Improving the performance of a MEMS-IMU system based on a false state-space model by using a fading factor adaptive Kalman filter

In this study, we introduce a novel algorithm, the low error rate adaptive fading Kalman filter (LERAFKF), designed to predict system states in the presence of uncertainty in both the system matrix and the model. The purpose of developing the LERAFKF is to address challenges arising from measurement difficulties, system parameter uncertainties, and state-space model inaccuracies. Several studies have utilized the Kalman filter (KF) and extended Kalman filter (EKF) algorithms to handle uncertainties in system parameters, corrupted measurements with unknown covariances, and incorrectly defined system modeling. Our work distinguishes itself by proposing a new approach that achieves lower error and deviation rates by combining the current Kalman estimation algorithm and the fading factor adaptive filter. To achieve this goal, we transformed the KF into an adaptive KF by introducing a forgetting factor, and the algorithm was subsequently reconfigured to calculate an optimized forgetting factor. In this study, we conducted simulations and measurements using both linear and nonlinear systems. The linear system represents the motion of an object, and the simulation involved measurements from the inertial navigation system (INS) sensor, specifically the Pololu IMU01b three-axis inertial measurement unit (IMU) sensor. We employed the SDI33 system with 9 degrees of freedom (DoF) mounted on a three-axis rotary table for the nonlinear system. This system simulates a missile as a 4th-order nonlinear system. Our findings demonstrate that the proposed LERAFKF filter outperforms KF and EKF in estimating system states, particularly in measurement-related error scenarios. Mean square error analysis further confirmed that LERAFKF exhibited the lowest error values, showcasing superior performance over KF and EKF in linear and nonlinear systems.