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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"You can see that the center of the ellipse shifted by a small amount (from 10 to 10.90) because the position changed. The ellipse also elongated, showing the correlation between position and velocity. How does the filter compute new values for $\\mathbf{\\bar P}$, and what is it based on? Note that I set the process noise `Q` to zero each time, so it is not due to me adding noise. It's a little to early to discuss this, but recall that in every filter so far the predict step entailed a loss of information. The same is true here. I will give you the details once we have covered a bit more ground."
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"You can see that the center of the ellipse shifted by a small amount (from 10 to 11.35) because the position changed. The ellipse also elongated, showing the correlation between position and velocity. How does the filter compute new values for $\\mathbf{\\bar P}$, and what is it based on? Note that I set the process noise `Q` to zero each time, so it is not due to me adding noise. It's a little to early to discuss this, but recall that in every filter so far the predict step entailed a loss of information. The same is true here. I will give you the details once we have covered a bit more ground."
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]
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},
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{
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