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.

A Kalman filter approach for accurate 3-D motion estimation from a sequence of stereo images

Abstract: This paper presents a Kalman filter approach for accurately estimating the 3-D position and orientation of a moving object from a sequence of stereo images. Emphasis is given to finding a solution for the following problem incurred by the use of a long sequence of images: the images taken from a longer distance suffer from a larger noise-to-signal ratio, which results in larger errors in 3-D reconstruction and, thereby, causes a serious degradation in motion estimation. To this end, we have derived a new set of discrete Kalman filter equations for motion estimation: (1) The measurement equation is obtained by analyzing the effect of white Gaussian noise in 2-D images on 3-D positional errors (instead of directly assigning Gaussian noise to 3-D feature points) and by incorporating an optimal 3-D reconstruction under the constraints of consistency satisfaction among 3-D feature points. (2) The state propagation equation, or the system dynamic equation, is formulated by describing the rotation between two consecutive 3-D object poses, based on quaternions and representing the error between the true rotation and the nominal rotation (obtained by 3-D reconstruction) in terms of the measurement noise in 2-D images. Furthermore, we can estimate object position from the estimation of object orientation in such a way that an object position can be directly computed once the estimation of an object orientation is obtained. Simulation results indicate that the Kalman filter equations derived in this paper represent an accurate model for 3-D motion estimation in spite of the first-order approximation used in the derivation. The accuracy of this model is demonstrated by the significant error reduction in the presence of large triangulation errors in a long sequence of images and by a shorter transition period for convergence to the true values.

An Alternative Look at the Constant-Gain Kalman Filter for State Estimation Over Erasure Channels

Abstract: This technical note studies state estimation problems subject to data loss. We consider a class of switched estimators, where missing data is replaced by optimal estimates. The considered class of estimators encompasses a number of estimation schemes proposed in the literature. We show that the estimator that minimizes the steady-state estimation error covariance within that class, is given by a constant-gain Kalman filter which was previously proposed as an alternative to the Kalman filter with intermittent observations. As a by-product of our results, we derive expressions that allow one to compare, analytically, popular suboptimal data-dropout compensation mechanisms.

Automating the implementation of Kalman filter algorithms

Abstract: autofilter is a tool that generates implementations that solve state estimation problems using Kalman filters. From a high-level, mathematics-based description of a state estimation problem, autofilter automatically generates code that computes a statistically optimal estimate using one or more of a number of well-known variants of the Kalman filter algorithm. The problem description may be given in terms of continuous or discrete, linear or nonlinear process and measurement dynamics. From this description, autofilter automates many common solution methods (e.g., linearization, discretization) and generates C or Matlab code fully automatically. autofilter surpasses toolkit-based programming approaches for Kalman filters because it requires no low-level programming skills (e.g., to "glue" together library function calls). autofilter raises the level of discourse to the mathematics of the problem at hand rather than the details of what algorithms, data structures, optimizations and so on are required to implement it. An overview of autofilter is given along with an example of its practical application to deep space attitude estimation.

A new form of the extended Kalman filter for parameter estimation in linear systems with correlated noise

Abstract: A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least-squares or Panuska's method. Convergence properties of the proposed algorithm are studied, and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed, and an extension to an estimator for randomly varying parameters is outlined.

Application of an extended Kalman filter to parameter identification of an induction motor

Abstract: An extended Kalman filter is used to identify the parameters of an induction motor using measurements of the stator voltages, currents, and rotor speed. A model of the induction motor in the state space and the Kalman filter algorithm are shown. This filter is applied to the parameter identification of an inverter-fed induction motor. A simple and practical method of setting the covariance matrices of the noises, which are important in the Kalman filter algorithm, is proposed. The starting values of the state and parameter vectors as well as the covariance matrix of the estimation error are then shown, and, finally, the results of parameter identification are shown. The results demonstrate that the filter is capable of identifying the parameters. >