I've been and I've seen. It is a fence. A very long fence. You can't cross it with bare hands, and if you try, you will be shot.
This is not the case when dozens of bulldozers simultaneously cross the fence and many thousands of trained terrorists coming out of tunnels and cross the fence through the openings. If you don't have prior intelligence, you can't stop it.
"In addition the Moon has no atmosphere and is constantly bombarded by radiation from the Sun that causes the soil to become electrostatically charged." - You can use a magnetic or electric field to push the soil away
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...
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.
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 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.
Thanks for your feedback! Actually the KF concept is generic, but as mentioned above:
"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."
So it is right to say that the implementation of the KF is tightly coupled to the system. Getting that part right is usually the hardest step.
The tutorial actually predates ChatGPT by quite a few years (first published in 2017). Today, I do sometimes use ChatGPT to fix grammar, but I am responsible for the content and it is always mine.
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.
That's a good article. I also like the visual approach there. My goal here was a bit different. I walk through a concrete radar example step by step, and use multiple examples throughout the tutorial to build intuition and highlight common pitfalls.