Power Series for Noise Attenuation in Linear Regression Parameter Estimation ⋆
Résumé
The constant parameter identification problem is considered for a linear regression model assuming that the noise is sufficiently small comparing to the regressor. Introducing a nonlinear transformation, the estimation is performed for an extended regression dependent on the powers of the unknown parameters and the disturbance, where the influence of the latter is attenuated. It is shown that such a transformation preserves the excitation of regressor under reasonable assumptions. The quality improvement is demonstrated in numerical experiments.
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