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Bayesian spectrum estimation of unevenly sampled nonstationary data

Spectral estimation methods typically assume stationarity and uniform spacing between samples of data. The non-stationarity of real data is usually accommodated by windowing methods, while the lack of uniformly-spaced samples is typically addressed by methods that “fill in” the data in some way. This paper presents a new approach to both of these problems: We use a non-stationary Kalman filter within a Bayesian framework to jointly estimate all spectral coefficients instantaneously. The new method works regardless of how the signal samples are spaced. We illustrate the method on several data sets, showing that it provides more accurate estimation than the Lomb-Scargle method and several classical spectral estimation methods.