Approaches for improvement of reliability of the Prony’s method computation

Abstract

Abstract Parametric spectral analysis methods such as the Prony’s method can estimate the frequencies and amplitudes of a signal, conforming to their model, with great precision. At the same time, the addition of noise to the signal can lead to a complete model breakdown which leads to erroneous parameter values. This is especially true for the impulse noise. The article explores several possible algorithms which can be applied to the Prony’s method in order to refine the results and make them more noise resistant. Such algorithms include signal segmentation methods where the results of each segment processing influence the final estimate as well as the conceptually related method of point skipping. An approach based on the use of non-Euclidean norms as a measure of the linear algebraic equation system’s solution quality is developed and tested. Initially, the methods are applied to model digital signals, comprised of harmonic components with varying complex frequencies and amplitudes. Additive white Gaussian and impulse noise is added to the model signals. The results are then applied to the noisy results of a real-life synthetic aperture synthesis experiment obtained in the intermediate zone of radiation.