A trend filtering approach for change point detection in MOX gas sensors

Detecting changes in the response of metal oxide (MOX) gas sensors deployed in an open sampling system is a hard problem. It is relevant for applications such as gas leak detection in coal mines [1], [2] or large scale pollution monitoring [3],[4] where it is unpractical to continuously store or transfer sensor readings and reliable calibration is hard to achieve. Under these circumstances it is desirable to detect points in the signal where a change indicates a significant event, e.g. the presence of gas or a sudden change of concentration. The key idea behind the proposed change detection approach is that a change in the emission modality of a gas source appears locally as an exponential function in the response of MOX sensors due to their long response and recovery times. The proposed method interprets the sensor response by fitting piecewise exponential functions with different time constants for the response and recovery phase. The number of exponentials is determined automatically using an approximate method based on the L1-norm. This asymmetric exponential trend filtering problem is formulated as a convex optimization problem, which is particularly advantageous from the computational point of view. The algorithm is evaluated with an experimental setup where a gas source changes in intensity, compound, and mixture ratio, and it is compared against the previously proposed Generalized Likelihood Ratio (GLR) based algorithm [6]. ALGORITHM The proposed algorithm is inspired by the piecewise linear trend filtering proposed in [5]: