Real-time oscillation-like noise filtering I am making real-time measurements, which are affected by some noise. This noise has oscillating pattern, i.e. the total signal tends to oscillate around the mean value. The examples of measurements are shown in figures below.





Filtering this noise after the signal is received is quite straitforward - we may use mean filter, for example.

What I would like to do is to implement real-time noise filtering, so that filtered signal would be close to its constant mean value.

What kind of methods of filtering could you recommend? I thought about Kalman filter, but the state model is unknown. Maybe there is something else?..

P.S. I am totally unexperienced in signal processing, please excuse me for any ignorance.

UPD: I am not considering mean filters, because the two pictures below represent only particular stages of evolution. It means that the signal evolves in an unpredictable manner in between. Mean filter usually leads to loss of information about such evolution.
Marcus and Ben have very clearly identified the problem: the signal is simply too small relative to the least significant bits (LSBs) of the "virtual machine"'s ADC. The sensible solution is to increase the signal by use of gain. From the provided plots, a signal gain around 100 would be a good starting value. Alternatively, the ADC resolution would have to be increased (> 4 more bits), so the LSBs would be smaller. In a real system, the first option would be the only feasible option, since amplifiers are relatively inexpensive and high resolution ADCs are most certainly not. Since the goal is real-time noise filtering, rather than Lazarus filtering, i.e., post-mortem reversal of fatal mis-quantization, dithering and signal averaging is ruled out.