# 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!

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