Real-time angle estimation in IMU sensors: An adaptive Kalman filter approach with forgetting factor

In recent years, the applications of Inertial Measurement Unit (IMU) sensors have witnessed significant growth across multiple fields. However, challenges regarding angle estimation using these sensors have emerged, primarily because of the lack of accuracy in accelerometer-based dynamic motion measurements and the associated bias and error accumulation when combined with gyroscope integration. Consequently, the Kalman filter has become a popular choice for addressing these issues, as it enables the sensor to operate dynamically. Despite its widespread use, the Kalman filter requires precise noise statistics estimation for optimal noise cancellation. To accommodate this requirement, adaptive Kalman filter algorithms have been developed for estimating zero-mean Gaussian process matrix ($Q$) and measurement matrix ($R$) variances. This study introduces a real-time adaptive approach that employs a forgetting factor to precisely estimate roll and pitch angles in a 6-axis IMU. The study’s novelty lies in its algorithm, which computes the forgetting factor based on the estimation error of the last samples in the sequence. Experimental results for roll angle indicate that, in response to a step change signal, this method achieves a 54%, 39%, and 70% reduction in RMS error relative to the raw sensor data, traditional Kalman filter, and a hybrid adaptive method, respectively. Moreover, this technique exhibits significant improvements in both fixed and sinusoidal conditions for roll and pitch angles, successfully carrying out tasks within required timescales without failures related to computation time.