一种利用修正牛顿迭代的时差定位算法

针对传统基于迭代求解的时差定位算法中容易出现的发散问题，提出了一种新的基于修正牛顿迭代的时差定位算法．该算法首先利用辅助变量将非线性时差定位方程组转化为一组关于辐射源位置的伪线性方程，在此基础上把时差定位问题转化为约束加权最小二乘优化问题；然后，利用基于特征值修正的牛顿法进行定位解算，同时为了减少迭代次数，通过二次插值法对一维优化问题进行寻优求解，给出了迭代步长因子的求取过程；最后，通过仿真分析验证了所提算法的有效性．

TDOA location algorithm based on modified Newton iterations

For the divergence problem of traditional iterative process based location algorithms, a new modified Newton algorithm for the passive location from time differences of arrival (TDOA) is proposed. The proposed algorithm firstly reorganizes the nonlinear TDOA equations into pseudo-linear ones by using an auxiliary parameter, and a constrained weighted least-squares minimization is developed for the positioning problem instead of the Maximum Likelihood estimator. A modified Newton method based on eigenvalue modification is then applied to obtain the emitter position. In order to reduce the number of iterations, an appropriate iteration step size is computed via one-dimensional optimization by the quadratic interpolation method. Simulation results demonstrate the effectiveness of the proposed algorithm.