高速鐵路CPIII軌道精調控制網數據處理

1、測繪工程1101自由網平差約束網平差置平平差觀測值權確定近似坐標推算誤差方程推導平差與精度評定lxBV0PlBxPBBTTPlBPBBxTT11PBBQTxx NNNNNNNN)()(PlBNxTNQxx XYXYSmmT000101101000010100PlBSSNxTT100YXKYXYXcossinsincosdKcKbYaXsincos，YXdcbaXYYXVVyx00001001 本次工程實例截取了一段CPIII控制網兩相鄰測站的觀測數據，儀器測角中誤差0.5，測距精度1+1ppm。兩個測站(Z16705、Z16706)共觀測16個CPIII點（167317168302）和一個加密

2、點（167JMP22），共25個方向值和斜距，觀測示意圖如下： 近似坐標推算（1）以單個測站為單位定義假定坐標系，具體的定義方法是：假設CPIII自由測站邊角交會網第一個測站點的站心坐標為(0，0)，第一個測站點至觀測的第一個CPIII點的坐標方位角為000000；（2）按極坐標法計算各點的坐標。當計算的坐標中，有一定數量的CPII點，暫且計算出在假定坐標系下的坐標，用于之后的置平；（3）令下一個測站的測站點坐標為(0，0)，該測站點到其觀測的第一個CPIII點的方位角為0，先用極坐標法求出該測站下所有點的坐標，然后依據相鄰兩測站公共觀測點解算出轉換參數完成向前一測站所有點的坐標轉換。將重復上

3、述（2）、（3）過程，則可完成全部CPIII點和測站點近似坐標的推算。推算后的近似坐標如下：目標點號XY加密點號XY測站點號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 誤差方程推導 （1）水平方向誤差方程：已知坐標反算方位角公式：將上式用泰勒公式展開取常數項和一次項得：令誤差方程可簡寫為：測站定向角：)()()()(arctanjjkkjjkkjkxXxXyYyY00002002002002000jkjkkjkjkjjkjkjjkjkjkjkSYxSYySXxS

5、Y 00200jkjkjkjkSSYasin 00200jkjkjkjkSSXbcos 000jkjkjjkjkjkjkkkijjjkLLZLllybxaybxazv)(nLZnjkjkj100)(方向編號方向觀測值XY近似邊長近似方位角（rad） 近似方位角（）系數(左a右b)常數（-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方向編號方向觀測值XY近似邊長近似方位角（rad） 近似方位角（）系數(左a右b)常數（-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方向編號觀測邊長XY近似邊長系數(左a右b)常數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方向編號觀測邊長XY近

16、似邊長系數(左a右b)常數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 自由網平差計算與精度評定：（1）平差計算系數矩陣（表達通式）自由網平差.xlsxbbabababababababababaabababababababababaB000000000

19、00000000000000000000000000000000000000000000010000001000000100000000100000001-方向值距離基準條件：坐標改正數：常數項按先方向后距離的順序依次羅列：0170170202010100002211101010101010010101010101XYXYXYXYXYSjjjjTTJMPJMPjCPIIIjCPIIIppppyxyxyxyxZZx2222221121Tssslllllll25212521點號概略坐標改正數（m） 平差坐標協(xié)因數精度估算(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）精度評定觀測值改正數（方向值、距離）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平距觀測值中誤差（方向值、距離）Z16705Z1670600.10.20.30.40.50.60.7167317167318167319167320167321167322167323167324167325167326167327167328167JMP22方向值（）00.10.20.30.40.50.60.7167321167322167323167324167325167326167327167