Discussion

Kalman Filter

alex_be: Author here.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.

magicalhippo: I just glossed through for now so might have missed it, but it seemed you pulled the process noise matrix Q out of a hat. I guess it's explained properly in the book but would be nice with some justification for why the entries are what they are.

renjimen: You lead with "Moreover, it is an optimal algorithm that minimizes state estimation uncertainty." By the end of the tutorial I understood what this meant, but "optimal algorithm" is a vague term I am unfamiliar with (despite using Kalman Filters in my work). It might help to expand on the term briefly before diving into the math, since IIUC it's the key characteristic of the method.

alex_be: To keep the example focused and reasonably short, I treated Q matrix as given and concentrated on building intuition around prediction and update. But you're right that this can feel like it appears out of nowhere.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.

seanhunter: Firstly I think the clarity in general is good. The one piece I think you could do with explaining early on is which pieces of what you are describing are the model of the system and which pieces are the Kalman filter. I was following along as you built the markov model of the state matrix etc and then you called those equations the Kalman filter, but I didn't think we had built a Kalman filter yet.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.

lelandbatey: Kalman filters are very cool, but when applying them you've got to know that they're not magic. I struggled to apply Kalman Filters for a toy project about ten years ago, because the thing I didn't internalize is that Kalman filters excel at offsetting low-quality data by sampling at a higher rate. You can "retroactively" apply a Kalman filter to a dataset and see some improvement, but you'll only get amazing results if you sample your very-noisy data at a much higher rate than if you were sampling at a "good enough" rate. The higher your sample rate, the better your results will be. In that way, a Kalman filter is something you want to design around, not a "fix all" for data you already have.