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针对传统最小二乘(LS)定位算法在噪声较大时会出现有偏估计的问题。首先详细推导了传统两步最小二乘算法在时差角度联合定位场景下的理论偏差,给出了出现偏差的原因;其次对误差均值加入二次约束条件,提出一种基于时差角度联合定位的改进算法,并详细推导新算法的理论偏差以及均方误差。相比于其他加限制条件的方法,新算法能有效降低估计偏差,另外由于其不需要进行特征值分解且能得到闭式解,计算复杂度较小。仿真结果表明,新算法在保持原有均方误差(MSE)的前提下能显著降低估计偏差,其定位偏差与最大似然估计器相当。
Aiming at the traditional least square (LS) location algorithm, there is a problem of bias estimation when the noise is large. Firstly, the theoretical deviation of the traditional two-step least squares algorithm in the joint localization of time difference angle is deduced in detail, and the reason of the deviation is given. Second, the quadratic constraint condition is added to the error mean, and an improved joint positioning based on the time difference is proposed Algorithm, and derive the theoretical deviation and mean square error of the new algorithm in detail. Compared with other methods, the new algorithm can effectively reduce the estimation error. In addition, because it does not require eigenvalue decomposition and can obtain closed solutions, the computational complexity is small. Simulation results show that the new algorithm can significantly reduce the estimation error under the premise of keeping the original mean square error (MSE), and the positioning error is equal to the maximum likelihood estimator.