基于约束加权最小二乘的时差频差联合定位算法

针对运动目标源定位问题，提出了一种基于约束加权最小二乘(Constrained Weighted Least-Squares, CWLS)的时差频差定位算法。该算法利用目标源到达多个接收站的时差和频差信息，对目标源的位置和速度进行估计。通过引入中间变量，将时差频差非线性方程转换成伪线性方程(中间变量与目标源位置和速度之间存在约束关系)，再对此约束条件引入拉格朗日乘子技术，将此伪线性方程的求解转化为求条件极值问题，创造性地求解了此非线性定位方程，提高了定位精度，并能满足实时性和全局收敛要求。仿真实验表明，该算法在保持相近复杂度的同时，进一步提高了定位性能，优于两步加权最小二乘算法，在噪声较高时仍然能达到克拉美罗下限。

Constrained weighted least-squares algorithm for moving source location using TDOA and FDOA measurements

By utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers, a constrained weighted least-squares (CWLS) algorithms for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates can be exploited to constrain the solution. And, on basis of convolute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly, which can allow real-time implementation as well as ensure global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least squares(WLS) approach especially for higher measurement noise level, which makes the Cramér-Rao lower bound(CRLB) at a sufficiently high noise level before the threshold effect occurs possible.