Vision-only Terrain Referenced Navigation and Uncertainty Analysis for Unmanned Aircraft

Abstract

A vision-only navigation system is addressed for autonomous navigation of unmanned aircraft with monocular camera as the only sensor. Typical vision-based navigation algorithms blend inertial navigation data with vision measurements and other available information to estimate vehicle's position. In this paper, however, we propose an approach that replaces the inertial navigation system by a translational motion estimate obtained by the camera. This method shares a concept of terrain referenced navigation in that the height measurements by camera are compared to terrain data to construct an observation model. The particle filter based on Bayesian tracking is employed to combine the translation estimate and measured heights of feature points which contain unknown correlation. Furthermore, uncertainty analysis for the proposed navigation scheme is addressed. Numerical simulations are conducted to verify the feasibility of the proposed method. Nomenclature 01 R = rotation of camera between time instances 0 t and 1 t 01 T = translation of camera between time instances 0 t and 1 t 0 ( ) i t p = set of feature points in an image at time instance 0 t P = reconstructed 3D point on ground L x = error covariance matrix of pixel coordinates H X = jacobian matrix of homography matrix with respect to pixel coordinates H L = error covariance matrix of homography matrix T L = error covariance matrix of camera translation R X = jacobian matrix of rotation matrix with respect to euler angles

Vision-based navigation for unmanned aircraft using ground feature points and terrain elevation data

“…where C is a normalizing constant and P d is the sum of elevation difference of each feature point. The above equation becomes the observation model using information of the DEM to update position and attitude of the camera which corresponds to equation (10). Compared to a Gaussian model, an exponential model is generally known to have heavier tails and tends to produce more robust estimation results.…”

“…It is computed from a set of eight or more point matches in two calibrated cameras. The term eightpoint algorithm, as a generalization of homography geometry used in the previous works, [10][11][12][13] is usually used to denote the method to compute the essential matrix regardless of the number of matched points. As addressed in Hartley and Sturm, 15 the eight-point algorithm has been used for many tasks such as projective transformation, scene reconstruction, image rectification, outlier detection, and stereo matching.…”

“…Some studies [6][7][8][9][10][11][12][13] utilized the visual measurements to achieve the goal of controlling error accumulation [6][7][8] used in image matching by either image sequences or lidar-based data while some studies [9][10][11][12][13] employed the DEM and visual feature points in the observation model of estimation filters. An approach proposed by Zhang et al 13 is to obtain height measurements of feature points on the ground and use them to update aircraft position estimate.…”

“…That is, the Euler angle update was executed only for yaw angle. Our previous studies, [10][11][12] motivated by Zhang's works, adopted a homography relationship between successive two images for the vision-based navigation approach. In fact, the homography cannot provide accurate solution because it considers ground as a plane.…”

“…The main objective of this article is to investigate how to eliminate the assumptions of the studies [10][11][12][13] introduced above. This article presents a new methodology of the vision-based TRN algorithm which allows us to update velocity and attitude, as well as position, by using visual measurements.…”