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Finite-time estimation of multiple exponentially-damped sinusoidal signals: a kernel-based approach. (English) Zbl 1429.93364

Summary: The problem of estimating the parameters of biased and exponentially-damped multi-sinusoidal signals is addressed in this paper by a finite-time identification scheme based on Volterra integral operators. These parameters are the amplitudes, frequencies, initial phase angles, damping factors and the offset. The proposed strategy entails the design of a new kind of kernel function that, compared to existing ones, allows for the identification of the initial conditions of the signal-generator system. The worst-case behavior of the proposed algorithm in the presence of bounded additive disturbances is fully characterized by input-to-state stability arguments. Numerical examples including the comparisons with some existing tools are reported to show the effectiveness of the proposed methodology.

MSC:

93E10 Estimation and detection in stochastic control theory
93B28 Operator-theoretic methods
93B35 Sensitivity (robustness)
93D25 Input-output approaches in control theory
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References:

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