Estimation of polyharmonic signal parameters

Abstract

A new algorithm was proposed to estimate all parameters of the polyharmonic signal such as frequencies, amplitudes, phases, and shifts. Exponential convergence to zero of the errors of estimating the desired parameters was shown. The algorithm features noise-immunity to additive noise in the measurement channel. The dynamic dimensionality of the estimation algorithm is 3k, where k is the number of harmonics,

Improved Transients in Multiple Frequencies Estimation via Dynamic Regressor Extension and Mixing

“…Sketch of the proof. The proof of Proposition 1 follows the proof given in [16]. Substituting (6), it is easy to show that the estimation errorθ(t) obeys the following differential equatioṅ…”

“…In this section we consider a multiple frequencies estimation method, proposed in [14] and further extended in [15], [16]. This method is based on State-Variable Filter (SVF) approach, see [17], [18].…”

Relaxation for online frequency estimator of bias‐affected damped sinusoidal signals based on Dynamic Regressor Extension and Mixing

“…An estimation convergence condition for (21) with scalar regressor and parameter is more straightforward than for original regression model (5). The standard gradient method can be used for identification 33 of the obtained models .̂l…”

“…The key step of the proposed relaxation is to apply DREM to the original linear regression model (5). After that, we obtain two separate first-order linear regressions.…”

Identification of multi-sinusoidal signals with direct frequency estimation: An adaptive observer approach

“…The dynamic order of the adaptive observers is further reduced in [23], [31] and [14], resulting in estimators of dimension 3n for unbiased signals and (3n + 1) th -order if the bias is considered. In the more recent contributions [4] and [26] the dimension of the adaptive system is further reduced to 3n th for a biased multi-sinusoidal signal. While dimensionality reduction is an important aspect to decrease the complexity of the adaptive observer, consistent effort has been devoted also to increase the robustness of the algorithm in facing saturated signals or unstructured measurement perturbations.…”