基于MATLAB的子午线收敛角计算方法及其精度分析

MATLAB-Based Meridian Convergence Angle Calculation Method and Its Accuracy Analysis

子午线收敛角是坐标方位角α和大地方位角A精确转换的关键参数,针对不同子午线收敛角计算公式在不同纬度所计算的子午线收敛角存在差异的问题,利用MATLAB软件对4种子午线收敛角计算进行编程,并在经差为3.5°处应用不同公式来计算子午线收敛角并分析精度。结果表明:子午线收敛角较差随着纬度变化而变化,在中纬度有峰值,两端较差较小;利用简化公式γ=sin B·l计算的子午线收敛角精度在0.01"~0.1",其精度在跨经线50km内已经满足实际生产需要。

Meridian convergence angle is a key parameter for the accurate conversion of coordinate azimuth α and geodetic azimuth A.In order to solve the problem that the meridian convergence angle calculated by different meridian convergence angle calculation formulas at different latitudes is different, this paper uses the mathematical software MATLAB to analyze the four The calculation of the convergence angle of the seed meridian is programmed to realize the calculation, and the convergence angle of the meridian is calculated and analyzed by applying different formulas at the longitude difference of 3.5°. The results show that the convergence angle difference of the meridian varies with the latitude, with a peak in the middle latitude and a small difference at both ends;Using the simplified formula γ=sinB·l the accuracy of the calculated meridian convergence angle is 0.01 " ~ 0.1", and its accuracy has met the actual production needs within 50 km of the trans meridian line.