基于泰勒加权最小二乘算法的水下TDOA/FDOA联合定位方法

针对水下复杂的定位场景中，两阶段加权最小二乘算法因为忽视噪声平方项而造成的定位不精确问题，本文提出了一种基于泰勒加权最小二乘算法的水下到达时间差和到达频率差(Time difference of arrival and frequency difference of arrival, TDOA/FDOA)联合定位方法。该方法首先通过加权最小二乘算法求解目标粗估计位置和速度；然后通过求解TDOA/FDOA测量值的泰勒展开式构造定位误差方程，用迭代的方法不断更新目标估计位置和速度；最后，当定位误差足够小或达到最大迭代次数的时候，算法停止运行并输出目标估计位置和速度。仿真表明，在噪声方差小于10分贝时，本文算法的位置和速度估计的均方根误差能够接近或约等于克拉美罗下界。 

Underwater TDOA/FDOA joint localization method based on Taylor-weighted least squares algorithm

Aiming at the problem of inaccurate localization caused by the two-stage weighted least squares algorithm ignoring the noise square term in the complex underwater localization scene, this paper proposes an underwater TDOA/FDOA joint localization method based on the Taylor-weighted least squares algorithm. This method first solves the rough estimated position and velocity of the target through the weighted least squares algorithm. Then constructs the localization error equation by solving the Taylor expansion of the TDOA /FDOA measurement values, and continuously updates the estimated position and velocity of the target by an iterative method. Finally, when the localization error is small enough or the maximum number of iterations is reached, the algorithm stops running and outputs the estimated target position and velocity. Simulation shows that when the noise variance is less than 10 decibels, the root mean square error of the position and velocity estimation of the algorithm in this paper can be close to or approximately equal to the Cramer-rao lower bound.