随着电子信息技术的不断发展以及硬件制造水平的持续提高，采用无人机组进行无源定位在民用和军事领域受到广泛关注，尤其是在边防监控、军事侦察和目标检测等方向，无源定位技术具有不可代替的作用。深入研究无源定位在不同定位场景下的应用，有益于丰富和完善日常生活中的定位需求，也有益于提高国家在电子对抗方面的军事实力，具有重大的现实意义。

       本文围绕无人机组无源定位技术的应用，在前人的基础上对TDOA 和FDOA无源定位技术中的四站定位技术的解决方法进行了研究，理论情况下，三维空间中四台无人机获取的三组时差定位方程或六组时频差联合的定位方程即可估计辐射源的位置或位置与速度，然而定位方程中存在与辐射源位置和速度的相关项，造成待估计参数增多，从而导致采用加权最小二乘类方法直接求解定位方程时，至少需要五台无人机接收站，因此，本在对实际问题进行建模并详细推导求解过程，对采用四台无人机的无源定位方法进行了研究，提出了四台无人机定位时模糊解问题的解决方法。本文的主要研究成果如下:

       第一，针对四台无人机定位地面辐射源遇到的模糊解问题，本文改进了基于双迭代思想的加权最小二乘算法，首先从时差定位模型出发，得到关于辐射源到参考站的距离的二次方程，再根据时频差联合定位模型以及二次方程的解得到含模糊解的辐射源位置和速度的估计结果。随后，从估计结果中选出高度分量绝对值最低的解作为最优初始估计值。最后构建并求解关于辐射源参数误差的方程，对最优初始估计值进行误差补偿，得到定位结果。仿真实验表明，采用四台无人机进行定位时，高度筛选方式可以筛选出真实解，提高了定位结果的可靠性，保证了最优初始估计值为接近真实辐射源参数的解。

       第二，针对四站定位时，待估计参数增多的问题，本文通过连续的多个时刻的TDOA观测信息，建立多时刻时差定位模型，避免了方程伪线性化操作，多时刻方案不会增加无人机接收站数目，而是以匀速运动模型将各时刻的观测量联系起来，扩充了定位方程个数，实现了方程线性化。同时研究了多时刻TDOA观测信息的定位方法，引入定位误差修正的思想对TSWLS算法进行改进，降低了测量误差对TSWLS算法的影响，提高了算法的定位精度，实现了对多站TDOA测量序列定位问题的解析求解。仿真实验表明，改进的TSWLS算法定位方法在四台无人机定位的情况下，定位精度得到了有效提升。

        With the continuous development of electronic information technology and the continuous improvement of hardware manufacturing level, the use of unmanned aerial units for passive positioning has received widespread attention in both civil and military fields, especially in border monitoring, military reconnaissance, and target detection. Passive positioning technology plays an irreplaceable role. Deeply studying the application of passive positioning in different positioning scenarios is beneficial for enriching and improving the positioning requirements in daily life, and also for improving the military strength of the country in electronic countermeasures, which has significant practical significance.

        This thesis focuses on the application of passive positioning technology for unmanned aerial vehicles, and studies the solution methods of four station positioning technology in TDOA and FDOA passive positioning technology based on previous research. In theory, three sets of time difference positioning equations or six sets of time frequency difference joint positioning equations obtained by four unmanned aerial vehicles in three-dimensional space can estimate the position or position and velocity of the radiation source, However, there are related terms related to the position and velocity of the radiation source in the positioning equation, resulting in an increase in the number of parameters to be estimated. This leads to the need for at least five drone receiving stations when using weighted least squares methods to directly solve the positioning equation. Therefore, in this study, we modeled the actual problem and derived the solution process in detail, and studied the passive positioning method using four drones, A solution to the fuzzy solution problem during the positioning of four unmanned aerial vehicles has been proposed. The main research results of this thesis are as follows:

 

        Firstly, in response to the fuzzy solution problem encountered by four unmanned aerial vehicles in locating ground radiation sources, this thesis improves the weighted least squares algorithm based on the double iteration idea. Firstly, starting from the time difference positioning model, a quadratic equation is obtained for the distance from the radiation source to the reference station. Then, based on the time frequency difference joint positioning model and the solution of the quadratic equation, the estimation results of the radiation source position and velocity containing the fuzzy solution are obtained. Subsequently, the solution with the lowest absolute value of the height component is selected from the estimation results as the optimal initial estimation value. Finally, an equation about the parameter error of the radiation source is constructed and solved, and error compensation is performed on the optimal initial estimation value to obtain the positioning result. Simulation experiments have shown that when using four unmanned aerial vehicles for positioning, the height screening method can filter out true solutions, improve the reliability of positioning results, and ensure that the optimal initial estimation value is a solution close to the true radiation source parameters.

        Secondly, in response to the problem of increasing the number of parameters to be estimated during four station positioning, this thesis establishes a multi time time difference positioning model by continuously observing TDOA information at multiple times. Unlike equation pseudolinearization, the multi time scheme does not increase the number of drone receiving stations, but instead uses a uniform motion model to connect the observations at each time, expanding the number of positioning equations, and achieving equation linearization. At the same time, the positioning method for multi time TDOA observation information was studied, and the idea of positioning error correction was introduced to improve the TSWLS algorithm. This reduced the impact of measurement errors on the TSWLS algorithm, improved the positioning accuracy of the algorithm, and achieved analytical solutions for the positioning problem of multi station TDOA measurement sequences. The simulation experiment shows that the improved TSWLS algorithm positioning method effectively improves the positioning accuracy in the case of four unmanned aerial vehicles positioning.

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