Based on the time differences of arrival (TDOA) and frequency differences of arrival (FDOA) measurements of the given planar stationary radiation source, the joint TDOA/FDOA location algorithm which solves the location of the target directly is proposed. Compared with weighted least squares (WLS) methods, the proposed algorithm is also suitable for well-posed conditions, and gets rid of the dependence on the constraints of Earth's surface. First of all, the solution formulas are expressed by the radial range. Then substitute it into the equation of the radial range to figure out the radial range between the target and the reference station. Finally use the solution expression of the target location to estimate the location of the target accurately. The proposed algorithm solves the problem that WLS methods have a large positioning error when the number of observation stations is not over-determined. Simulation results show the effectiveness of the proposed algorithm, including effectively increasing the positioning accuracy and reducing the number of observatories.

中文翻译：

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使用适定 TDOA 和 FDOA 测量直接解决固定源位置

基于给定平面静止辐射源的到达时间差(TDOA)和到达频率差(FDOA)测量结果，提出了直接求解目标位置的TDOA/FDOA联合定位算法。与加权最小二乘法(WLS)相比，该算法也适用于适定条件，摆脱了对地球表面约束的依赖。首先，求解公式用径向范围表示。然后将其代入径向距离方程，计算出目标与参考站之间的径向距离。最后利用目标位置的解表达式来准确估计目标的位置。该算法解决了WLS方法在观测站数不超定时定位误差较大的问题。仿真结果表明了该算法的有效性，包括有效提高定位精度和减少观测站数量。