最小二乘逐步、序列推估的实现与应用分析

Realization and Application of Least Square Stepwise Estimation and Sequential Estimation

在不考虑系统性参数的条件下,利用两步推估的基本思想,通过推导三步推估、四步推估归纳出逐步推估的通用表达公式,并在理论上证明了逐步推估与一般推估的等价性。实际算例表明,在观测值总个数3 700以内,六步推估在不同的观测值分组情况下均取得最好的计算效果,其计算结果不仅准确且计算效率提高了至少8倍。对于逐步推估的特殊情况——序列推估进行了应用分析,实际算例表明,序列推估的计算效率较一般推估、逐步推估降低很多。

Based on mathematical induction ,the general expression of stepwise estimation is established. In order to verify the performance of stepwise estimation, 100 unsurveyed gravity anomaly are estimated by known airborne gravity anomaly using three-step estimation, four-step estimation, five-step estimation, and six-step estimation, respectively. The results show that the six-step estimation gives the best results and its computation efficiency is increased by at least 8 times in three cases （observation quantities is I 133,2 636,3 686）, respectively. At the same time ,the six-step estimation is also the inflexion of the stepwise es- timation. In the same case as stepwise estimation, the results of sequential estimation is identical to the stepwise estimation. But the computation efficiency is much lower than that of the common least square collocation. The main reason is that a lot of circulation computation decreases the efficiency of the algorithm although there are not more inversion operation in the program. The conclusion can be made that the stepwise estimation is recommended in practice and the sequential estimation should be carefully used.