Abstract-In this paper, the problem of intrusion detection using passive infrared sensors (PIR) is investigated. We study the output PIR signal in the light of the intruder's trajectory and the geometry of the sensor's field of view (FOV) and propose an inverse-square law that describes the relation of incident heat flux to the distance. The signal is modeled by a sum of exponentially modulated sinusoids. Consequently, the intrusion detection is formulated as a hypothesis testing problem and we propose an exponentially windowed periodogram (EWP) detector, which is also able to detect the direction of movement. The simulation results shows the superior performance of the EWP detector when compared to conventional detectors such as the traditional periodogram detector and the energy detector over large distances. Furthermore, results show nearly 100% correct detection of the direction of movement.