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针对双星对地面已知高度目标辐射源到达时间差(TDOA)和到达频率差(FDOA)无源定位过程中存在卫星1位置矢量、两卫星位置矢量差以及两卫星速度矢量差三者共面问题,提出了一种获得目标位置三维解析解的算法,并指出当且仅当两卫星位置矢量和速度矢量四者共线时才无解。分析了共面但不共线和共线2种情况,给出了不同情况下的解析解,并且当两卫星位置矢量共线时可以将定位问题化简为简单的一元二次方程求解问题,可以有效降低求解复杂度和减少虚根数量。此外,当三矢量共面时还可以改善星下点区域的定位精度。仿真实验验证了所提算法的有效性。
In view of the existence of satellite 1 position vector, two satellite position vector difference and two satellite velocity vector difference in the known target TDOA and FDOA passive orientation on the ground, An algorithm to obtain the three-dimensional analytic solution of the target position is proposed. It is pointed out that there is no solution if and only if the four satellite position vectors and velocity vectors are collinear. Two cases of coplanar but no collinearity and collinearity are analyzed, and the analytical solutions are given under different conditions. When two satellite position vectors are collinear, the localization problem can be reduced to a simple one-quadratic equation to solve the problem. Can effectively reduce the complexity of the solution and reduce the number of imaginary roots. In addition, when the three vector coplanar can also improve the positioning accuracy of the area under the stars. Simulation experiments verify the effectiveness of the proposed algorithm.