Built-in self-scaling method for kernel-based estimation in the presence of nonlinear distortion

This paper proposes the use of perturbation signals with harmonic suppression in combination with prior steady-state gain for impulse response estimation of linear systems corrupted with nonlinear distortion. The proposed method allows the effects of nonlinear distortion on the linear estimate to be eliminated or reduced and enables the prior information to be incorporated into the estimation by a direct extension of the standard kernel-based (KB) formulation into the built-in self-scaling (BS) method. Theoretical derivation proves that the BS method can preserve the property of harmonic suppression in perturbation signals. The bias and variance in the impulse response estimate are derived theoretically and analyzed in detail. The findings confirmed that the proposed approach leads to high estimation accuracy and low uncertainty, without increasing computational complexity or measurement time. Furthermore, the method can readily extend to multi-input multi-output systems. The feasibility of the proposed technique is illustrated through a real experiment on an electronic nose, where the response is important in the food industry process automation for increasing both efficiency and reliability of distinguishing volatile compounds. The proposed approach was shown to be superior to both the standard KB estimation and a competing method utilizing information on the prior steady-state gain.