Detection performance analysis of an ultrasonic presence sensor

An ultrasonic sensor that employs moving target processing based on differential echo processing and occupant tracking is considered for indoor occupant presence detection. We present a simple statistical model to analyze the presence detection performance of such a sensor. The probability distributions of the differential power signal are first obtained under vacancy and occupancy conditions. We then study the influence of occupant tracking and derive an upper bound on the probability of false alarm. Experimental data is used to verify that the presented analytical statistical models match actual distributions of the differential power.