Kernel-Based Impulse Response Estimation With Prior DC Gain Using Built-In Self-Scaling Technique

Abstract

A method is proposed for kernel-based impulse response estimation incorporating the prior dc gain by extending the standard Bayesian formulation to the unconstrained least squares framework. It has a key feature of built-in self-scaling (BS) first with respect to the reliability of the measurements and second with respect to the number of measurements. The proposed technique is able to achieve, in general, higher estimation accuracy and lower uncertainty when compared with the standard kernel-based formulation and a method which first estimates the step response and then constructs the impulse response of the system. This BS approach has a further advantage of being computationally efficient, since it does not introduce additional hyperparameters for tuning. An application on a real hot air blower illustrates that the proposed approach is feasible for practical implementation. Trends related to error and uncertainty with respect to data length and noise level are also presented for the first time to analyze the efficacy of the proposed method in comparison with the other methods, thus enhancing the significance of the work to the measurement community.