Implicit Extended Kalman Filter Research Articles

Implicit Extended Kalman Filter for Optical Terrain Relative Navigation Using Delayed Measurements

The exploration of celestial bodies such as the Moon, Mars, or even smaller ones such as comets and asteroids, is the next frontier of space exploration. One of the most interesting and attractive purposes from the scientific point of view in this field, is the capability for a spacecraft to land on such bodies. Monocular cameras are widely adopted to perform this task due to their low cost and system complexity. Nevertheless, image-based algorithms for motion estimation range across different scales of complexities and computational loads. In this paper, a method to perform relative (or local) terrain navigation using frame-to-frame features correspondences and altimeter measurements is presented. The proposed image-based approach relies on the implementation of the implicit extended Kalman filter, which works using nonlinear dynamic models and corrections from measurements that are implicit functions of the state variables. In particular, here, the epipolar constraint, which is a geometric relationship between the feature point position vectors and the camera translation vector, is employed as the implicit measurement fused with altimeter updates. In realistic applications, the image processing routines require a certain amount of time to be executed. For this reason, the presented navigation system entails a fast cycle using altimeter measurements and a slow cycle with image-based updates. Moreover, the intrinsic delay of the feature matching execution is taken into account using a modified extrapolation method.

An Implicit UKF for Satellite Stellar Refraction Navigation System

The stellar refraction navigation is a type of autonomous celestial navigation method for satellites that uses high-accuracy star sensors to obtain the stellar refraction. The apparent height and the stellar refraction angle are two kinds of measurements for the satellite stellar refraction navigation system. A better navigation performance can be achieved by the stellar refraction angle rather than the refraction apparent height. However, the measurement model of the stellar refraction angle is an implicit function, which needs an implicit filter method. A new implicit unscented Kalman filter (UKF) method is proposed and applied to the satellite stellar refraction navigation system in this paper. The main difference between the classical UKF and the implicit UKF lies in the measurement update. First, since the implicit measurement model can be rearranged into an equation whose one side is zero, the vector of zeros is regarded as the equivalent measurement, and the difference between the predicted measurement and its true value is utilized for updating the predicted state and its covariance matrix. Second, the measurement noise and its covariance matrix are transformed based on the unscented transformation principle. In addition, the implicit UKF is compared with the implicit extended Kalman filter (IEKF), the iterative IEKF, and the UKF. Simulations show that the proposed implicit UKF method can obtain about 19.0% and 17.5% improvements in three-dimensional root mean square position estimation compared to the IEKF and the iterative IEKF, respectively. Although the navigation performance of the UKF is close to the implicit UKFs, the computational time of the implicit UKF is much shorter than the UKFs. In addition, the sensitivities of the four different Kalman filters to the star sensor's faults and the atmosphere perturbation are compared, respectively.

Online camera-gyroscope autocalibration for cell phones.

The gyroscope is playing a key role in helping estimate 3D camera rotation for various vision applications on cell phones, including video stabilization and feature tracking. Successful fusion of gyroscope and camera data requires that the camera, gyroscope, and their relative pose to be calibrated. In addition, the timestamps of gyroscope readings and video frames are usually not well synchronized. Previous paper performed camera-gyroscope calibration and synchronization offline after the entire video sequence has been captured with restrictions on the camera motion, which is unnecessarily restrictive for everyday users to run apps that directly use the gyroscope. In this paper, we propose an online method that estimates all the necessary parameters, whereas a user is capturing video. Our contributions are: 1) simultaneous online camera self-calibration and camera-gyroscope calibration based on an implicit extended Kalman filter and 2) generalization of the multiple-view coplanarity constraint on camera rotation in a rolling shutter camera model for cell phones. The proposed method is able to estimate the needed calibration and synchronization parameters online with all kinds of camera motion and can be embedded in gyro-aided applications, such as video stabilization and feature tracking. Both Monte Carlo simulation and cell phone experiments show that the proposed online calibration and synchronization method converge fast to the ground truth values.

UKF for Integrated Vision and Inertial Sensors Based on Three-View Geometry

An unscented Kalman filter (UKF) is derived for integrating vision with inertial measurements from gyros and accelerometers sensors based on three-view geometry. The main goal of the proposed method is to provide better estimations compared to the implicit extended Kalman filter introduced by Indelman . The UKF uses a selected set of points to more accurately map the probability distribution of the measurement model than the linearization of the extended Kalman filter, leading to faster convergence from inaccurate initial conditions in estimation problems. The proposed method is validated using a statistical study based on simulated navigation and synthetic images data.

Real-Time Vision-Aided Localization and Navigation Based on Three-View Geometry

A new method for vision-aided navigation based on three-view geometry is presented. The main goal of the proposed method is to provide position estimation in GPS-denied environments for vehicles equipped with a standard inertial navigation system (INS) and a single camera only, without using any a priori information. Images taken along the trajectory are stored and associated with partial navigation data. By using sets of three overlapping images and the concomitant navigation data, constraints relating the motion between the time instances of the three images are developed. These constraints include, in addition to the well-known epipolar constraints, a new constraint related to the three-view geometry of a general scene. The scale ambiguity, inherent to pure computer vision-based motion estimation techniques, is resolved by utilizing the navigation data attached to each image. The developed constraints are fused with an INS using an implicit extended Kalman filter. The new method reduces position errors in all axes to the levels present while the first two images were captured. Navigation errors in other parameters are also reduced, including velocity errors in all axes. Reduced computational resources are required compared with bundle adjustment and simultaneous localization and mapping (SLAM). The proposed method was experimentally validated using real navigation and imagery data. A statistical study based on simulated navigation and synthetic images is presented as well.