In this paper, an adaptive, autocovariance-based event detection algorithm is proposed, which can be used with micro-electro-mechanical systems (MEMS) accelerometer sensors to build inexpensive and power efficient event detectors. The algorithm works well with low signal-to-noise ratio input signals, and its computational complexity is very low, allowing its utilization on inexpensive low-end embedded sensor devices. The proposed algorithm decreases its energy consumption by lowering its duty cycle, as much as the event to be detected allows it. The performance of the algorithm is tested and compared to the conventional filter-based approach. The comparison was performed in an application where illegal entering of vehicles into restricted areas was detected.