Kalman: different equations for same states [closed]

Hi guys :)

I've got a very theoretical Kalman-filter-related question that and I hope that someone has an idea how to solve this: How is it possible to use 'different' state equations for the same states?

In detail: I have an RC-car and I can use a Kalman filter to fuse GPS and IMU data to an estimate of position, velocity and heading. However, the basic Kalman-equations do not account for the car dynamics! Instead, they only integrate IMU acceleration and find an optimal estimate together with orientation and GPS. Since I know the car's dynamics (e.g. it can only move longitudinally) I would like to use this information as well. Problem: I'm getting multiple equations for the same states.

It would be awesome if you have any ideas! I can't be the only one dealing with this issue but I can't find anything about it in literature. Please also let me know if my problem is not clear enough and I'll be glad to give some more information.

Thank you very much in advance for any help!

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Closed for the following reason question is off-topic or not relevant. Please see http://wiki.ros.org/Support for more details. by tfoote close date 2016-10-29 18:29:12.121030

This is not ROS releated. Please ask it on a more general purpose forum.

( 2016-10-29 18:29:06 -0500 )edit

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Short answer would be that you cannot have multiple governing equations for your system dynamics. My suggestions is to simplify your dynamics, propagate your system model using only the longitudinal acceleration sensor value from your IMU. The rest of your state can be constrained and you can simply propagate them at each time-step with no change.

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Thank you for your answer! I've spent some more time on going through Kalman theories and I think I understand it now. There are actually ways to combine different models (by weighting them differently) but they normally yield systems that are more difficult to understand.

( 2016-11-15 16:29:32 -0500 )edit

No problem! Would you mind sharing where you read this? I'm interested in learning more about weighted models in Kalman filtering :) Did you by any chance mean multi-modal Kalman filters a.k.a Gaussian Mixture models?

( 2016-11-18 16:42:09 -0500 )edit