传感器位置误差下的多辐射源时差定位代数解算法

An Algebraic Solution for TDOA Positioning of Multiple Disjoint Sources in the Presence of Sensor Position Errors

两步加权最小二乘是求解基于时差的多辐射源定位问题的经典线性方法,但是其存在额外的开方运算和矩阵求逆时存在的缺秩等问题。针对传感器位置存在误差时的多辐射源定位问题,提出一种改进的两步加权最小二乘代数解算法。所提算法可避免额外的开方运算和矩阵求逆时存在的缺秩。仿真结果表明,所提方法在传感器位置存在误差时,对多个辐射源目标的定位均方误差可以达到克拉美罗界,并且与传统两步加权最小二乘方法相比具有更低的均方误差和更高的稳健性。

The two-step weighted least squares(2WLS)algorithm is a well-known linear method in the time difference of arrival(TDOA)positioning of multiple disjoint sources.However,it suffers additional square operation and rank deficiency when solving the inverse matrix.Addressing locating multiple disjoint sources in the presence of sensor position errors,an improved 2WLS algebraic solution is proposed.Compared with the conventional 2WLS algorithm,a different linearization technique is employed in the second WLS step,by which the additional square operation and the problem of rank deficiency when solving the inverse matrix are avoided.Simulation results demonstrate that the Cramér-Rao lower bound performance for multiple disjoint sources could be achieved analytically in the presence of sensor position errors,and the solution has lower localization errors and higher robustness than the conventional 2WLS step.