一种基于二阶锥规划的新时差定位算法

A New TDOA Location Algorithm Based on Second Order Cone Programming

针对传统时差定位算法在量测噪声较大情况下定位性能不佳的缺点,提出了一种基于二阶锥规划的新时差定位算法。该算法通过凸松弛和引入惩罚项,将难以求解的用户位置最大似然估计问题转换为一个易于求解的二阶锥规划问题,并将松弛问题的最优解作为用户位置的初始估计,利用传统的泰勒级数展开法得到最终定位结果。仿真给出了不同基站数目及量测噪声下算法的定位性能。仿真结果表明,在量测噪声较大的情况下,新算法的定位精度仍可以逼近理论克拉美罗下限,而且算法中惩罚因子的选取范围易于确定。

The traditional TDOA（Time Difference of Arrival） location algorithms have large performance loss as the measurement noise is high. To overcome this drawback, this paper proposes a new effective TDOA location algo- rithm based on second order cone pmgramming（SOCP）. By int_mducing a penalty term and relaxing the equality constrains, the nonlinear and nonconvex maximum likelihood estimation problem for user position is tmnsfomed into a convex optimization problem, named second order cone programming that can be efficiently solved by mod- em interior point methods. The optimal solution of relaxed problem is used as the initial guess for traditional Taylor method to estimate the user position. The simulation provides the location performance versus measurement noise under different numbers of base station. Simulation results show that the performance of proposed algorithm can attain the Cramer- Rao lower bound as the noise variance is high. The intervals of penalty factor are also dis- cussed in this paper.