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Continuous glucose monitoring (CGM) devices can be very useful in diabetes management. Unfortunately, their use in online applications, e.g., for hypo/hyperalert generation, is made difficult by random noise measurement. Remarkably, the SNR of CGM data varies with the sensor and with the individual. As a consequence, approaches in which filter parameters are not allowed to adapt to the current SNR are likely to be suboptimal. In this paper, we present a new online methodology to reduce noise in CGM signals by a Kalman filter (KF), whose unknown parameters are adjusted in a given individual by a stochastically based smoothing criterion exploiting data of a burn-in interval. The performance of the new KF approach is quantitatively assessed on Monte Carlo simulations and 24 real CGM datasets. Our results are compared with those obtained by a moving-average (MA) filtering approach with fixed parameters currently in use in likely all commercial CGM devices. Results show that the new KF approach performs much better than MA. For instance, on real data, for comparable signal denoising, the delay introduced by KF is about 35% less than that obtained by MA.