针对利用最小二乘配置处理多波束测深数据,存在二次曲面数学模型通常无法精确表征海底地形的整体变化趋势以及观测数据存在粗差或异常点时,常规方法给出的协方差函数不能精确表征其统计特性的问题,本文提出了一种抗差最小二乘配置迭代解法.该方法首先进行协方差函数和观测值方差阵初始化,以多面函数拟合趋势项,然后应用等价权抗差估计并通过迭代计算,最终给出稳健的协方差函数参数解及最小二乘配置解.利用本文提出的方法及传统的方法处理实测的多波束测深数据,试验结果表明,相比于传统的方法,本文提出的方法能够较好地表征海底地形的整体变化趋势,一定程度上克服了多波束测深数据中粗差或异常点的影响.相比于传统的抗差方法,本文方法更为有效地识别出测深数据中异常点,推估效果较好,具有稳健性.%In the process of dealing with multi-beam bathymetry data by least squares collocation,the quadric curved mathematical modelof trend term can not express accurately the whole variation trend of seafloor topography in general.Moreover,the covariance function estimated by general method is incapable of accurately expressing statistical characteristics with the multi-beam bathymetry data contains gross errors or outliers.So the iterative algorithm of robust least squares collocation is proposed in this paper.Firstly,the initialweight matrix of observations and the initial parameters of covariance function are both given in this method,then the trend term is fitted by polyhedral function and equivalent weights scheme is applied into robust estimation in this method.Finally,the robust parameters of covariance function and solutions of least squares collocation are iteratively calculated.The experimental results show that the method proposed in this paper can express well the whole variation trend of seafloor topography and overcome the effect of gross error or outlier in multi-beam bathymetry data to a certain extent. Compared with the conventional robust method,the proposed method in this paper more effectively probes the outliers in bathymetry data with the robust and better predicted results.
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