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传统时差(TDOA)定位模型通过引入中间变量来得到线性方程,需要两步求解过程且该模型不适合多运动站连续定位。为此,引入无需中间变量的时差定位模型,并在此基础上提出了一种约束加权最小二乘定位算法。首先将基于该模型的时差定位问题转换为加权最小二乘问题,然后推导代入时差测量值后观测矩阵和观测向量的误差项,将其每一列表示为确定矩阵与随机时差测量噪声向量乘积的形式,并基于此推导了关于目标状态的二次约束方程,最终只需通过广义特征值分解来得到目标状态估计,并推导了该估计的解析表达式。仿真结果表明所提算法的连续定位性能逼近克拉美罗-限且所得定位解渐近无偏。
The TDOA localization model derives the linear equation by introducing intermediate variables, which requires a two-step solution and the model is not suitable for continuous positioning of multi-sports stations. Therefore, a time-varying positioning model without intermediate variables is introduced. Based on this, a constrained weighted least squares positioning algorithm is proposed. Firstly, the time-difference positioning problem based on this model is transformed into a weighted least-squares problem, and then the error term of the observation matrix and the observation vector after substituting the time difference measurement value is deduced. Each column is represented as a product of the determination matrix and the random time difference measurement noise vector Based on this, the quadratic constraint equation about the target state is deduced. Finally, the target state estimation is obtained by generalized eigenvalue decomposition and the analytical expression of the estimation is deduced. The simulation results show that the proposed algorithm has the continuous locating performance approaching the limit of clarithromycin - and the resulting localization solution is asymptotically unbiased.