基于四面体六棱长的三站测时差立体定位方法

针对在三站测时差立体定位中辐射源位置不能唯一确定的情形,提出一种简单易懂、计算方便、可操作性强的解析解方法,以解决求解双曲面方程组的繁琐问题。首先利用三站相互之间的距离、由量测时差值换算得到的两个距离差值,以及辐射源至主站的距离(设为变量r)总共6个参数,立足于已知6条边长判断能否构成四面体的理论,求得r的取值范围;然后在r的值域范围内任意给定某个具体值,加上已知三站的地理位置,通过解三元一次方程组的形式获得目标在三站所在平面内垂直投影的坐标(设为变量X_h),并计算出目标至垂直投影的距离(设为变量h);最后由X_h和h给出目标在地心地固直角坐标系下的坐标。

An Algorithm of Tri-station 3D TDOA Positioning Based on Six Side-length Values of a Tetrahedron

Aimed at the ambiguity occurring in the passive tri-station 3D TDOA positioning system, a simple,lowly-computational and highly-operable algorithm is proposed to resolve the hyperbolic location equations. Firstly,using six parameters which includes the distances between every two stations, the distance differences obtain from two measured time differences,and the distance between the radiation source and the main station(let it be r),simultaneously based on the theory of judging whether six positive number be able to construct the lengths of a tetrahedron's six sides,the permissive value range of r is gotten. Secondly,for any value of r in the permissive range,the detailed positions of three stations is given,the coordinate of the target's vertical projection (let it be Xh)in the plane of three stations can be calculated by resolving three-variable linear equations. Moreover,the distance between the target and the projection (let it be h)can be also calculated. Lastly,the target's earth-center and earth-fixed(ECEF)coordinate is analytically expressed by the parameters of X h and h.