Online Input Signal Design for Kernel-Based Impulse Response Estimation

Abstract

This article considers online input signal design for kernel-based estimation of impulse responses where the input signal is designed one bit at a time while simultaneously performing the identification. A method referred to as the direct spectrum shaping (DSS) method is proposed based on the biased Cramér–Rao lower bound, combined with detailed analysis of two popular choices of kernels. With no gradient computations, the DSS technique is able to achieve comparable accuracy but with a significant reduction in computational times by a factor of more than 370 compared with the existing Bayesian A-optimality (BAO) technique. The BAO technique, in general, attains higher estimation accuracy for oscillatory systems whereas the DSS approach is superior for systems with smoother impulse responses. The DSS method possesses further advantages of simplicity of implementation and low crest factor due to the signal being binary. An application example on a simulated curing oven in the glove manufacturing industry illustrates the potential impact of the DSS method.