An algebraic approach for human posture estimation in the sagittal plane using accelerometer noisy signal

Our aim is to develop an algebraic approach to estimate human posture in the sagittal plane using Inertial Measurement Unit (IMU) providing accelerations and angular velocities. For this purpose, we address the issue of the estimation of the amplitude, frequency and phase of a biased and noisy sum of three sinusoidal waveform signals on a moving time horizon. The length of the time window being small, the estimation must be done within a fraction of the signal's period. The problem is solved via an algebraic method. The efficiency of our approach is illustrated by computer simulations.