基于最大似然估计的TDOA/FDOA无源定位偏差补偿算法

在到达时差/到达频差(TDOA/FDOA)无源定位系统中,定位问题的非线性使得定位的结果存在偏差,特别是在噪声较大或者接收站布站不合理的情况下,定位的偏差尤其显著。针对这一问题,提出了一种基于最大似然估计的偏差补偿算法。该方法分为3步:首先,利用最大似然估计器对目标的位置和速度进行求解;其次,通过利用目标定位的估计值和含噪的测量值,对目标的位置和速度偏差值进行理论分析和推导;最后,将最大似然估计解减去理论偏差值,得到经过偏差补偿的新的目标定位解。理论分析和实验仿真证明,在一定噪声的情况下,所推导的目标位置和速度的理论偏差值与实际偏差值相符,并且经过偏差补偿后的定位算法,在保持目标定位的均方根误差(RMSE)与原最大似然算法一致的情况下,目标的位置和速度偏差值远远小于原最大似然算法的偏差值,目标定位精度得到了有效的提高。

Bias compensation algorithm based on maximum likelihood estimation for passive localization using TDOA and FDOA measurements

In the time differences/frequency differences of arrival (TDOA/FDOA) passive localization system, the nonlinear nature of the localization problem creates bias to a location estimate. When the measurement noise is large and the geolocation geometry is poor, the bias of localization is significant. In order to solve the problem, a novel bias compensation localization algorithm based on maximum likelihood estimation is proposed. The algorithm locates the target in three steps. Firstly, it starts by solving the target location using the maximum likelihood estimator. Secondly, using the estimated location and noisy data measurements, the theoretical bias of the target location estimate is derived in the second step. Finally, the bias compensated result is derived by subtracting theoretical bias from the maximum likelihood solution. Theoretical analysis and actual results verify that the theoretical bias of target position and velocity matches very well with simulation when the noise is small, and the bias compensation algorithm can reduce the bias effectively while keeping the same root mean square error (RMSE) with the original maximum likelihood algorithm, meanwhile the target localization performance is improved effectively.