486 was my dream. Unfortunately, my parents didn't have money for it. I bought my first PC in 1999 - a Pentium 2. I invested a lot of money in the monitor; computers become obsolete very quickly, while a monitor can serve for many years. Surprisingly, flat monitors appeared soon after...

Yeah but the first LCD screens sucked. Poor color rendition and not usable for gaming. In the early 2000s you were better off sticking with your CRT.

Thanks a lot for your detailed and valuable comments. I will definitely include them in the tutorial. If you have additional comments, I would be happy to hear them.

Interesting. It sounds like you ended up with a data-driven estimator. Did you have a chance to compare the data-driven and model-based approaches?

The map is the data model.

When doing Kalman filters, you usually have the basic form of the dynamics in the linear system, but the coefficients are usually determined experimentally (since things like mass is hard to estimate)

Additionaly, because i have direct integrator control (i.e when my target is at setpoint, my control input is 0), all I need is a proportional gain that is small enough for the system to not go unstable. And i have a physical low pass filter of the motor rotor inertia.

Classic :)

I have a chapter in my book that introduces sensor fusion as a concept. If you want to dive deeper into the sensor fusion topic, I would recommend Bar-Shalom's or Blackman's book.

Thanks for your feedback. I am thinking of writing a second volume with more advanced and less introductory topics, but I haven't decided yet. It is a serious commitment and it will take years to complete. If I take this decision, I will consider a chapter on LQG.

Small clarification: nonlinear Kalman filters are suboptimal. EKF relies on linear approximations, and UKF uses heuristic approximations.

Kalman filter is about combining uncertain measurements, and human observations could be viewed as noisy sensors. On the other hand, the standard KF assumes unbiased sensors with Gaussian noise, and I don't know if those assumptions hold for human witnesses.

That's an interesting wrinkle. How would you model the potential bias in order to neutralize it though? Or would enough measurements simply cancel out any bias (or be very likely to)?

It is always a good idea to include outliers treatment in KF algorithm to filter out weird measurements.

Ah but then you just move the error case to outlier detection.

True. It's about managing the risk rather than eliminating it. If you remove an outlier, you get a missing measurement and, as a result, higher uncertainty (error). But it is still better than keeping the outlier.

I agree that Kalman filters are not magic and that having a reasonable model is essential for good performance.

Higher sampling rates can help in some cases, especially when tracking fast dynamics or reducing measurement noise through repeated updates. However, the main strength of the Kalman filter is combining a model with noisy measurements, not necessarily relying on high sampling rates.

In practice, Kalman filters can work well even with relatively low-rate measurements, as long as the model captures the system dynamics reasonably well.

I also agree that it's often something you design into the system rather than applying as a post-processing step.

That's a fair question. My goal with the site was to make as much material available for free as possible, and the core linear Kalman filter content is indeed freely accessible.

The book goes further into topics like tuning, practical design considerations, common pitfalls, and additional examples. But there are definitely many good free resources out there, including the one you linked.