基于两步最小二乘定位的偏差改进算法

Improved bias algorithm for localization using two-step least square

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。

Bias of a source location estimate using classical least square （LS） algorithm is significant when the noise is large. This paper started by deriving the theoretical bias of the time-differences-of-arrival （TDOA） and angle-of-arrival （AOA） positioning which used the classical two-step LS algorithm and found the reason which caused the bias. Then the im- proved TDOA and AOA algorithm was proposed by adding the quadratic constraints to the expectation of the error. Com- pared to other methods with constraints, the novel algorithm can reduce the bias considerably. Furthermore, because the new algorithm does not require eigenvalue decomposition and can obtain the closed-form solution, it has little computation load. Simulation shows that the new method can reduce the bias significantly and obtain the original mean-square error （MSE）. The improved algorithm is able to lower the bias to the same level as the maximum likelihood estimator.