In the high-precision low-temperature experiments, noise immunity has long been an important issue. We consider the problem of measuring the slowly changing data in the presence of both white noise and sudden, short noise spikes. The Kalman filter is applied to attenuate the white noise and a spike detecting algorithm is applied to remove spikes resulting from the charged particles. Experimental data show that, with the Kalman filter, the RMS of the measurement noise in a 0.5 Hz bandwidth can be attenuated from 4 nK to 0.2 nK in the best case. A simple spike detecting algorithm worked effectively to remove spikes without increasing the random noise level.