Kernel-Based Impulse Response Estimation Using Perturbation Signals With Harmonic Suppression

This letter proposes the use of perturbation signals with harmonic suppression for kernel-based (KB) impulse response estimation of the underlying linear dynamics of a system corrupted by nonlinear distortion. In particular, signals with harmonic multiples of two suppressed can eliminate the effects of even order nonlinear distortion on the linear estimate, whereas signals with harmonic multiples of two and three suppressed can further reduce the effects of odd order nonlinear distortion, significantly improving the estimation accuracy. It is shown that the KB formulation effectively avoids the lack of persistency of excitation problem encountered in the classical least squares when such signals are applied, thus allowing a shorter experimentation time. An application on an electronic nose achieves a drastic reduction in the output mean square error by a factor of 9.2 through the utilization of a signal with harmonic suppression.