改进二阶锥松弛和泰勒级数展开在TDOA无源定位中的应用

TDOA Passive Location Based on Improvement of Second Cone Relaxation and Taylor-series Estimation

针对二阶锥松弛算法无法对凸包外的目标进行有效定位的问题,本文提出基于改进二阶锥松弛和泰勒级数展开的TDOA定位算法。首先,给出在视距条件下接收站位置信息无误差的TDOA定位的加权最小二乘模型;其次,简要分析凸包问题的形成原因,并提出解决思路,即在传统二阶锥松弛算法的基础上增加新的惩罚项,使松弛后的约束条件进一步逼近原问题约束,从而有效解决二阶锥松弛定位中的凸包问题。与此同时,文中还给出了新增惩罚项的选取准则;再次,将松弛后的模型转换成二阶锥形式进行求解;最后用二阶锥松弛算法的估计值作为初始值进行泰勒迭代,进一步提高估值精度。仿真结果表明本文算法有效,可以对凸包外的目标实现高精度定位,其RMSE曲线逼近克拉美罗下限。

Since the second order cone relaxation algorithm cannot locate the target, which is out of the convex hull of the problem. In this paper, improved TDOA location second order cone relaxation and Taylor series expansion algorithm can be based on. First of all, the weighted least squares model of TDOA is given in the line of sight conditions with receiving station location information without error; secondly, causes a brief analysis of the convex hull, and puts forward the solution, that is taking the original non convex optimization model into a convex optimization model of relaxation, relaxation of the equality constraints adding a new penalty term based on traditional second order cone relaxation algorithm. In order to solve the convex hull problem for second order cone relaxation, it should make the constraint relaxation a further approximation of the original problem constraints At the same time, the criterion to choose the new penalty term is given in this paper; thirdly, the problem can be solved after the relaxation model turns into second-order cone form; finally, an estimated value of second order cone relaxation algorithm is used as the initial value of Taylor iteration to further improve the precision of estimates. The simulation results show that the algorithm is effective, which can achieve high precision positioning of the convex hull of target, and its RMSE curve approaching the CRB bound.