Identification of Multi-sinusoidal Signals with Direct Frequency Estimation: An Adaptive Observer Approach

This paper addresses the problem of estimating the frequencies, amplitudes and phases of the n sinusoidal components of a possibly biased multi-sinusoidal signal. The proposed adaptive observer allows the direct adaptation of the frequency estimates with a relatively low dynamic order 3n + 1 (3n for an unbiased signal). The stability analysis proves the global exponential convergence of the estimation error and the robustness to additive norm-bounded measurement perturbations.