EEG is really the only solid way. After that, temperature and heart rate can give decent estimates combined with movement data (like a fitbit, which still only generally gets to about 70% agreement with EEG). Movement alone is generally a relatively poor estimate, IMO. Who knows, it may work OK for some. Try it and see. If one has really solidly regular sleep rhythms, movement plus timing may give decent results.

p.s. I hated having the phone in the bed. I kept knocking it over onto the floor in the night, waking me up and bothering my wife. The fitbit is much better in that regards (just started using it).