Posted by alex_be 2 hours ago
I recently updated the homepage of my Kalman Filter tutorial with a new example based on a simple radar tracking problem. The goal was to make the Kalman Filter understandable to anyone with basic knowledge of statistics and linear algebra, without requiring advanced mathematics.
The example starts with a radar measuring the distance to a moving object and gradually builds intuition around noisy measurements, prediction using a motion model, and how the Kalman Filter combines both. I also tried to keep the math minimal while still showing where the equations come from.
I would really appreciate feedback on clarity. Which parts are intuitive? Which parts are confusing? Is the math level appropriate?
If you have used Kalman Filters in practice, I would also be interested to hear whether this explanation aligns with your intuition.
The derivation of the Q matrix is a separate topic and requires additional assumptions about the motion model and noise characteristics, which would have made the example significantly longer. I cover this topic in detail in the book.
I'll consider adding a brief explanation or reference to make that step clearer. Thanks for pointing this out.
Your early explanation of the filter (as a method for estimating the state of a system under uncertainty) was great but (unless I missed it) when you introduced the equations I wasn't clear that was the filter. I hope that makes sense.
In Kalman filter theory there are two different components:
- The system model
- The Kalman filter (the algorithm)
The state transition and measurement equations belong to the system model. They describe the physics of the system and can vary from one application to another.
The Kalman filter is the algorithm that uses this model to estimate the current state and predict the future state.
I'll consider making that distinction more explicit when introducing the equations. Thanks for pointing this out.
You're right that the term can feel vague without that context. I’ll consider adding a short clarification earlier in the introduction to make this clearer before diving into the math. Thanks for the suggestion.
The challenge would be to keep it intuitive and accessible without oversimplifying. Still, it could be an interesting direction to explore.
See for example: https://rlabbe.github.io/Kalman-and-Bayesian-Filters-in-Pyth...
Is there something in this particular resource that makes it worth buying?
if you dont want to buy the book, most of the linear kalman filter stuff is available for free: https://kalmanfilter.net/kalman-filter-tutorial.html