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Basis of the Kalman Filter [pdf]

239 点作者 fzliu3 个月前

11 条评论

esafak3 个月前
They also had nice tutorials on particle filters. I can&#x27;t find the one I wanted but these are close:<p><a href="https:&#x2F;&#x2F;cecas.clemson.edu&#x2F;~ahoover&#x2F;ece854&#x2F;refs&#x2F;Djuric-ParticleFilter.pdf" rel="nofollow">https:&#x2F;&#x2F;cecas.clemson.edu&#x2F;~ahoover&#x2F;ece854&#x2F;refs&#x2F;Djuric-Partic...</a><p><a href="https:&#x2F;&#x2F;eprints.lancs.ac.uk&#x2F;id&#x2F;eprint&#x2F;53537&#x2F;1&#x2F;Introduction_to_BPF_2013_IEEE_SPM.pdf" rel="nofollow">https:&#x2F;&#x2F;eprints.lancs.ac.uk&#x2F;id&#x2F;eprint&#x2F;53537&#x2F;1&#x2F;Introduction_t...</a><p><a href="https:&#x2F;&#x2F;ieeeoes.org&#x2F;wp-content&#x2F;uploads&#x2F;2021&#x2F;02&#x2F;BPF_SPMag_07.pdf" rel="nofollow">https:&#x2F;&#x2F;ieeeoes.org&#x2F;wp-content&#x2F;uploads&#x2F;2021&#x2F;02&#x2F;BPF_SPMag_07....</a>
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thundercarrot3 个月前
If Q and R are constant (as is usually the case), the gain quickly converges, such that the Kalman filter is just an exponential filter with a prediction step. For many people this is a lot easier to understand, and even matches how it is typically used, where Q and R are manually tuned until it “looks good” and never changed again. Moreover, there is just one gain to manually tune instead of multiple quantities Q and R.
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aktenlage3 个月前
It took years after I learned the Kalman Filter as a student, until I actually intuitively understood the update of the covariances. Most learning sources (including the OP) just mechanically go through the computations of the a-posterior covariance, but don&#x27;t bother with an intuition other than &quot;this is the result of multiplying two gaussians&quot;, if anything at all.<p>I wrote down a note for myself where I work this out, if anyone is interested: <a href="https:&#x2F;&#x2F;postbits.de&#x2F;kalman-measurement-update.html" rel="nofollow">https:&#x2F;&#x2F;postbits.de&#x2F;kalman-measurement-update.html</a>
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ckrapu3 个月前
I&#x27;ve seen the Kalman filter presented from a few different angles and the one that made the most sense to me was the one from a Bayesian methods class that speaks only in terms of marginal and conditional Gaussian distributions and discards a long of the control theory terminology.<p>This was one of the books we used: <a href="https:&#x2F;&#x2F;link.springer.com&#x2F;chapter&#x2F;10.1007&#x2F;978-1-4757-9365-9_4" rel="nofollow">https:&#x2F;&#x2F;link.springer.com&#x2F;chapter&#x2F;10.1007&#x2F;978-1-4757-9365-9_...</a>
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carabiner3 个月前
Kalman filter is the &quot;learn python in 24 hours&quot; for HN.
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adamnemecek3 个月前
The Kalman Filter is an instance of the Generalized Distributive Law <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Generalized_distributive_law" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Generalized_distributive_law</a><p>So is the Fast Fourier transform, Viterbi algorithm, dynamic programming, message passing and a trillion other things.
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JohnKemeny3 个月前
See also<p>Kalman Filter Explained Simply (2024, 89 comments) <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39343746">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39343746</a><p>A non-mathematical introduction to Kalman filters for programmers (2023, 97 comments) <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=36971975">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=36971975</a>
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lawrenceyan3 个月前
In the realm of autonomous vehicles, early sensor fusion systems relied heavily on the usage of Kalman Filters for perception.<p>The state of the art has now been supplanted by large deep learning models in the present day, primarily relying on end-to-end trained Transformer networks.<p>This may be familiar to you in the context of LLMs which have recently become popular, but they were actually first successfully utilized in autonomous vehicles (invented by researchers at Google and implemented in production at Waymo almost immediately).
chubs3 个月前
As a developer I always found these maths-first approaches to Kalman filters impenetrable (I guess that betrays my lack of knowledge, I dare cast no aspersions on the quality of these explanations!). However, if like me, it helps with the learning curve to implement it first, here&#x27;s a 1-dimensional version simplified from my blog:<p><pre><code> function transpose(a) { return a } &#x2F;&#x2F; 1x1 matrix eg a single value. function invert(a) { return 1&#x2F;a } const qExternalNoiseVariance = 0.1 const rMeasurementNoiseVariance = 0.1 const fStateTransition = 1 let pStateError = 1 let xCurrentState = rawDataArray[0] for (const zMeasurement in rawDataArray) { const xPredicted = fStateTransition * xCurrentState const pPredicted = fStateTransition * pStateError * transpose(fStateTransition) + qExternalNoiseVariance const kKalmanGain = pPredicted * invert(pPredicted + rMeasurementNoiseVariance) pStateError = pPredicted - kKalmanGain * pPredicted xCurrentState = xPredicted + kKalmanGain * (zMeasurement - xPredicted) &#x2F;&#x2F; Output! } </code></pre> <a href="https:&#x2F;&#x2F;www.splinter.com.au&#x2F;2023&#x2F;12&#x2F;14&#x2F;the-kalman-filter-for-programmers&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.splinter.com.au&#x2F;2023&#x2F;12&#x2F;14&#x2F;the-kalman-filter-for...</a>
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kombine3 个月前
I find this lecture series give a good introduction on Bayesian theory of filtering: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=pVyltJnXlAI&amp;list=PLTD_k0sZVYFqjFDkJV8GE2EwfxNK59fJY&amp;index=12" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=pVyltJnXlAI&amp;list=PLTD_k0sZVY...</a>
pandemic_region3 个月前
For the lesser developer gods here, can someone give an example of a real life business case where (s)he has effectively used this? Explain like you&#x27;re talking to a guy who has done CRUD most of his life.
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