Hi Peter,
If there is large amount of daylight available at your starecase, most of the infrared sensors won’t work. You can try the ultrasonic sensors. Again installing a very high voice frequency device inside your house is not a good idea. If exeposed to the ultrasonic voice 24 hours a day it may affect those who are inside the house, in many ways.
I suggest to go for PIR sensor, an IR sensor again, but it is basically a motion sensor. It compares the radiation from human body against the radiation from the wall and hence the day light won’t affect the sensitivity much. It has high sensitivity to moving human beings.
http://www.engineersgarage.com/articles/what-is-passive-infrared-pir-sensor?page=2
http://www.engineersgarage.com/contribution/pir-sensor-based-alarm-system