Kalman Filter textbook using Ipython Notebook. This book takes a minimally mathematical approach, focusing on building intuition and experience, not formal proofs. Includes Kalman filters, Extended Kalman filters, unscented filters, and more. Includes exercises with solutions.
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@rlabbe I just started working through the Jupyter notebooks. Your intuitive approach to the subject matter is very refreshing. I do have a question/observation about the material in Chapter 3... I find the discussion of the product vs sum of "Gaussians" a bit confusing. It seems that you are discussing the sum of Gaussian random "variables" and the product of Gaussian probability "distributions". The sum of two independent Gaussian random variables is also Gaussian-distributed. The product of two Gaussian random variables is not, in general, Gaussian-distributed.
Having now made it through Chapter 4... I think the source of the confusion is that, in both cases, we are really talking about operations on Gaussian "distributions" rather than random "variables" . The mathematical operation involved in the "prediction" step is really a convolution, rather than a sum, of Gaussian "distributions", which can be shown to be a Gaussian "distribution" with mean and variance as described in Chapter 3. At least, that's what I think after reading Chapter 4... Looking forward to further enlightenment in the upcoming chapters... :-)
In chapter 6: Multivariate Kalman Filters, in the part
what if 𝑥=𝑥˙Δ𝑡 ? (set F00 to 0, the rest at defaults)
leads to the following plot of $𝐏=𝐅𝐏𝐅^𝖳$:
But I can't get the idea behind it, I mean how is the variance for x (position) reduced to minimum ? On using 𝑥0 = 0, the resulting matrix for P is:
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Hi @rlabbe I came across the part "Stable Computation of the Posterior Covariance" and couldn't understand how the Joseph-equation-derived-covariance mitigates a non-optimal K (Kalman gain) ? I see that to be possible only when a different method is used to compute K.
Can you please help ?