Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

Kalman filter formulation of low-Level television image motion estimation

Abstract: The problem of television image motion estimation is formulated as an application of Kalman filter theory. The nonuniform image motion present in a television scene is represented as the state variable of a randomly driven difference equation. A new approach is then introduced for linearizing measurement equations that arise in low-level image velocity estimation. Kalman filter theory is applied to the problem of optimally solving the nonuniform motion estimation problem based upon the image motion model and the linearized measurement equations.

A Hybrid Particle-Ensemble Kalman Filter for Lagrangian Data Assimilation

Abstract: Lagrangian measurements from passive ocean instruments provide a useful source of data for estimating and forecasting the ocean’s state (velocity field, salinity field, etc.). However, trajectories from these instruments are often highly nonlinear, leading to difficulties with widely used data assimilation algorithms such as the ensemble Kalman filter (EnKF). Additionally, the velocity field is often modeled as a high-dimensional variable, which precludes the use of more accurate methods such as the particle filter (PF). Here, a hybrid particle–ensemble Kalman filter is developed that applies the EnKF update to the potentially high-dimensional velocity variables, and the PF update to the relatively low-dimensional, highly nonlinear drifter position variable. This algorithm is tested with twin experiments on the linear shallow water equations. In experiments with infrequent observations, the hybrid filter consistently outperformed the EnKF, both by better capturing the Bayesian posterior and by bet...

The Extended Kalman Filter as a Parameter Estimator for Linear Systems

Abstract: The extended Kalman filter is an approximate filter for nonlinear systems, based on first-order linearization. Its use for the joint parameter and state estimation problem for linear systems with unknown parameters is well known and widely spread. Here a convergence analysis of this method is given. It is shown that in general, the estimates may be biased or divergent and the causes for this are displayed. Some common special cases where convergence is guaranteed are also given. The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case. The scheme can then be interpreted as maximization of the likelihood function for the estimation problem, or as a recursive prediction error algorithm.

Invariant EKF Design for Scan Matching-aided Localization

Abstract: Localization in indoor environments is a technique which estimates the robot's pose by fusing data from onboard motion sensors with readings of the environment, in our case obtained by scan matching point clouds captured by a low-cost Kinect depth camera. We develop both an Invariant Extended Kalman Filter (IEKF)-based and a Multiplicative Extended Kalman Filter (MEKF)-based solution to this problem. The two designs are successfully validated in experiments and demonstrate the advantage of the IEKF design.