Planar-Based Visual Inertial Navigation: Observability Analysis and Motion Estimation

Abstract

In this paper, we address the problem of ego-motion estimation by fusing visual and inertial information. The hardware consists of an inertial measurement unit (IMU) and a monocular camera. The camera provides visual observations in the form of features on a horizontal plane. Exploiting the geometric constraint of features on the plane into visual and inertial data, we propose a novel closed form measurement model for this system. Our first contribution in this paper is an observability analysis of the proposed planar-based visual inertial navigation system (VINS). In particular, we prove that the system has only three unobservable states corresponding to global translations parallel to the plane, and rotation around the gravity vector. Hence, compared to general VINS, an advantage of using features on the horizontal plane is that the vertical translation along the normal of the plane becomes observable. As the second contribution, we present a state-space formulation for the pose estimation in the analyzed system and solve it via a modified unscented Kalman filter (UKF). Finally, the findings of the theoretical analysis and 6-DoF motion estimation are validated by simulations as well as using experimental data.

Planar-based visual inertial navigation

“…Finally, the observability analysis for the proposed model is suggested as a future work. Such analysis can reveal interesting results regarding the observable directions along the normal of the plane [9]. …”

“…This model is derived based on the standard additive error definition for the position, velocity, and biases (δ x x−x), and quaternion error for the rotational Euler angles (δ q [1 θ 2 ] ), see [9] for derivations. We define the INS error state vector as…”

“…n k = [n a n g n δ a n δ g ] is the process noise (assumed to be zero-mean wide-sense stationary) with the corresponding diagonal covariance matrix Q ∈ R 15×15 , C( Cq G ) is the estimated rotation matrix, andâ = a m −b a , see [9] for details.…”

“…Several methods have been proposed in [9], where the properties of the planar features on a horizontal plane are explicitly used to derive the system state-space model; advantages and different aspects in this visual-inertial navigation system including motion estimation, horizontal plane feature detection, and observability analysis have been also addressed in [9]. In contrast to the earlier works, the proposed method in this paper is not restricted to horizontal planar features, but rather it is generalized for arbitrary planar features.…”

Visual-Inertial Navigation: A Concise Review

“…With the similar idea, in [74,129,160], the observability of IMU-camera (monocular, RGBD) calibration was analytically studied, which shows that the extrinsic transformation between the IMU and camera is observable given generic motions. Additionally, in [161,162], the system with a downward-looking camera measuring point features from horizontal planes was shown to have the observable global z position of the sensor.…”