连续观测系统的平差模型与有色噪声补偿

摘要/Abstract

摘要：

现代测量技术多依赖于各种连续对地观测系统。有色噪声在影响参数估计的同时，还蕴含了地球科学研究所需的大量有用信息。本文讨论了连续平差模型及最小二乘解，将有限维空间中的测量平差问题推广至无穷维空间，从信号分析角度讨论了观测有色噪声的消除方法。研究表明，连续观测方程的最小二乘解可由经典最小二乘解的极限导出；有色噪声对解的影响是系统性的，然而通过合理的观测方案设计可以实现参数的无偏估计

关键词: 测量平差, 连续观测, 最小二乘, 有色噪声, Hilbert空间

Abstract:

Nowadays, surveying technique mainly relies on continuous earth observation systems. In practice, while the precision and the reliability of estimated parameters are seriously affected by colored noises, these colored noises contain a great amount of useful information to the earth science. On the one hand, the affection caused by these colored noises should be taken into account to the adjustment model, on the other hand, as useful signals these colored noises can be accurately identified and extracted by Fourier analysis. In this paper, a continuous adjustment model is introduced with respect to the colored noises, and then we generalize the traditional adjustment theory from the finite space to the infinite space so called as Hilbert space. This extension is to provide a new technique to perform the continuous observational system design, Fourier analysis as well as the parameter estimation. It shows that the Gramer’s determinant provides maximization criteria in the system optimization design as well as a rule in diagnosing the adjustment model. Related with the definition of the integral, the least squares solution of the continuous adjustment model becomes the limit of the traditional least squares solution in finite space. Moreover, the influence caused by the colored noises is systematic, but it can be eliminated by optimally designing the observational system and the observational scheme.

Key words: adjustment, continuous observation, least squares, colored noise, Hilbert space

中图分类号:

p208

薛树强杨元喜. 连续观测系统的平差模型与有色噪声补偿[J]. 测绘学报.

Xue shuqiang Yuanxi Yang. Adjustment Model and Colored Noise Reduction of Continuous Observation System[J]. Acta Geodaetica et Cartographica Sinica.

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