L1范数估计平差原理及抗差性分析

观测值中的粗差探测,长期以来是平差中的难题。L1范数估计作为高效抗差估计方法,具有高鲁棒性,在抗差估计领域取得了良好效果。在小样本观测情形下,利用抗差估计中一次范数最小法对观测值进行平差处理是一种高效的处理方法。为此,研究观测值中存在较大粗差时,最小二乘和L1范数估计的抗差性,并详细叙述L1范数的平差原理。试验结果表明,由于存在粗差观测,最小二乘残差不能真实反映粗差,不具有抗差性;而L1范数准确探测到异常观测值,并取得良好的抗差结果。

The detection of gross errors in observed values is a difficult problem in adjustment for a long time.L1 norm estimation,as an efficient method of robust estimation,has high robustness and has achieved good results in the field of robust estimation.In the case of small sample observation,it is an efficient method to adjust the observed values by using the minimum first order norm method of robust estimation.For this reason,the tolerance of least square and L1 norm estimators is studied when there are large gross errors in the observed values,and the adjustment principle of L1 norm is described in detail.The experimental results show that the least square residuals can not reflect the gross errors and have no tolerance due to the existence of gross errors observation.However,the L1 norm detects the abnormal values accurately and achieves good tolerance results.