采用频率测量实现目标定位具有成本低、可靠性高的特点,仅利用到达频率差(frequency difference of arrival,FDOA)测量,提出了一种静态目标位置的精确定位方法.针对所建立的频率测量方程的高度非线性这一问题,通过引入辅助变量,将其转化为矩阵形式的伪线性方程;然后利用半正定松弛(semi-definite relaxation,SDR)方法将非凸的加权最小二乘(weighted least square,WLS)问题松弛为半正定规划(semi-definite programming,SDP)问题,从而进一步精确估计未知变量;最后对所提出方法的均方根误差(root-mean-square error,RMSE)进行了分析,以验证其性能.仿真结果表明,在较低的高斯噪声水平下,所采用的半正定松弛方法的性能能够达到克拉美罗下界(Cramer-Rao lower bound,CRLB),且该算法对几何形状具有较高的鲁棒性;此外,在使用较少数量的传感器时,其RMSE性能要优于两阶段加权最小二乘(two-stage weighted least square,TSWLS)法.
Target localization method based on semi-definite relaxation with frequency difference of arrival
The use of frequency measurements to achieve target positioning is characterized by low cost and high reli-ability.Using only frequency difference of arrival(FDOA)measurements,a precise localization method for static tar-get position was proposed.To address the highly nonlinear of the established frequency measurement equation,it was transformed into a pseudo-linear equation in matrix form by introducing auxiliary variables.Then the non-convex weighted least squares(WLS)problem was relaxed into a semi-definite programming(SDP)problem by using the semi-definite relaxation(SDR)method,so as to further accurately estimate the position of unknown variables.Fi-nally,the root mean square error(RMSE)of the proposed method was analyzed to verify its performance.The simula-tion results show that the performance of the adopted semi-definite relaxation method is able to reach the Cramer-Rao lower bound(CRLB)at lower Gaussian noise levels and the algorithm is highly robust to geometry.In addition,its RMSE performance is better than that of the two-stage weighted least square(TSWLS)method for a smaller number of sensors.
frequency measurementfrequency difference of arrivalsemi-definite relaxationsemi-definite program-mingstatic target positioning
万方数据
维普
