Experimental research in noise influence on estimation precision for polyharmonic model frequencies. Natalia Vysotska

Abstract. Parameter estimating based on measured values for polyharmonic models can be carried out by known three stage method. Its first stage is getting "balancing coefficients" (using linear LS-method); second stage - evaluating harmonic frequencies by solving so-called "frequency polynomial"; third stage - MLS-estimating of harmonic amplitudes and phases. Mentioned scheme gives absolute precise results in case of noise-free data. Noises or measuring errors distort all parameters of harmonic model. Here the most important is the precision of frequencies evaluating, which are derived of "balancing coefficients" via "frequency polynomial", because even small differences in frequencies lead to large inaccuracy in amplitudes and phases. This paper presents experimental comparison of several approximating schemes, that can be used to restore "balancing coefficients" (and so the frequencies), in order to select the most accurate one. It was stated that all examined estimating schemes are almost equivalent under low-noise conditions. One scheme, the approximation based on integrating of difference equations on sliding interval proves statistically the most precise, when noise level is raised.

Keywords. Polyharmonic model, parameter estimation, noise influence, identification.

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