基于TDOA/AOA混合的高精度室内可见光定位算法

为了提高室内三维空间的定位精度,提出了一种基于联合到达时间差与到达角度(time difference of arrival/angle of arrival,TDOA/AOA)信息的混合定位算法。由于构建的目标函数具有非凸性,采用传统定位算法在目标函数求解过程中会出现局部最优解的问题。因此,针对该问题,将目标函数转成二次约束二次规划问题,通过引入半定松弛(semi-definite relaxation,SDR)方法将目标函数转换为二阶锥规划(second order cone programming,SOCP)问题,寻找全局最优解。其次,针对SOCP无法对凸包外的目标进行有效定位的问题,在该算法的基础上引入了惩罚项,使松弛后的约束条件进一步逼近原始约束条件,解决了定位过程中的凸包问题。数值仿真结果表明:在10m×10m×3m的三维定位空间内,选取40×40个测试点,平均定位误差为1.39cm,可实现室内三维空间高精度定位。与传统的混合定位算法相比,均能够获得较高的定位精度。

Hybrid TDOA/AOA algorithm based high accuracy indoor visible light positioning

In order to achieve high positioning accuracy in indoor three-dimensional space, a hybrid positioning algorithm based on the combining of the time difference of arrival and angle of arrival (TDOA/AOA) information is proposed. Firstly, due to the non-convexity of the objective function, a local optimal solution occur in the process of solving the objective function by the traditional hybrid localization algorithm. Therefore, in order to solve this problem, a semi-definite relaxation (SDR) method is introduced. It can transform the objective function into a second-order cone programming problem (SOCP), which is a quadratic constrained quadratic programming problem. Then a global optimal solution can be obtained. Secondly, to deal with the problem that the SOCP method cannot effectively locate the target outside the convex hull, a penalty term is introduced. It can make the relaxed constraint condition approximate to the original problem constraints and solve the convex hull problem in the process of positioning. The numerical simulation results show that the average positioning error is 1.39 cm with 40×40 test points selected in the three-dimensional positioning space in the size of 10 m×10 m×3 m. The result shows that the algorithm can achieve high localization accuracy in three-dimensional space. Compared with other traditional hybrid positioning algorithms, it can obtain higher positioning accuracy.