Fixed typo in chapter 8.

08-Designing-Kalman-Filters.ipynb

@@ -407,7 +407,7 @@
     "$$\\mathbf{x} = \n",
     "\\begin{bmatrix}x & \\dot{x} & y & \\dot{y}\\end{bmatrix}^\\mathsf{T}$$\n",
     "\n",
-    "There is nothing special about this organization. I could have used $\\begin{bmatrix}x & y & \\dot{x} &  \\dot{y}\\end{bmatrix}^\\mathsf{T}$ or something less logical. I just need to be consistent in the rest of the matrices. I like keeping positions and locations next to each other because it keeps the covariances between positions and velocities in the same sub block of the covariance matrix. In my formulation `P[1,0]` contains the covariance of of $x$ and $\\dot{x}$. In the alternative formulation that covariance is at `P[2, 0]`. This gets worse as the number of dimension increases (e.g. 3D space, accelerations).\n",
+    "There is nothing special about this organization. I could have used $\\begin{bmatrix}x & y & \\dot{x} &  \\dot{y}\\end{bmatrix}^\\mathsf{T}$ or something less logical. I just need to be consistent in the rest of the matrices. I like keeping positions and velocities next to each other because it keeps the covariances between positions and velocities in the same sub block of the covariance matrix. In my formulation `P[1,0]` contains the covariance of of $x$ and $\\dot{x}$. In the alternative formulation that covariance is at `P[2, 0]`. This gets worse as the number of dimension increases (e.g. 3D space, accelerations).\n",
     "\n",
     "Let's pause and address how you identify the hidden variables. This example is somewhat obvious because we've already worked through the 1D case, but other problems won't be obvious There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n",
     "\n",