针对基于到达时差量测的多站无源定位系统,提出了一种基于半定松弛的时差定位方程求解方法。该方法首先将 关于目标位置估计的非凸二次优化问题转换成等价的非凸半定规划问题,然后通过秩1松弛得到一个凸优化问题,最后 对松弛半定规划问题的最优解进行秩1近似,从而提取出最终的目标位置估计。计算机仿真结果表明这种松弛解法可以 有效求解目标位置。

An effective semi-definite relaxation method for source location based on the time difference of arrivals in passive location system is proposed in this paper. Firstly, it converts the original nonconvex quadratic optimization problem of source position into an equivalent nonconvex semi-definite programming problem, and then relaxes the nonconvex rank-1 constraint to obtain a convex optimization problem. Finally, it extracts a rank-1 component form the global optimum solution of relaxed semi-definite programming and serves as a good approximate of original difficult problem. The computer simulation results show that the semi-definite relaxation method can effectively solve the source localization problem.