Numerical Differentiation From Noisy Signals: A Kernel Regularization Method to Improve Transient-State Features for the Electronic Nose

As the simplest feature extraction, traditional hand-crafted transient-state features have been widely used in the area of electronic noses (e-noses). However, the influence of noise in the calculation of numerical differentiation leads to inaccuracy and instability in extracting these features. To tackle this issue, a novel numerical differentiation algorithm is proposed, which uses kernel-based regularization. The proposed method can provide accurate and stable transient-state features by directly estimating high-order derivatives from the noise-contaminated sensor's reading. The feature representation is a prerequisite for the good performance of e-noses. Nevertheless, it should be noted that this performance in real applications can still be affected by other factors, such as sensor drift and the disturbance of nontarget odors. These issues can be addressed by applying a framework of domain adaptation and one-class classification. The proposed method and the adopted framework are verified in a field experiment, which identifies the odor of four targets and two disturbance whiskies measured by a self-designed e-nose system. The classification accuracy with traditional features is improved from $\mathbf{71.90\%}$ to $\mathbf{86.36\%}$ , showing the good potential of the proposed method for application in the area of e-noses.