This tutorial explains the Kalman Filter from Bayesian Probabilistic View and as a special case of Bayesian Filtering.
As part of this tutorial, some of the essential foundational concepts such as the notion of Latent Variable Models, Bayes' Theorem, Markov Chain, State Space Modeling, and LG-SSM are also explained.
Here is a notebook showing the application of Kalman Filter on a Synthetic Dataset. The notebook uses Tensorflow Probability. What makes TFP interesting is that it can work in batch mode and make use of accelerators like GPU & TPU.
colab.research.google.com/dri...
The link to the paper which shows full derivation of Kalman Filter equations
arxiv.org/pdf/1910.03558.pdf
Look at Section 8 (the last section). Also, pay attention to the symbols/notations (x vs z).
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