Sensor fusion algorithms allow the combination of many heterogeneous data types to make sophisticated decisions. In many situations, these algorithms give increased performance such as better detectability and/or reduced false alarm rates. To achieve these benefits, typically some system or signal model is given. This work focuses on the situation where the event signal is unknown and a false alarm criterion must be met. Specifically, the case where data from multiple passive infrared (PIR) sensors are processed to detect intrusion into a room while satisfying a false alarm constraint is analyzed. The central challenge is the space of intrusion signals is unknown and we want to quantify analytically the probability of false alarm. It is shown that this quantification is possible by estimating the background noise statistics and computing the Mahalanobis distance in the frequency domain. Using the Mahalanobis distance as the decision metric, a threshold is computed to satisfy the false alarm constraint.