A model based on a harmonic oscillator describing human walking and balance with the sinusoidal trajectory of the center of mass of a subject during gait is presented. This model allows overcoming the traditional drift due to the double integration of raw acceleration data. The protocol uses a single 3D accelerometer worn at the pelvis level. The system computes the spatiotemporal gait and balance parameters when the subject is walking with or without aids. An incremental methodological approach is proposed and followed in the implementation and accuracy assessment. Eleven healthy subjects have participated to the study performing 6 trials over a fixed linear walking path at a self-selected speed. For reference, the protocol has imposed the execution of 52 steps whose length has been fixed at 60 cm. Different processing methods have been implemented and tested. The model identifies steps, walking time, and stepping frequency with an excellent reliability (absolute percentage accuracy error < 5%). When the information about the expected step length is given to the model, the percentage error in the measure of walking distance and speed is 3.25%. Without this input, this error rises to 4.95%, while for the anthropometric method is 3.68%.