基于多目标优化模型的无人机纯方位无源定位问题研究

Research on Bearing-Only Passive Location of Unmanned Aerial Vehicle Based on Multi-Objective Optimization Model

本文主要研究了无人机遂行编队飞行中的纯方位无源定位问题。根据多目标优化模型,利用三角测位算法、贪婪算法、动态规划模型等,对被动接收信号无人机的定位位置信息进行估计,实现了对无人机遂行编队飞行位置的调整。针对问题一的(1)问,考虑无人机对自身的高度的感知,仅在二维空间考虑问题,建立极坐标系。根据被动接收信号的无人机与发射信号无人机之间的角度关系分成四种情况进行分类讨论,运用正弦定理、三角形的性质等几何知识找到无人机间的角度与距离的关系,求解出不同无人机对应的距离与角度,从而建立被动接收信号无人机的定位模型。针对问题一的(2)问,考虑发射信号无人机编号未知,无法直接用三角定位法求解,所以假设还需要两架无人机发射信号,将四架发射信号无人机根据双站交叉定位算法进行排列组合,利用三角测量定位法及正弦定理、三角形的性质等几何知识联立方程组,求解方程组得到唯一坐标解,从而证明假设成立,即除FY00和FY01之外,还有两架无人机发射信号。针对问题一的(3)问,考虑除FY00和FY01外其余无人机位置均略有偏差,利用贪婪算法并建立多目标规划模型,选择发射信号的无人机,使得每一架被动接收信号无人机位置偏差最小,进而总体圆形编队与规定圆周间的偏差达到最优解,从而得到调整方案。针对问题二,考虑到无人机不一定处于同一高度,所以在三维空间中建立直角坐标系。为避免误差较大,选取相邻三个无人机作为发射信号的无人机,采用动态规划及多目标优化模型依次找到无人机的最佳方位,从而得到调整方案。本文的特色在于将三角测量定位法、动态规划与多目标规划模型相结合,运用贪婪算法通过局部最优解来推导全局最优解,在保证求解精度的同时,极大减少了运算的时间和复杂程度,为日后无人机遂行编队飞行中的纯方位无源定位问题和定位调整问题提供了参考依据。

In this paper, the problem of bearings-only passive location in formation flying of unmanned aerial vehicles is mainly studied. According to the multi-objective optimization model, the positioning po-sition information of unmanned aerial vehicles (UAVs) receiving passive signals is estimated by us-ing triangle positioning algorithm, greedy algorithm and dynamic programming model, and the flying position of UAV tunneling formation is adjusted. For the first question (1), the UAV’s percep-tion of its own height is considered, and the problem is only considered in two-dimensional space, and the polar coordinate system is established. According to the angle relationship between un-manned aerial vehicles receiving signals passively and unmanned aerial vehicles transmitting sig-nals, it is classified and discussed in four situations. The relationship between angles and distances between unmanned aerial vehicles is found by using geometric knowledge such as sine theorem and triangle properties, and the corresponding distances and angles of different unmanned aerial vehicles are solved, thus establishing the positioning model of unmanned aerial vehicles receiving signals passively. In response to question (2) of the first question, considering that the number of unmanned aerial vehicles (UAVs) transmitting signals is unknown, it can’t be directly solved by triangulation, so it is assumed that two UAVs are needed to transmit signals. Four UAVs transmit-ting signals are arranged and combined according to the bistatic cross positioning algorithm, and the equations are simultaneously solved by using triangulation positioning method, sine theorem, triangle properties and other geometric knowledge, and the unique coordinate solution is obtained, thus proving that the hypothesis is established, that is, besides FY00 and FY01, there are two UAVs transmitting signals. In order to solve the question (3) of the first question, considering that the po-sitions of other UAVs are slightly deviated except FY00 and FY01, the greedy algorithm is used to establish a multi-objective programming model, and the UAVs that transmit signals are selected to minimize the position deviation of each UAV that passively receives signals, and then the deviation between the overall circular formation and the specified circumference reaches the optimal solu-tion, so as to obtain the adjustment scheme. Aiming at the second problem, considering that drones are not necessarily at the same height, a rectangular coordinate system is established in three-dimensional space. In order to avoid large error, three adjacent UAVs are selected as the UAVs transmitting signals, and the optimal orientation of UAVs is found in turn by using dynamic programming and multi-objective optimization model, so as to get the adjustment scheme. The characteristic of this paper is to combine triangulation positioning method, dynamic programming and multi-objective programming model, and use greedy algorithm to derive the global optimal so-lution through local optimal solution, which greatly reduces the time and complexity of operation while ensuring the accuracy of solution, and provides a reference for bearings-only passive posi-tioning and positioning adjustment in future UAV formation flying.