GNSS/MEMS-INS Integration for Drone Navigation Using EKF on Lie Groups

This article adopts a matrix Lie group dynamic model aggregating in a single element position, velocity, attitude, and inertial measurement unit (IMU) biases. Relying on Kalman filtering on Lie groups, it develops an extended Kalman filter inbuilt into a smoother for loosely coupled integration of global navigation satellite-based system/inertial navigation system (GNSS/INS), tailored for postprocessing applications. The design is motivated by a drone-borne differential interferometric SAR (DinSAR) application requiring high-precision navigation information for short-flight missions using low-cost microelectromechanical systems (MEMS) sensors. The filter and the Rauch-Tung-Striebel (RTS) smoother are both implemented and validated. To cope with heading alignment, the article presents a Bayesian algorithm to initialize the heading value since magnetometers are useless and the INS gyroscopes lack gyro-compassing precision. Also, a statistical test addresses the practical issue of outlier rejection for GNSS detrimental data. This article uses synthetic data for comparison with classic navigation schemes based on multiplicative quaternions and Euler angles. A DinSAR imagery reconstitution field test shows better performance than state-of-the-art commercial software.