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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.


Papers
More filters
Proceedings ArticleDOI
01 Jan 1975
TL;DR: In this paper, an upper triangular factorization of the filter error covariance matrix is proposed, i.e. P = UDUT, which is similar to the square root information filter.
Abstract: In this paper we describe a fresh approach to the discrete linear filtering problem. Our method involves an upper triangular factorization of the filter error covariance matrix, i.e. P = UDUT. Efficient and stable measurement updating recursions are developed for the unit upper triangular factor, U, and the diagonal factor, D. This paper treats only the parameter estimation problem; effects of mapping, inclusion of process noise and other aspects of filtering are treated in separate publications. The algorithm is surprisingly simple and, except for the fact that square roots are not involved, can be likened to square root filtering. Indeed, like the square root filter our algorithm guarantees nonnegativity of the computed covariance matrix. As in the case of the Kalman filter, our algorithm is well suited for use in real time. Attributes of our factorization update include: efficient one point at a time processing that requires little more computation than does the optimal but numerically unstable conventional Kalman measurement update algorithm; stability that compares with the square root filter and the variable dimension flexibility that is enjoyed by the square root information filter. These properties are the subject of this paper.

65 citations

Proceedings ArticleDOI
02 Aug 2010
TL;DR: In this paper, a generalized multiplicative extended Kalman filter (GMEKF) was proposed to estimate the position and velocity vectors and the orientation of a flying rigid body.
Abstract: In this paper, we propose a “Generalized Multiplicative Extended Kalman Filter” (GMEKF) to estimate the position and velocity vectors and the orientation of a flying rigid body, using measurements from lowcost Earth-fixed position and velocity, inertial and magnetic sensors. Thanks to well-chosen state and output errors, the gains and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as it is the case for the standard Multiplicative Extended Kalman Filter (MEKF). We recover thus the fundamental properties of the Kalman filter in the linear case, especially the convergence and optimality properties, for a large set of trajectories, and it should result in a better convergence of the estimation. We illustrate the good performance and the nice properties of the GMEKF on simulation and on experimental comparisons with a commercial system.

65 citations

Proceedings ArticleDOI
11 Dec 1996
TL;DR: It is shown that the latter state vector always performs better by considering the linearization error made in the extended Kalman filter applied either to a time-continuous model or a discretized model.
Abstract: A standard approach to tracking is to use the extended Kalman filter (EKF) applied to a nonlinear state-space model. We compare two conceivable choices of state variables for modeling civil aircrafts. One where Cartesian velocities are used and one where absolute velocity and heading angle are used. In both choices, Cartesian coordinates are used for position and angular velocity for turning. It is shown that the latter state vector always performs better. This is proven by considering the linearization error made in the extended Kalman filter applied either to a time-continuous model or a discretized model. The result is supported by a Monte Carlo simulation study.

65 citations

Journal ArticleDOI
TL;DR: In this article, a nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary) to solve the nonlinear estimation process without linearizing the system.
Abstract: A novel Kalman filtering technique is presented that reduces the mean-square-error (MSE) between three-dimensional (3D) actual angular velocity values and estimated ones by an order of magnitude (when compared with the MSE resulting from direct measurements) even under extremely low signal-to-noise ratio conditions. The filtering problem is nonlinear in nature because the dynamics of 3D angular motion are described by Euler's equations. This nonlinear set of differential equations state that the angular acceleration in one axis is proportional to the torque applied to that axis, and to the products of angular velocity components in the other two axes of rotation. Instead of using extended Kalman filtering techniques to solve this complex problem, the authors developed a new approach where the nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary). The first model describes the time progression of the state vector containing the linear terms, while the other characterizes the propagation of the state vector containing the nonlinearities. This makes it possible to run two interlaced discrete-linear Kalman filters simultaneously. One filter estimates the values of the state vector containing the linear terms, while the other estimates the values of the state vector containing the nonlinear terms in the system. These estimates are then recombined, solving the nonlinear estimation process without linearizing the system. Thus, the new approach takes advantage of the simplicity, computational efficiency and higher convergence speed of the linear Kalman filter form and it overcomes many of the drawbacks typical of conventional extended Kalman filtering techniques. The high performance and effectiveness of this method is demonstrated through a computer simulation case study. >

64 citations

Journal ArticleDOI
TL;DR: In this article, the problem of initializing the Kalman filter for non-stationary time series models is considered, and the same results can be obtained with a suitable initialization of the ordinary Kalman Filter.
Abstract: . The problem of initializing the Kalman filter for nonstationary time series models is considered. Ansley and Kohn have developed a ‘modified Kalman filter’ for use with nonstationary models to produce estimates from what they call a ‘transformation approach’. We show that the same results can be obtained with a suitable initialization of the ordinary Kalman filter. Assuming there are d starting values for the nonstationary series, we initialize the Kalman filter using data through time d with the transformation approach estimate of the state vector and its associated error covariance matrix at time d. We give details of the initialization for ARIMA models, ARIMA component models and dynamic linear models. We present an example to illustrate how the results may differ from results obtained under more naive initializations that have been suggested.

64 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202348
2022162
202120
20208
201914
201851