We look at the derivation of the famous Kalman filter starting with the least-squares fit.
The folder attached in this link contains the python code that goes along with the detailed tutorial (pdf is available here).
KFTutorial.ipynb in the folder is the jupyter-notebook to simulate 4 problems:
- Least-squares fit/estimation of a time-series data
- Recursive least-square estimator
- A simple 1-dimensional stochastic differential equation
- Using Kalman-Bucy filter to estimate the position of a Brownian particle in a harmonic potential
The folder also contains the LaTeX-sources files and figures in the article.
This work was done in collaboration with Vishaal Krishnan.