约束最小二乘无源定位算法的求解与分析

针对约束最小二乘无源定位算法中最优Lagrange乘数的求解问题，提出了新的计算方法。通过详细分析该定位算法的最优化问题求解过程，给出了求解最优Lagrange乘数的准确公式，同时将其转化为等价的多项式方程，并推导了相应的多项式方程系数。通过仿真实验，分析了最小二乘定位算法的性能，重点分析了最优Lagrange乘数的选取对算法性能的影响，并给出了经验选取方法，验证了所提方法的正确性和有效性。

Solution and analysis of constrained least square passive location algorithm

In order to obtain the optimal Lagrange multiplier of the constrained least square passive location algorithm, a new method is proposed. With the detail analysis of the solving process of the optimization problem, the explicit formula for solving the Lagrange multiplier is obtained. At the same time, the formula is converted to an equivalent polynomial equation, and the coefficients are deduced. With detail simulation experiments, the performance of the least square location algorithms is analyzed, and the impact of the Lagrange multiplier selection is also analyzed. Moreover, the experiential selecting method is given, and the correctness and validness of the proposed algorithm are attested.