Sensor Fusion INS/GNSS based on Fuzzy Logic Adaptive Error-State Kalman filter and Unscented Kalman filter

Abstract

In this work, a Fuzzy Logic Adaptive Control (FLAC) is used to correct an Error-State Kalman Filter (ESKF) and an Unscented Kalman Filter (UKF) in a loosely coupled INS/GNSS system. The FLAC is used to prevent the Kalman Filter (KF) to diverge or to reach to a high bound solution when the Inertial Measurement Unit (IMU) presents a dominant 1/f flicker noise. First, the ESKF and UKF implementation were tuned to achieve the optimal solution when the IMU has only white noise. Secondly, a 1/f flicker noise was applied to the IMU, making both Kalman Filters implementation achieve a suboptimal solution. And thirdly, a FLAC was used to correct both ESKF and UKF when coloured noise is present. The results evidence the influence of coloured noise in the system, which makes both Kalman Filter implementations reach to a large error bound solution. After analyzing the Kalman Filter behaviour with coloured noise, a novel FLAC methodology was defined. The FLAC combines the observation of both the residuals and the states error covariance and apply the correction using the exponential weighted parameter when the error covariance presents a higher than expected value, and a process noise injection when the residuals are broader than expected. The application of the proposed FLAC methodology figures out as the best solution to deal with the coloured noise, leading to a final solution that improves the navigation accuracy for all the states, preserving the stability of the error covariance matrix. Finally, the results for ESKF are compared against the results for the UKF. It was showed that, although both Kalman filter implementations bring equivalent outcomes, the UKF is slightly less sensitive to disturbances.