Basis could be radar sensor, which can measure distance you are
targeting :
Learn how to use the RCWL-0516 Microwave Radar Proximity sensor to detect motion with the Arduino. Wire the sensor and we'll write a sample sketch for you to get started with the sensor.
Of course code has to accommodate when not appropriate to alarm, and
you would need to distinguish is it grandma or a stranger in vicinity. I would
assume you would also want to know if she has fallen, code + accelerometer
could accomplish that.
Because this is life support designer would want immunity from lawsuit, eg.
aggressive insurance company, so need to work under corporate umbrella......are
there federal standards that have to be incorporated.....
Regards, Dana.