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You can put a glass shim near the sensor so it blocks the infrared radiation from the opposite side of the staircase. You can adjust it so it only triggers up to half of the way ?
Sorry for the previous comment, i didn't understand the problem properly, the issue can be solved in code, you may want to add a time period in which the sensor input is ignored to avoid that false trigger. But it's up to you to play with the timing until you find a solution that works best for you. I've gone with a 2.5s delay after the leds started turning off.
Very nice!I've also fiddled around with a lighting solution for my stairs to replace the traditional light bulb and came up with this:http://imgur.com/a/FWpA0Basically the same idea (PIR sensors and an atmega328) with a few tweaks. For me the goal was powering the thing with a 5V 1A phone charger (or a power bank), I wanted it to light up even if it was no power coming from the wall.