Could the Kalman Filter idea be applied to human witnesses to an event, where you model the person as a faulty sensor?
Understanding the Kalman filter with a simple radar example
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Re: Understanding the Kalman filter with a simple radar example
#52Author 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 measurem…
I read and enjoyed your book a few months ago when a friend recommened it to me. I've been interested in control theory for a few years, but I'm still definitely a beginner when it comes to designing good control systems and have never done it professionally. I've been in the process of writing a tutorial on how PID filters work for a much younger audience. As a result, I've been looking back at the original tutorial…
Yeah. Building things step by step often makes complex topics much easier to understand.
Re: Understanding the Kalman filter with a simple radar example
#53Could the Kalman Filter idea be applied to human witnesses to an event, where you model the person as a faulty sensor?
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.
Re: Understanding the Kalman filter with a simple radar example
#54Spending few weeks trying to understand Kalman filterm, I figured out that I need to understand all if the following: 1. Model of system 2. Internal state 3. How is optimal estimation defined 4. Covariance (statistics) Kalman filter is optimal estimation of internal state and covariance of system based on measurements so far. Kalman process/filter is mathematical solution to this problem as the system is evolving bas…
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.
Re: Understanding the Kalman filter with a simple radar example
#55When learning the Kalman filter, it clicks in place much faster when there are two or more inputs with different noise profiles. That's why it exists and that's what was its original use-case. Yet virtually all tutorials stick to single-input examples, which is really an edge case. This site is no exception.
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.
Re: Understanding the Kalman filter with a simple radar example
#56The missile knows...
Classic :)
Re: Understanding the Kalman filter with a simple radar example
#57Author 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 measurem…
Tangent but I love the accessibility menu you have. Made it super easy to tweak the page to be more readable for me
It's a free accessibility widget by Sienna. I tweaked the CSS to adapt it to the https://kalmanfilter.net/ style.
You can find it here: https://accessibility-widget.pages.dev/
Re: Understanding the Kalman filter with a simple radar example
#58I really loved this one: https://www.bzarg.com/p/how-a-kalman-filter-works-in-picture...
I feel like people overcomplicate even the "simple" explanations like the OPs and this one. Basically, a Kalman filter is part of a larger class of "estimators", which take the input data, and run additional processing on top of it to figure out the true measurement. The very basic estimator a low pass filter is also an "estimator" - it rejects high frequency noise, and gives you essentially a moving average. But is…
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?
Re: Understanding the Kalman filter with a simple radar example
#59Earlier quoted context omitted.
Yeah, I try to err on the side of not using them unless the accuracy obtained through more robust methods is just a no-go, because there are so many ways they can suddenly and irrecoverably fail if some sensor randomly produces something weird that wasn't accounted for. Which happens all the time in practice.
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.
Re: Understanding the Kalman filter with a simple radar example
#60Author 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 measurem…
I think that this was a great intro into Kalman filtering.
The one important point that I think warrants a small paragraph near the end is that the example you gave is a way of doing forecasting (estimating the future state) and nowcasting (estimating the current state), but Kalman filters can also be used retrospectively to do retrocasting (using the present data to get a better estimate of the past).
Nowcasting and retrocasting are concepts that a lot of people have trouble with. That trouble is the crux of the Kalman filter ... combining (noisy) measurements with (noisy) dead reckoning gives us (better) knowledge. For complete symmetry, it is important to point out that we can't just use old measurements to describe the past any more than we should only use current and past measurements to define our estimate of the present.