Text on Approximating Q

Discussed approximating Q by only assigning a value to the
lower rightmost term.

07_Kalman_Filter_Math/Kalman_Filter_Math.ipynb

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         "array([[ 0.33333333,  0.5       ],\n",
         "       [ 0.5       ,  1.        ]])"
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+      "### Simplification of Q\n",
+      "\n",
+      "Through the early parts of this book I used a much simpler form for $\\mathbf{Q}$, often only putting a noise term in the lower rightmost element. Is this justified? Well, consider the value of $\\mathbf{Q}$ for a small $\\Delta t$"
+     ]
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+     "input": [
+      "common.Q_continuous_white_noise(dim=3, dt=0.05, spectral_density=1)"
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+        "array([[  1.56250000e-08,   7.81250000e-07,   2.08333333e-05],\n",
+        "       [  7.81250000e-07,   4.16666667e-05,   1.25000000e-03],\n",
+        "       [  2.08333333e-05,   1.25000000e-03,   5.00000000e-02]])"
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+      "We can see that most of the terms are very small. Recall that the only Kalman filter using this matrix is\n",
+      "\n",
+      "$$ \\mathbf{P}=\\mathbf{FPF}^T + \\mathbf{Q}$$\n",
+      "\n",
+      "If the values for $\\mathbf{Q}$ are small relative to $\\mathbf{P}$\n",
+      "than it will be contributing almost nothing to the computation of $\\mathbf{P}$. Setting $\\mathbf{Q}$ to \n",
+      "\n",
+      "$$Q=\\begin{bmatrix}0&0&0\\\\0&0&0\\\\0&0&\\sigma^2\\end{bmatrix}$$\n",
+      "\n",
+      "while not correct, is often a useful approximation. If you do this you will have to perform quite a few studies to guarantee that your filter works in a variety of situations. Given the availability of functions to compute the correct values of $\\mathbf{Q}$ for you I would strongly recommend not using approximations. Perhaps it is justified for quick-and-dirty filters, or on embedded devices where you need to wring out every last bit of performance, and seek to minimize the number of matrix operations required. "
+     ]
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