Abstract:

 The affection caused by the colored noises should be taken into account to the adjustment model. As useful signals, these colored noises should be accurately identified and extracted by Fourier analysis. A continuous adjustment model is introduced with respect to the colored noises, and then it can be generalized 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 or compensated by optimally designing the observational system.