The consequences of a fall on an elderly person can be reduced if the accident is attended by medical personnel within the first hour. Independent elderly people often stay alone for long periods of time, being in more risk if they suffer a fall. The literature offers several approaches for detecting falls with embedded devices or smartphones using a triaxial accelerometer. Most of these approaches have not been tested with the target population or cannot be feasibly implemented in real-life conditions. In this work, we propose a fall detection methodology based on a non-linear classification feature and a Kalman filter with a periodicity detector to reduce the false positive rate. This methodology requires a sampling rate of only 25 Hz; it does not require large computations or memory and it is robust among devices. We tested our approach with the SisFall dataset achieving 99.4% of accuracy. We then validated it with a new round of simulated activities with young adults and an elderly person. Finally, we give the devices to three elderly persons for full-day validations. They continued with their normal life and the devices behaved as expected.