You could try to get a passive IR detector as well. i have seen cheap ones that come with a connection for a lamp and a timer and a daylight detector.
And are suited for outdoor use.
Instead of a lamp you could connect a wall adapter that powers the ultra sonic repelling the device. And it might help to cover up the daylight connector.
Something similar as this one i bought long ago.
edit :
If you do get an passive ir detector with relay out, make sure you also have a sort of main switch inside near your door to disable the power. Otherwise, people with dogs you do want to have around are not going to be happy with you. And make sure you an ultra sonic generator with over a 100dB sound level.