Difference between revisions of "Extended Kalman Filtering on Manifolds"
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{{ProjectProposal | {{ProjectProposal | ||
|title=Extended Kalman Filtering on Manifolds | |title=Extended Kalman Filtering on Manifolds | ||
| − | |description=Extended Kalman filtering is a well known technique for the estimation of the state of a dynamical system also used in robotics for localization and mapping. However in the basic formulation it assumes all variables to live in an Euclidean space while some components may span over the non-Euclidean 2D or 3D rotation group SO(2) or SO(3). It is thus possible to write tha Extended Kalman filter to operate on Lie Groups to take into account the presence of manifolds (http://www.ethaneade.org/latex2html/lie/lie.html). We are interestend in investigation this further applying it to the EKF- | + | |image=SE3_Manifold.jpg |
| − | + | |description=Extended Kalman filtering is a well known technique for the estimation of the state of a dynamical system also used in robotics for localization and mapping. However in the basic formulation it assumes all variables to live in an Euclidean space while some components may span over the non-Euclidean 2D or 3D rotation group SO(2) or SO(3). It is thus possible to write tha Extended Kalman filter to operate on Lie Groups to take into account the presence of manifolds (http://www.ethaneade.org/latex2html/lie/lie.html). We are interestend in investigation this further applying it to the EKF-SLAM framework we have developed. | |
| − | Material | + | '''''Material:''''' |
*papers about Manifold based optimization and space representations | *papers about Manifold based optimization and space representations | ||
| − | + | *C++ framework for EKF-SLAM | |
| − | Expected outcome: | + | '''''Expected outcome:''''' |
*An extended Kalman filter which uses this new representation | *An extended Kalman filter which uses this new representation | ||
| − | + | '''''Required skills or skills to be acquired:''''' | |
| − | Required skills or skills to be acquired: | + | |
*Good mathematical background | *Good mathematical background | ||
| − | *C++ programming under Linux | + | *C++ programming under Linux |
| − | |tutor=MatteoMatteucci | + | |tutor=MatteoMatteucci;SimoneCeriani;DavideCucci |
|start=2012/04/01 | |start=2012/04/01 | ||
|studmin=1 | |studmin=1 | ||
| Line 22: | Line 21: | ||
|level=Ms | |level=Ms | ||
|type=Thesis | |type=Thesis | ||
| − | |status= | + | |status=Closed |
}} | }} | ||
Latest revision as of 01:36, 22 December 2014
| Title: | Extended Kalman Filtering on Manifolds |  Image:SE3_Manifold.jpg |
| Description: | Extended Kalman filtering is a well known technique for the estimation of the state of a dynamical system also used in robotics for localization and mapping. However in the basic formulation it assumes all variables to live in an Euclidean space while some components may span over the non-Euclidean 2D or 3D rotation group SO(2) or SO(3). It is thus possible to write tha Extended Kalman filter to operate on Lie Groups to take into account the presence of manifolds (http://www.ethaneade.org/latex2html/lie/lie.html). We are interestend in investigation this further applying it to the EKF-SLAM framework we have developed.
Material:
Expected outcome:
Required skills or skills to be acquired:
| |
| Tutor: | MatteoMatteucci (matteo.matteucci@polimi.it), SimoneCeriani (ceriani@elet.polimi.it), DavideCucci (cucci@elet.polimi.it) | |
| Start: | 2012/04/01 | |
| Students: | 1 - 2 | |
| CFU: | 20 - 20 | |
| Research Area: | Robotics | |
| Research Topic: | none | |
| Level: | Ms | |
| Type: | Thesis | |
| Status: | Closed |
