An approach to estimation a signal composed from several unknown frequencies

The problem of estimation of a signal composed of multiple harmonic signals and its decomposition into its parameters - the frequencies, amplitudes and phases is dealt with. The existing approaches for estimation of signals with unknown frequencies are reviewed. The presented approach is an extension of estimation algorithm of one harmonic signal with a constant unknown frequency. This approach is based on the fact that a single harmonic signal can be represented as a rotating two dimensional vector thus equations of motion of a rotating vector are exploited and application of state space representation is enabled. Generalization to a signal with multiple harmonic is presented. The estimator is the State Dependent Differential Riccati Equation (SDDRE) based estimator. Simulations demonstrate the vitality of the approach.