并肩三角形的几何定理和代数约束

Geometric Theorems and Algebraic Constraints of Side-by-Side Triangles

在对空中和海上目标的跟踪过程中,目标的航迹与雷达之间经常会构成一种特殊的"边并边"的三角关系。针对这种特殊的三角关系,引入了平面和球面并肩三角形的概念,研究了它们的几何定理和代数约束关系。针对实际作战环境中可能出现的目标运动状态发生变化或部分量测信息丢失问题,分别利用并肩三角形的边角关系和传统处理方法进行了目标跟踪的仿真实验。实验结果表明:传统处理方法往往由于运动模型的不匹配或量测间隔较大的原因,跟踪误差较大。所提出的并肩三角形的边角关系,能够充分利用具有边角关系的量测信息,得到较为理想的跟踪效果,证明了并肩三角形边角关系在实际作战过程中的适应性和有效性。

A special relation of side-by-side triangles forms between the target tracks and the radars in the air or on the sea.In the view of these special triangles,the paper introduces some definitions of side-byside triangles on a plane or a sphere,and investigates their geometric theorems and algebraic constraints.Aimed at the problems that target states change and the measurement information exists in shortages,the paper respectively uses the relation between sides and angles of a triangle and the traditional method to design the simulation.The simulation result shows that because of motion model mismatch or big measurement interval,the traditional method has many errors,while the method used by relation between sides and angles of side-by-side triangle draws a better result,and the adaptation and the effectiveness of side-by-side triangle in actual combat are tested and verified.