Kernel-Based Impulse Response Estimation With a Priori Knowledge on the DC Gain

This letter proposes a new kernel-based system identification method which uses a priori knowledge on the DC gain (i.e., the steady state response to the unit step input) of the system in addition to the prior on the impulse response. It is not easy to encode the prior on the DC gain to prior distributions for the impulse response estimation. This letter proposes a new method which first estimates the step response and then constructs the impulse response model of the system. In particular, we divide the step response into the steady state response and its residuals, and design a prior distribution for them based on a priori knowledge on the system. The effectiveness of the proposed method is verified by detailed numerical examples from the perspectives of estimation accuracy for both the impulse response and the step response.