I am wanting to have a device (using bluetooth I expect) regularly communicate between my Android Cellphone and a very portable device (like a tag), and if the devices are separated by more then a few meters for my cellphone to alarm (it would be cool if the device would alarm as well). I'm looking for something which will trigger if the distance between devices is more then 5 meters or so.
My cellphone is a [rooted] Android device (specifically an Xiaomi Mi A1). This means it has Bluetooth 4.2 (and LE - low energy) - The device DOES NOT have NFC, and I'd prefer not to use WIFI. As I will be travelling I don't want something which relies on cellular data.
I have found a few Android programs, but they mostly seem to either have extremely bad ratings or virtually no downloads. The possible exception is MiBand software, but it is unclear if this software has the required functionality, and I don't want to buy one to find this function is missing.
I'd prefer a solution (including hardware+international shipping) to cost less then US$40, and ideally less then $25. Any hardware I need to purchase should have a last at least 3 weeks between battery changes (assuming a battery is required).