What reasons do you have to think they are intentionally doing this? Are you afraid of harm? I really think this should be talked about with your doctor. It is possible that their same sleep pattern as yours is a coincidence.

I have learnt something in my therapy called an Evidence Checklist. I myself obsess over things and question people's intentions (in my case I am constantly thinking I am being watched and criticized). I have had some success with this.

Make two columns side by side and list off EVIDENCE YOU ARE BEING STALKED and then list off EVIDENCE YOU ARE NOT BEING STALKED. Yes it will take work but for me it has really allowed me to cope with my own fears. I encourage you to try this. At worse it won't change anything but at best it will allow you to better manage your anxiety. One thing it WILL do is allow you to better make the decision on whether you should take action like making that move.