Estimation of the power spectral density of phase: comparison of three methods

The power spectral density (PSD) of time error (or phase) is generally modeled as a sum of power laws from f^-4 (long term instabilities) to f⁰ (short term instabilities), but other features may be observed in the PSD. In this paper, we compare three estimation methods of the frequency PSD without assuming a particular model: a classical Fourier analysis, an estimation using discrete n^th differences and an analysis based on orthogonal polynomials. After a description of these methods, their advantages and drawbacks are reviewed in terms of computation, of spectral sensitivity and of adaptability to particular cases (small number of samples, unregularly spaced data, ...). This paper also deals with the statistics of the spectral estimates. The sensitivities of these three estimation methods are compared in the case of an assumed power law model