About: Invariant extended Kalman filter

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The invariant extended Kalman filter (IEKF) (not to be confused with the iterated extended Kalman filter) was first introduced as a version of the extended Kalman filter (EKF) for nonlinear systems possessing symmetries (or invariances), then generalized and recast as an adaptation to Lie groups of the linear Kalman filtering theory. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations have reduced dependence on the estimated value of the state. In some cases they converge to constant values on a much bigger set of

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rdf:type	work yago:WikicatNonlinearFilters yago:Artifact100021939 yago:Device103183080 yago:Filter103339643 yago:Instrumentality103575240 yago:Object100002684 yago:PhysicalEntity100001930 yago:Whole100003553
rdfs:label	Invariant extended Kalman filter (en)
rdfs:comment	The invariant extended Kalman filter (IEKF) (not to be confused with the iterated extended Kalman filter) was first introduced as a version of the extended Kalman filter (EKF) for nonlinear systems possessing symmetries (or invariances), then generalized and recast as an adaptation to Lie groups of the linear Kalman filtering theory. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations have reduced dependence on the estimated value of the state. In some cases they converge to constant values on a much bigger set of (en)
dcterms:subject	Nonlinear filters Signal estimation
Wikipage page ID	27461950 (xsd:integer)
Wikipage revision ID	1109096672 (xsd:integer)
Link from a Wikipage to another Wikipage	Quaternion Invariant (mathematics) Lie group State space Tangent space Nonlinear filters Signal estimation Kalman filter Group action Group automorphism Kalman filtering Simultaneous localization and mapping White Gaussian noise Exponential map (Lie theory) Extended Kalman filter Symmetry-preserving filter Transformation group Inertial navigation Attitude and Heading Reference Systems
sameAs	Invariant extended Kalman filter Invariant extended Kalman filter Invariant extended Kalman filter Invariant extended Kalman filter
has abstract	The invariant extended Kalman filter (IEKF) (not to be confused with the iterated extended Kalman filter) was first introduced as a version of the extended Kalman filter (EKF) for nonlinear systems possessing symmetries (or invariances), then generalized and recast as an adaptation to Lie groups of the linear Kalman filtering theory. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations have reduced dependence on the estimated value of the state. In some cases they converge to constant values on a much bigger set of trajectories than is the case for the EKF, which results in a better convergence of the estimation. (en)
gold:hypernym	Version
prov:wasDerivedFrom	wikipedia-en:Invariant_extended_Kalman_filter?oldid=1109096672&ns=0
page length (characters) of wiki page	12304 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Invariant_extended_Kalman_filter
is Link from a Wikipage to another Wikipage of	Kalman filter Extended Kalman filter List of statistics articles Moving horizon estimation Symmetry-preserving filter
is foaf:primaryTopic of	wikipedia-en:Invariant_extended_Kalman_filter

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