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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
Journal ArticleDOI
TL;DR: In this article, the relative performance of two major EnKF methods when the forecast ensemble is non-Gaussian is investigated. But the approach is based on the stability of the filtering methods against small model violations, using the expected squared L2 distance as a measure of the deviation between the updated distributions.
Abstract: Recently various versions of ensemble Kalman filters (EnKFs) have been proposed and studied. This work concerns, in a mathematically rigorous manner, the relative performance of two major versions of EnKF when the forecast ensemble is non-Gaussian. The approach is based on the stability of the filtering methods against small model violations, using the expected squared L2 distance as a measure of the deviation between the updated distributions. Analytical and experimental results suggest that both stochastic and deterministic EnKFs are sensitive to the violation of the Gaussian assumption, while the stochastic filter is relatively more stable than the deterministic filter under certain circumstances, especially when there are wild outliers. These results not only agree with previous empirical studies, but also suggest a natural choice of a free parameter in the square root Kalman filter algorithm.

69 citations

Proceedings ArticleDOI
01 Nov 2006
TL;DR: In this article, the authors describe a study and experimental verification of sensorless control of Permanent Magnet Synchronous Motor using the extended Kalman filter theory using only the measurement of the motor current for on-line estimation of speed, rotor position and load torque reconstruction.
Abstract: This paper describes a study and experimental verification of sensorless control of Permanent Magnet Synchronous Motor. This structure bases on the extended Kalman filter theory using only the measurement of the motor current for on-line estimation of speed, rotor position and load torque reconstruction. Control structure such as Kalman filtering, in real time requires a very fast signal processor in special way, adapted to perform complex mathematical calculations. The Digital Signal Processors have become cheaper and their performance greater. Without using position and torque sensors, it has become possible to apply described control structure as a cost-effective solution.

68 citations

Proceedings ArticleDOI
17 Jun 2013
TL;DR: A filtering algorithm for angular quantities in nonlinear systems that is based on circular statistics and switches between three different representations of probability distributions on the circle, the wrapped normal, the von Mises, and a Dirac mixture density is presented.
Abstract: Estimation of circular quantities is a widespread problem that occurs in many tracking and control applications. Commonly used approaches such as the Kalman filter, the extended Kalman filter (EKF), and the unscented Kalman filter (UKF) do not take periodicity explicitly into account, which can result in low estimation accuracy. We present a filtering algorithm for angular quantities in nonlinear systems that is based on circular statistics. The new filter switches between three different representations of probability distributions on the circle, the wrapped normal, the von Mises, and a Dirac mixture density. It can be seen as a systematic generalization of the UKF to circular statistics. We evaluate the proposed filter in simulations and show its superiority to conventional approaches.

68 citations

Book ChapterDOI
01 Jan 2008
TL;DR: This chapter introduces the Kalman filter, providing a succinct, yet rigorous derivation thereof, which is based on the orthogonality principle, and introduces several important variants of the Kal man filter, namely various Kalman smoothers, a Kalman predictor, a nonlinear extension, and adaptation to cases of temporally correlated measurement noise.
Abstract: The Kalman filter and its variants are some of the most popular tools in statistical signal processing and estimation theory. In this chapter, we introduce the Kalman filter, providing a succinct, yet rigorous derivation thereof, which is based on the orthogonality principle. We also introduce several important variants of the Kalman filter, namely various Kalman smoothers, a Kalman predictor, a nonlinear extension (the extended Kalman filter), and adaptation to cases of temporally correlated measurement noise.

68 citations

Journal ArticleDOI
TL;DR: The Kalman Filter is compared to the Particle Filter, which does not make any assumption on the measurement noise distribution, and the reconstructed state vector is used in a feedback control loop to generate the control input of the DC motor.
Abstract: State estimation is a major problem in industrial systems. To this end, Gaussian and nonparametric filters have been developed. In this paper the Kalman Filter, which assumes Gaussian measurement noise, is compared to the Particle Filter, which does not make any assumption on the measurement noise distribution. As a case study the estimation of the state vector of a DC motor is used. The reconstructed state vector is used in a feedback control loop to generate the control input of the DC motor. In simulation tests it was observed that for a large number of particles the Particle Filter could succeed in accurately estimating the motor's state vector, but at the same time it required higher computational effort.

68 citations


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