A Decoupled Fractional-Order Kalman Filter for Accelerometer Tilt Angle Estimation

Accelerometer-based tilt angle estimation is widely used in engineering monitoring, yet random noise and outliers degrade its accuracy. Integer-order Kalman filters suppress noise, but their Markovian model assumes that the current state alone is sufficient to predict the next, neglecting the influence of earlier states on slowly varying processes. Fractional-order Kalman filters incorporate historical states into the prediction. However, the conventional formulation shares a single transition matrix between the state and covariance predictions, underestimating the prediction uncertainty, while the memory mechanism propagates gross errors across iterations. To overcome these limitations, this paper proposes a decoupled fractional-order Kalman filter (DFKF). The method assigns independent transition matrices to the state and covariance predictions, where a scaling coefficient inflates the predicted covariance to lower the prediction weight and strengthen reliance on measurements. A front-end gross-error pre-elimination strategy combining second-order differencing with adaptive peak detection is further introduced to block outlier propagation at the source before it enters the memory mechanism. Simulations under varying noise levels and gross-error conditions show that DFKF achieves a mean RMSE (Root Mean Square Error) of 0.147°, representing reductions of 17.4% and 6.4% over KF (0.178°) and FKF (0.157°), respectively, and a mean MaxAE (Maximum Absolute Error) of 0.548°, outperforming KF and FKF by 24.5% and 10.3%. Under gross-error conditions, DFKF converges in 0.012 s on average, approximately 2.8 times faster than KF and FKF, and the pre-elimination strategy restores accuracy to near-error-free levels.