高速鐵路CPIII軌道精調(diào)控制網(wǎng)數(shù)據(jù)處理

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

2、點(diǎn)（167JMP22），共25個(gè)方向值和斜距，觀測示意圖如下： 近似坐標(biāo)推算（1）以單個(gè)測站為單位定義假定坐標(biāo)系，具體的定義方法是：假設(shè)CPIII自由測站邊角交會(huì)網(wǎng)第一個(gè)測站點(diǎn)的站心坐標(biāo)為(0，0)，第一個(gè)測站點(diǎn)至觀測的第一個(gè)CPIII點(diǎn)的坐標(biāo)方位角為000000；（2）按極坐標(biāo)法計(jì)算各點(diǎn)的坐標(biāo)。當(dāng)計(jì)算的坐標(biāo)中，有一定數(shù)量的CPII點(diǎn)，暫且計(jì)算出在假定坐標(biāo)系下的坐標(biāo)，用于之后的置平；（3）令下一個(gè)測站的測站點(diǎn)坐標(biāo)為(0，0)，該測站點(diǎn)到其觀測的第一個(gè)CPIII點(diǎn)的方位角為0，先用極坐標(biāo)法求出該測站下所有點(diǎn)的坐標(biāo)，然后依據(jù)相鄰兩測站公共觀測點(diǎn)解算出轉(zhuǎn)換參數(shù)完成向前一測站所有點(diǎn)的坐標(biāo)轉(zhuǎn)換。將重復(fù)上

3、述（2）、（3）過程，則可完成全部CPIII點(diǎn)和測站點(diǎn)近似坐標(biāo)的推算。推算后的近似坐標(biāo)如下：目標(biāo)點(diǎn)號XY加密點(diǎn)號XY測站點(diǎn)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(dǎo) （1）水平方向誤差方程：已知坐標(biāo)反算方位角公式：將上式用泰勒公式展開取常數(shù)項(xiàng)和一次項(xiàng)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(shù)(左a右b)常數(shù)（-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(shù)(左a右b)常數(shù)（-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(shù)(左a右b)常數(shù)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(shù)(左a右b)常數(shù)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(wǎng)平差計(jì)算與精度評定：（1）平差計(jì)算系數(shù)矩陣（表達(dá)通式）自由網(wǎng)平差.xlsxbbabababababababababaabababababababababaB000000000

19、00000000000000000000000000000000000000000000010000001000000100000000100000001-方向值距離基準(zhǔn)條件：坐標(biāo)改正數(shù)：常數(shù)項(xiàng)按先方向后距離的順序依次羅列：0170170202010100002211101010101010010101010101XYXYXYXYXYSjjjjTTJMPJMPjCPIIIjCPIIIppppyxyxyxyxZZx2222221121Tssslllllll25212521點(diǎn)號概略坐標(biāo)改正數(shù)（m） 平差坐標(biāo)協(xié)因數(shù)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(shù)（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