低秩条件下双星TDOA和FDOA无源定位算法

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。

A passive location algorithm based on TDOA and FDOA of dual-satellite in the condition of unfiled rank

To solve the problem that the position vector of the first satellite,the position difference vector between dual satellites and the speed difference vector between dual satellites are coplanar when the fixed emitter with known altitude is located by dual satellites using time difference of arrival (TDOA) and frequency difference of arrival (FDOA),an analytic solution in three-dimensional spaces was proposed.The condition for no solution is only that the two position vectors and two speed vectors of dual satellites are collinear.The paper analyzes the two conditions of both coplanar but non-collinear and collinear.The analytic solutions of different conditions are given.The problem of location can be simplified into solving quadratic equation with one unknown when the position vectors of dual satellites are collinear,which alleviates the complexity of the problem solving and reduces the computational complexity.Besides,the positioning accuracy is enhanced in nadir point of dual satellites when the three vectors are coplanar.The algorithm was proved useful by simulation experiments.