﻿ 参数法CPⅢ精密三角高程控制网数据处理方法
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1. 兰州交通大学测绘与地理信息学院, 甘肃 兰州 730070;
2. 甘肃省地理国情监测工程实验室, 甘肃 兰州 730070

Parameter method data processing for CPⅢ precise trigonometric leveling network
LI Jianzhang1,2, YAN Haowen1,2
1. Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China;
2. Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China
Abstract: In view of the limitation of the difference method, a parameter CPⅢ adjustment method is proposed for precision trigonometric elevation network. The result proves that the proposed method, being simple, efficient and time-saving, avoids the negative influences caused by the correlation among the data acquired from the difference method, and thus improves the accuracy. In addition, the study is conducted about strict weight of the CPⅢ precision trigonometric elevation network. The result shows that when the vertical angle is smaller than 3°, the ranging error of trigonometric leveling can be dismissed, and the accuracy of CPⅢ precision triangulation elevation control network does not change significantly before and after strict weight determination.
Key words: CPⅢ leveling control network    precise trigonometric leveling    parameter method    minimum norm quadratic unbiased estimate

(1) 差分法平差模型的观测值是三测站6个三角高程观测值的线性组合，因此测量噪声远远大于非差观测值。

(2) 差分观测值不再是独立观测值，而是相关观测值。

(3) 当相邻两个目标与测站点不等距时，所形成的差分观测值中球气差影响残余量仍然比较大[15]

(4) 差分法观测值超限时，参与差分的两原始三角高程观测值全部作废，造成数据的浪费，因此数据利用率不高。

1 参数法CPⅢ精密三角高程平差模型

 图 1 CPⅢ精密三角高程控制网i测站观测 Fig. 1 Schematic diagram of i station observation at CPⅢ precision trigonometric leveling network

1.1 随机模型

n个三角观测值可以写出n个如上的微分式，其矩阵形式为

1.2 函数模型

(1)

(2)

j点为已知点，且其高程为Hj时，其误差方程为

(3)

(4)

1.3 球气差参数矩阵的优化

2 三角高程观测值严密定权

3 实例验证

 图 2 参数法、非参数法高程中误差曲线 Fig. 2 Parametric and non-parametric elevation error curves

 图 3 参数法、非参数法相邻点高差中误差曲线 Fig. 3 The curve diagram of the middle error of the height difference of the adjacent points for the parameter method and no parameter method

 图 4 参数法与精密水准测量所得高程估计值之差对比 Fig. 4 Schematic diagram of the comparison between the height estimate of the parameter method and the precision leveling survey

 图 5 参数法与精密水准测量所得高差估计值对比 Fig. 5 Schematic diagram of the comparison of height difference estimation between parameter method and precise leveling survey

 序号 线路长度/km 约束点数/mm 参数法 差分法 高程差异均值/mm 高程差异最大值/mm 相邻点高差差异均值/mm 相邻点高差差异最大值/mm 超限数 高程差异均值/mm 高程差异最大值/mm 相邻点高差差异均值/mm 相邻点高差差异最大值/mm 超限数 1 4 9 0.35 2.35 0.34 2.54 1 0.69 2.47 0.47 2.91 2 2 5 11 0.27 1.65 0.27 1.88 0 0.34 2.60 0.31 2.09 1 3 7 15 0.53 1.88 0.55 1.59 0 0.61 2.58 0.58 2.29 2 4 10 21 0.75 2.21 0.68 1.99 0 1.43 3.63 0.81 2.42 2 5 6 13 0.46 1.60 0.49 2.13 1 0.64 2.91 0.57 2.33 3 6 6 13 0.55 1.77 0.49 2.13 1 0.67 1.89 0.59 2.02 2 7 6 13 0.53 1.88 0.51 2.23 2 0.66 2.84 0.53 2.12 2 8 6 13 0.44 1.85 0.53 1.86 0 0.52 2.08 0.57 3.05 5 9 4 8 0.36 1.96 0.33 2.42 1 0.70 2.36 0.51 2.95 1 10 5 10 0.58 2.22 0.56 1.86 0 0.59 2.31 0.57 2.24 1

(1) 由试验可知，采用参数法消除精密三角高程测量中球气差的影响，可获得良好的效果，其解算精度明显优于差分法解算精度，而且随着约束点密度的降低，这种差异会更加明显。

(2) 严密定权前后，CPⅢ精密三角高程网解算结果未有显著变化。在进行CPⅢ控制测量时，线下工程已经完成，场地较为平坦，且目标点高于地面1 m左右且大致等高[23]。目标点距离仪器越近，竖直角绝对值越大。设水平距离最短为30 m，仪器横轴与目标点间高差最大为1.5 m，则竖直角绝对值最大不超过3°(现场实测数据中竖直角绝大多数小于1°)。假设测距误差为1 mm(实际更小)，则其对三角高程测量值的影响仅仅为0.05 mm，这个影响甚至小于棱镜在高程方向的安装误差的限差(0.2 mm)，因此可以忽略不计。由此可知，在CPⅢ精密三角高程测量中，测距误差可以忽略不计，不必进行严密定权，仅采用常规定权即可，试验数据也证明了这一点。

(3) 由图 2图 3可以看出，通过精密三角高程测量数据解算所得CPⅢ点高程中误差以及相邻CPⅢ点间高差中误差均符合规范要求，但在图 5中，水准测量方法所得高差估计值和参数法精密三角高程所得同名高差估计值的差值出现超限的情况。

4 结束语

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http://dx.doi.org/10.11947/j.AGCS.2019.20180265

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#### 文章信息

LI Jianzhang, YAN Haowen

Parameter method data processing for CPⅢ precise trigonometric leveling network

Acta Geodaetica et Cartographica Sinica, 2019, 48(4): 431-438
http://dx.doi.org/10.11947/j.AGCS.2019.20180265