基于极球面投影的极区格网等角航线

摘要

Traditional polar navigation usually uses grid navigation to implement great circle, which could cause problems that different grid direction of great circle makes against navigation control and great circle is not straight lines on the polar projection lead to principle error.To solve these problems, considering the idea that it is easier to navigaition control and plotting if the rumble route in the lower latitudes is straight lines on the mercator projection, a rumble route called grid rumble route which are straight lines on polar stereographic projection is suggested.Firstly, polar stereographic projection based on double projection and grid navigation are studied.Then the definition of grid rumble route and route equation is presented.Finally, compitational method of distance and grid direction for grid rumble route is provided.From the theoretical analysis and simulations, grid rumble route is approximate to great circle and great ellipse routes, the navigation distance is relatively short;thus, they are straight lines on the polar stereographic projection and grid direction is equal everywhere.Moreover, they can be used in conjunction with grid navigation method and polar stereographic projection, more applicable for the polar navigation.%针对传统极区航行通常采用格网导航执行大圆航线, 大圆航线上格网航向角不同不利于航行控制以及大圆航线在极区投影图上不完全投影为直线引起固有原理性误差的问题, 借鉴中低纬度地区等角航线上地理航向角相等以及在墨卡托投影图上为直线便于航行控制和绘算的思想, 提出了一种在极球面投影图中表现为直线的"等角航线"——格网等角航线.在研究双重投影的极球面投影以及格网导航方法的基础上, 提出了格网等角航线的定义, 推导了航线方程, 并根据该航线的航程和航向角计算方法进行航线仿真设计.理论分析和仿真验证表明:航线上格网航向角处处相等, 在极区投影图上表现为直线;格网等角航线与大圆航线、大椭圆航线相近, 航程较短.因此, 极区格网等角航线可以与格网导航方法、极球面投影精确配合应用, 适合于极区航行.