Tilt Estimation from an Accelerometer and a Gyroscope: A Simulation Comparison of Complementary and Kalman Filters

Estimating the tilt angle of a body from a low-cost inertial sensor requires combining an accelerometer, which is noisy but free of drift, with a gyroscope, which is smooth but drifts. This paper compares gyroscope integration, accelerometer-only estimation, a complementary filter and a two-state Kalman filter (angle and gyroscope bias) in a simulation of a body oscillating by ±40° with a gyroscope bias of 0.5 °/s, accelerometer noise of 3° and a 2 s linear-acceleration disturbance. After tuning on separate runs, the Kalman filter gave an RMSE of 0.29° before the disturbance, against 0.39° for the complementary filter and 3.01° for the accelerometer alone. During the disturbance the Kalman filter was less affected (7.6° versus 12.2°), but afterwards it needed time to recover and had a larger error (1.78°) than the complementary filter (0.42°). The study is a one-axis simulation and the ranking depends on the chosen disturbance and tuning. This is a simulation study; all results are outputs of the deposited Python code with assumed parameters. Source code is attached.