Abstract: 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.

Key words: indoor positioning, visible light communication, time difference of arrival (TDOA), angle of arrival (AOA), second-order cone programming (SOCP)