPjCPIIIjCPIIIppppyxyxyxyxZZx2222221121Tssslllllll25212521点号概略坐标改正数（m） 平差坐标协因数精度估算(mm)167317X-152.5250.000177-152.5255.13

20、E-061.3594141.442559Y-21.19895.89E-07-21.19896.47E-070.482671167318X-153.5290.000206-153.5295.19E-061.36641.442448Y-12.03794.00E-06-12.03795.93E-070.462177167319X-87.4120.000151-87.41184.59E-061.2853421.327553Y-14.334-6.50E-06-14.3343.06E-070.332105167320X-88.4255-0.00024-88.42575.88E-061.4543841.48

21、07Y-5.1697-2.50E-05-5.16972.15E-070.277921167321X-30.29590.000754-30.29522.16E-060.8811530.915767Y-7.85870.000167-7.85861.73E-070.2494167322X-31.36750.000429-31.3672.25E-060.9002380.911176Y1.2651-1.70E-051.26515.50E-080.140761167323X34.7488-0.0001934.74861.92E-060.831850.848542Y02.44E-0507.79E-080.1

22、67482167324X33.548-0.0009933.5471.76E-060.7950210.83277Y9.1645-0.000389.16411.71E-070.247886167325X99.71140.00040199.71181.83E-060.8123930.848361Y8.41330.0001818.41341.66E-070.244407167326X98.4557-0.0006598.45511.77E-060.7993520.816498Y17.5016-0.0005217.5017.70E-080.166447167327X164.58970.000295164.

23、592.30E-060.9102290.921645Y17.3020.00083817.30285.81E-080.144611167328X163.31020.000204163.31042.09E-060.8673390.91235Y26.4321-0.0003526.43172.23E-070.283028167329X229.3987-0.00014229.39864.67E-061.2969051.337879Y26.77362.90E-0526.77363.00E-070.328567167330X228.0261-0.0002228.02594.56E-061.2812941.3

24、38021Y35.8922-1.70E-0535.89224.13E-070.385468168301X294.1838-0.00033294.18355.18E-061.3650991.45757Y36.74096.90E-0536.7417.25E-070.510896168302X292.7402-0.0003292.73995.11E-061.355791.457518Y45.8557-3.70E-0545.85577.95E-070.534967167JMP22X-74.62950.000191-74.62934.58E-061.283831.305941Y-3.6371.18E-0

25、7-3.6371.59E-070.239294x xxQ 0yyyQ 022yxP（2）精度评定观测值改正数（方向值、距离）Z16705Z16706-1-0.8-0.6-0.4-0.200.20.40.6167321167322167323167324167325167326167327167328167329167330168301168302方向值-1-0.500.511.5167317167318167319167320167321167322167323167324167325167326167327167328167JMP22方向值-1.4-1.2-1-0.8-0.6-0.4-0.2

26、00.20.4167317167318167319167320167321167322167323167324167325167326167327167328167JMP22平距00.10.20.30.40.50.60.70.8167321167322167323167324167325167326167327167328167329167330168301168302平距观测值中误差（方向值、距离）Z16705Z1670600.10.20.30.40.50.60.7167317167318167319167320167321167322167323167324167325167326167327167328167JMP22方向值（）00.10.20.30.40.50.60.7167321167322167323167324167325167326167327167