My next answer does not include a specific implementation, and my experience does not include robotics. (I am a machine learning researcher, NLP, Field AI). However, I believe that my proposal for insufficient detail would be useful because your problem remains at a general level.
SLAM is one of the most famous areas that study how to estimate the location of consecutive robots according to sensor motors. In the field, there are many studies to estimate the location of robots according to sensor engines.
Researchers have studied SLAM methods for various specific situations, for example, in a slippery floor and in a complex room with shapes or with a noisy sensor, etc. I think your current settings are slightly less specific than in those studies.
So, if I were you, I would start by trying to use the standard SLAM method. I would pick up some popular and general methods from the SLAM tutorial and look for open source software that implements these methods.
As far as I know, Particle Filter (PF) is one of the most popular and successful methods in the SLAM field. PF is the extended Kalman filter dispersion (KF). PF is very easy to implement. Math is much simpler than KF. I think PF is worth a try in your situation.
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