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

TL;DR

This paper introduces a Lie Group-based Extended Kalman Filter and Smoother for GNSS/INS integration in drone navigation, enhancing accuracy for post-processing in low-cost MEMS sensor applications, validated through synthetic and real data.

Contribution

It develops a novel Lie Group-based EKF and RTS smoother for GNSS/INS integration, including a new heading initialization algorithm and outlier rejection method, tailored for drone DinSAR applications.

Findings

Lie Group EKF outperforms traditional methods in accuracy.

The proposed approach improves DinSAR processing results.

Real data experiments confirm better performance than commercial software.

Abstract

Building upon the theory of Kalman Filtering on Lie Groups, this paper describes an Extended Kalman Filter and Smoother for Loosely Coupled Integration of GNSS/INS tailored for post-processing applications. The approach employs a dynamic model on a matrix Lie Group that aggregates position, velocity, attitude, and the IMU biases as a single element of a Lie group. The development was motivated by a drone-borne Differential Interferometric SAR (DinSAR) application, which requires high-precision navigation information for short-flight missions using low-cost MEMS sensors. The filter and the Rauch-Tung-Striebel (RTS) smoother are both implemented and validated. The paper also presents a novel algorithm to initialize the heading value as an alternative to gyro-compassing or magnetometer-based alignments. The Mahalanobis Distance and the $\chi^2$-test are employed during the filter update step to address the practical issue of outlier rejection for the GNSS measurements. The paper uses synthetic data to compare classic navigation schemes based on multiplicative quaternions and Euler angles. Finally, real data experiments demonstrate that the Kalman Filter based on Lie Groups performs better DinSAR processing than state-of-the-art commercial software.