  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.
