Quality Assessment of Parametric Spectrum Estimation Using Kalman Filter

Spectral analysis of signals is fundamental to understanding their nature. The discovery of a Fast Fourier Transform algorithm, although groundbreaking, did not solve all the issues of frequency analysis. The main problems with FFT-based methods are: sensitivity to noise, frequency resolution vs. sample amount trade-off, spectral leakage for burst signals, and spectrum peak localization. In order to address these problems, parametric methods were developed. In this paper, we formulate the problem of spectral estimation as an exercise in system identification. The solution is found using a linear Kalman filter (KF) under the assumption that the signal is stationary during the estimated time window. To our knowledge, the Kalman filter has not yet been applied to the estimation of AR filter coefficients for spectral analysis. The quality of the proposed estimator was investigated and its performance was compared with popular methods of spectral analysis.