System identification for output-dependent bounded noises and its application in learning personalized thermal comfort model

When the output observation noise is output-dependent, identifying the unknown system parameters becomes challenging. Traditional methods based on Mean Square Error, even the ones with corrections still have biased estimations in this case. Many practical cases such as bounded sensor, uncertainty of expression in human involved system identification, and even in physiological or biological model identification actually have this problem. In this paper, some algorithms were proposed to obtain the unbiased estimation of parameters for input-output-nonlinear but identification-linear system under output-dependent bounded noise. We utilized the truncated probability distribution to model the noise and gave the unbiased estimation algorithms of the system parameters as well as noise parameter if unknown. Asymptotic properties of the algorithms indicate that the algorithms converge to the true parameters. Besides illustrative numerical example, we also utilized the algorithm in a real world application to identify the personalized thermal comfort model using human noisy voting data. Results revealed the effectiveness and applicability of the proposed algorithms.