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.
