In this paper, data-driven self-calibration al- gorithms for the low-cost gas sensors are designed. The sensor measurement errors happen due to the imperfect compensation for the variation of sensor component be- havior that is caused by changing of environmental fac- tors. To calibrate the sensors, the hidden Markov model is utilized to characterize the statistical dependency between the environmental factors and the variation of sensor com- ponent behavior. Considering the time-varying property of this dependency, a time-adaptive learning framework is further designed to update the hidden Markov model so that the time-varying drift process can be better tracked over a long term. More specifically, a time-adaptive expectation maximization learning approach is proposed to efficiently update the hidden Markov model parameters. A closed form of the convergence rate of this time-adaptive learning approach is derived, which provides a theoretical guaran- tee on the time efficiency as well as the computational efficiency. The performance of the scheme is illustrated in numerical experiments utilizing real data, which shows that long-term stable calibration performance can be achieved.