Relaxation barycentre iterative algorithm for solving parameter estimation of overdetermined distance locating equations
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摘要: 针对重心迭代法收敛速度缓慢的不足，基于残差最小步长准则，提出了一种松弛重心迭代法. 该方法依据残差最小性质，导出了松弛因子的确定公式，从而自适应调整迭代步长来提高重心迭代法的收敛效率. 松弛重心迭代法实质为最速下降法，具有迭代格式简单、无需矩阵求逆和计算海森矩阵的优点. 最后采用全球卫星导航系统（GNSS）定位数据和水下定位数据进行验证，结果表明松弛重心迭代法能够明显提高重心迭代法的收敛效率.Abstract: Based on the minimal residual criterion, a relaxtion method is proposed to improve the convergence efficiency of the barycentre method for solving the distance equations. The relaxation factor for adaptive selecting the iterative step of barycentre method is derived by the minimum residual criterion. The proposed method has the advantages of simple iterative format without the matrix inversion and to simplify the procedure without calculating the Hessian matrix. Finally, the novel method is performed to solve the data of GNSS and marine positioning examples to show its performance, and results show the numerical convergence experiments are performed to show the convergence efficiency improvment.
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表 1 单历元的BDS观测数据
PIN BDS 观测数据 原始伪距
观测值误差改正后的
伪距观测值X Y Z C01 −32336498.691170300 27035334.6172272 −530997.336384963 37581633.523 37621618.3830530 C04 −39605555.219279000 14461662.7104180 −597111.964141607 38714287.977 38625308.4036018 C03 −14694890.718294900 39484514.9430153 −1083213.045909430 37381556.109 37402904.6074830 C02 4407091.744023820 41911515.9224645 −160017.340241180 38197805.508 38332664.5088799 C10 −11409111.321746000 36904367.1362770 −17165960.237762200 39746847.555 39620859.3379616 C09 700961.084342367 24946380.9662288 34119298.890129900 36861131.133 36837362.3473803 C06 −17386842.618506700 20861890.1125707 32364939.219097600 36211192.336 36205291.5448028 
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表 2 不同算法的解算结果
算法 解算结果/m 时间/s k 高斯-牛顿法 −2704970.7611 4844895.0993 3855320.1275 0.0124 16 松弛重心迭代法 −2704970.7611 4844895.0993 3855320.1275 0.1633 1357 重心迭代法 −2704970.7611 4844895.0993 3855320.1275 0.4638 4708
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表 3 不同算法的解算结果
算法 解算结果/m 时间/s k 高斯-牛顿法 NAN NAN NAN NAN NAN 松弛重心迭代法 2438949.0219 492011.3614 2142.9263 2.1821 3297 重心迭代法 2438949.0219 492011.3614 2142.9263 132.4420 28280
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