This MEMS gravimeter at the University of Glasgow uses an interesting "optical shadow" detector.  And they have added tilt and temperature monitoring and compensation. They still have not calibrated all three axis, nor are they doing routine sun moon calibration, but seem to be making progress.

A High Stability Optical Shadow Sensor with Applications for Precision Accelerometers

https://arxiv.org/pdf/1711.01253.pdf

https://arxiv.org/abs/1711.01253

Field tests of a portable MEMS gravimeter

http://eprints.gla.ac.uk/151688/1/151688.pdf