一种线性校正到达时间差定位算法

针对到达时间差(TDOA)定位中出现的非线性估计问题，该文提出一种线性校正TDOA定位算法。首先将高度非线性的TDOA定位方程组转化为一组关于辐射源位置的伪线性方程，利用加权最小二乘(WLS)估计进行初始求解；然后在此基础上通过一阶泰勒级数展开把伪线性方程组转化为关于估计偏差的线性加权最小二乘问题并进行求解，分析了所提算法在测量误差较小时的有效性。最后提出了一种基于加权最小二乘估计的恒加速度运动辐射源的定位方法，相应的估计性能在测量误差较小时也接近克拉美罗界(CRLB)。计算机仿真结果验证了该算法的有效性。

A Linear-correction Based on Time Difference of Arrival Localization Algorithm

A novel Time Differences Of Arrival (TDOA) localization algorithm based on linear-correction is proposed to address the nonlinear problem of TDOA positioning. Firstly, the proposed algorithm reformulates the highly nonlinear TDOA equations into a set of pseudo-linear ones and the Weighted Least Squares (WLS) estimator is used to obtain the initial emitter position estimation. Then a linear weighted least squares problem with respect to the estimation bias is formulated through utilizing first-order Taylor-series expansion to the pseudo-linear equations. The effectiveness of the proposed method is theoretically analyzed under small noise postulation. Finally, the extension to the general case of moving emitter with constant acceleration localization scenario is also presented and the corresponding estimation accuracy can achieve the Cramer-Rao Lower Bound (CRLB) as well. Computer simulation results demonstrate the effectiveness of the proposed algorithm.