A universal two-way approach for estimating unknown frequencies for unknown number of sinusoids in a signal based on eigenspace analysis of Hankel matrix

We develop a novel approach to estimate the \(n\) unknown constituent frequencies of a noiseless signal that comprises of unknown number, \(n\), of sinusoids of unknown phases and unknown amplitudes. The new two-way approach uses two constraints to accurately estimate the unknown frequencies of the sinusoidal components in a signal. The new approach serves as a verification test for the estimated unknown frequencies through the estimated count of the unknown number of frequencies. The Hankel matrix, of the time domain samples of the signal, is used as a basis for further analysis in the Pisarenko harmonic decomposition. The new constraints, the existence factor and the component factor, have been introduced in the methodology based on the relationships between the components of the sinusoidal signal and the eigenspace of the Hankel matrix. The performance of the developed approach has been tested to correctly estimate any number of frequencies within a signal with or without a fixed unknown bias. The method has also been tested to accurately estimate the very closely spaced low frequencies.