基于正则化约束总体最小二乘的TDOA/FDOA无源定位方法

目前在基于到达时间差(TDOA)和到达频率差(FDOA)的多站无源定位模型中,噪声的干扰、接收站和目标位置的不合理分布以及接收站的个数均会对定位模型中的系数矩阵造成影响,因此在实际的求解过程中系数矩阵可能会出现病态的问题,这在很大程度上会对定位结果产生影响。为了进一步在系数矩阵出现病态的情况下确保定位精度,提出了一种基于正则化约束总体最小二乘(RCTLS)的闭式解析法。该方法分为两步,第一步针对TDOA/FDOA定位问题建立基于RCTLS思想的定位模型,同时基于最小化均方误差的准则求解正则化参数,之后通过数学推导给出该模型的闭式解析解;第二步是利用约束条件建立关于第一步估计误差的方程并进行求解,最后利用求得的解对第一步的估计结果进行修正。仿真结果表明:本文方法通过牺牲了无偏性取得了低于两步加权最小二乘法(TSWLS)和约束总体最小二乘法(CTLS)的均方根误差(RMSE),而且在系数矩阵出现病态的情况下,其定位性能较TSWLS方法和CTLS方法也更为稳定。

Passive TDOA/FDOA location based on regularized constrained total least squares

The interference of noise, the unreasonable distribution of receivers and target, and the number of receivers all affect the coefficient matrix in the multi-station passive positioning model based on time difference of arrival (TDOA) and frequency difference of arrival (FDOA). Therefore, the coefficient matrix may be ill-conditioned in the actual solution process, which will affect the positioning accuracy to a large extent. A closed-form analytical method based on regularized constrained total least squares (RCTLS) was proposed to further improve the positioning accuracy when the coefficient matrix was ill-conditioned. The method was divided into two steps. In the first step, the positioning model based on RCTLS method was established to solve the positioning problem using TDOA and FDOA, and the regularization parameter was solved based on the criterion of minimizing mean square error. Then, the closed-form analytical solution of the model could be obtained by mathematical operation. The second step was to establish the equation of the estimation error obtained from the first step utilizing the constraint conditions, which was then solved. Finally, the obtained solution was used to modify the estimation results of the first step. Simulation results show that the root mean square error (RMSE) of the proposed method was lower than those of two-stage weighted least squares (TSWLS) and constrained total least squares (CTLS) methods through sacrificing unbiasedness, and the positioning performance was more stable than those of TSWLS and CTLS methods in the case of ill-conditioned coefficient matrix.