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Merge branch 'master' of https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

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Roger Labbe 2018-05-05 09:16:04 -07:00
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08-Designing-Kalman-Filters.ipynb
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@ -1798,7 +1798,7 @@
"\n",
"As I've mentioned, you may place the variables in $\\mathbf x$ in whatever order you choose. For example, you could define a 1D constant acceleration as $\\mathbf x = \\begin{bmatrix}\\ddot x & x & \\dot x\\end{bmatrix}^\\mathsf T$. I can't imagine why you would want that order, but it is possible.\n",
"\n",
"Let's do something more reasonable. Design a second order filter for a robot moving in 2D, where $\\mathbf x = \\begin{bmatrix}x & y & \\dot x & \\dot y \\end{bmatrix}^\\mathsf T$. In this chapter we have been using $\\mathbf x = \\begin{bmatrix}x & \\dot x & \\dot y & \\dot y \\end{bmatrix}^\\mathsf T$.\n",
"Let's do something more reasonable. Design a second order filter for a robot moving in 2D, where $\\mathbf x = \\begin{bmatrix}x & y & \\dot x & \\dot y \\end{bmatrix}^\\mathsf T$. In this chapter we have been using $\\mathbf x = \\begin{bmatrix}x & \\dot x & y & \\dot y \\end{bmatrix}^\\mathsf T$.\n",
"\n",
"Why would you choose a different ordering? As you'll see in a moment, changing the order of $\\mathbf x$ changes the order of most of the rest of the filter's matrices. Depending on what data you want to inspect, such as the correlations in $\\mathbf P$, various orderings of $\\mathbf x$ can make that easier or more difficult.\n",
"\n",