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Sorry, I didn't see this before now. The covariance should continue to grow regardless if your driving forward or in reverse because all motion (forward, backward, sideways etc..) introduces uncertainties and motion errors that is then integrated. So the covariance matrix of the odometric position estimate should be a strictly positive value
See section 5.2.4 here: https://github.com/Sollimann/CleanIt/blob/main/autonomy/docs/autonomous_mobile_robots.pdf
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I agree with everything you said. However, no matter what I do (except adding the abs in the derivative
The
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