Discrete EKF with pairwise Time Correlated Measurement Noise for Image-Aided Inertial Integrated Navigation

Abstract

ABSTRACT:An image-aided inertial navigation implies that the errors of an inertial navigator are estimated via the Kalman filter using the aiding measurements derived from images. The standard Kalman filter runs under the assumption that the process noise vector and measurement noise vector are white, i.e. independent and normally distributed with zero means. However, this does not hold in the image-aided inertial navigation. In the image-aided inertial integrated navigation, the relative positions from optic-flow egomotion estimation or visual odometry are pairwise correlated in terms of time. It is well-known that the solution of the standard Kalman filter becomes suboptimal if the measurements are colored or time-correlated. Usually, a shaping filter is used to model timecorrelated errors. However, the commonly used shaping filter assume that the measurement noise vector at epoch k is not only correlated with the one from epoch 1  k but also with the ones before epoch 1  k . The shaping filter presented in this paper uses Cholesky factors under the assumption that the measurement noise vector is pairwise time-correlated i.e. the measurement noise are only correlated with the ones from previous epoch. Simulation results show that the new algorithm performs better than the existing algorithms and is optimal.

Camera auto-calibration in GPS/INS/stereo camera integrated kinematic positioning and navigation system

“…An image-aided inertial navigation system (IA-INS) implies that the errors of an inertial navigator are estimated via the Kalman filter using measurements derived from images. The image-based navigation algorithms, such as visual odometry (VO) (Konolige et al 2011;Scaramuzza and Fraundorfer 2011;Gopaul et al 2014Gopaul et al , 2015 or visual Simultaneous Localization and Mapping (SLAM) (Durrant-Whyte and Bailey 2006; Williams and Reid 2010;Lategahn et al 2011;Alcantarilla et al 2012), usually assume that a camera system is calibrated prior to its use and the calibration parameters do not change over time. The internal camera parameters (focal length, principal point and lens distortion) and the external camera parameters (baseline and relative orientation between cameras, lever-arms and bore-sight angles with respect to the inertial measurement unit (IMU)) are required to relate the image coordinates with the object coordinates in the scene.…”

Multi-frame Visual Odometry in Image-Aided Inertial Navigation System

“…its diagonal and off-diagonal block matrices are non-zero. Therefore, the block matrices in C epochwise can be obtained sequentially as described in [4]. Matrix C is a lower triangular matrix.…”