| 自适应Lp估计及其在照相天体测量中的应用 |
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| 引用本文： | 吴杰,李正心.自适应Lp估计及其在照相天体测量中的应用[J].天文学报,1996,37(2):132-139. |
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| 作者姓名： | 吴杰 李正心 |
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| 作者单位： | 中国科学院上海天文台 |
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| 摘 要： | Ｐ范分布是一个广义的测量误差分布族．众所周知的正态分布只是其ｐ＝２时的一个特例．因此，与正态分布和最小二乘估计相比，Ｐ范分布和相应的Ｌｐ估计（最小ｐ范估计）可描述和处理类型更广泛的测量误差．针对具体的测量数据，推断其实际误差之Ｐ范分布的Ｐ值，然后依此进行最或然估计，此即自适应Ｌｐ估计．本文介绍了Ｌｐ估计的性质．较为详细地讨了Ｌｐ估计的效率和自适应Ｐ值的具体求解方法；并且还针对鬼星团照相天体测量数据的归算，给出了一个实际应用的例子．结果表明，所处理的观测误差并不服从正态分布；此时自适应Ｌｐ估计的引入将带来显著优于最小二乘估计的结果．
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| 关 键 词： | P范分布，最小P范估计，自适应估计 |
ADAPTIVE L_p ESTIMATION AND ITS APPLYING IN PHOTOGRAPHIC ASTROMETRY |
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| Wu Jie, Li Zheng-xin,Wang Jia-ji.ADAPTIVE L_p ESTIMATION AND ITS APPLYING IN PHOTOGRAPHIC ASTROMETRY[J].Acta Astronomica Sinica,1996,37(2):132-139. |
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| Authors: | Wu Jie Li Zheng-xin Wang Jia-ji |
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| Institution: | Shanghai Astronomical Observatory Sinica Shanghai 200030 |
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| Abstract: | p-norm distribution is an extensive distribution family of measuring errors.The well-known normal distribution is only a special one in the family when p=2.Therefore the p-norm distribution and the Lp estimation (least p-norm estimation)can describe and treat more extensive measuring errors. For each concrete measuringdata set, first, detect the real distribution of the data by adaptive method, ascertainthe value of p, and then Carry on the Lp estimation. ms process is called adaptiveLp estimation. In this paper, the properties of Lp estimation are introduced.Also theefficiency of Lp estimation and the solution of adaptive p are discussed in detail. Atthe end, a real example of Praesepe photographic astrometry is gived. The result ofthe example indicates: the measuring errors treated do not obey normal distribution.In this case the adaptive Lp estimation will give better result than the LS estimation. |
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| Keywords: | P-norm distribution Least p-norm estimation Adaptive estimation |
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