Merge pull request #408 from PebetoUofC/proof-read-ag-1

Proof read ag 1

10-Unscented-Kalman-Filter.ipynb

@@ -785,10 +785,10 @@
     "\n",
     "$$ \n",
     "\\boldsymbol{\\chi}_i = \\begin{cases}\n",
-    "\\mu + \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right ]_{i}& \\text{for i=1 .. n} \\\\\n",
-    "\\mu - \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} &\\text{for i=(n+1) .. 2n}\\end{cases}\n",
+    "\\mu + \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right ]_{i}& i=1..n \\\\\n",
+    "\\mu - \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} &i=(n+1)..2n\\end{cases}\n",
     "$$\n",
-    "The $i$ subscript chooses the i$^{th}$ roth vector of the matrix.\n",
+    "The $i$ subscript chooses the i$^{th}$ row vector of the matrix.\n",
     "\n",
     "In other words, we scale the covariance matrix by a constant, take the square root of it, and ensure symmetry by both adding and subtracting it from the mean. We will discuss how you take the square root of a matrix later.\n",
     "\n",
@@ -1191,7 +1191,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for elevation angle [1]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n",
+    "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for elevation angle [3]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n",
     "\n",
     "The design of $\\mathbf Q$ requires some discussion. The state is $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are down range distance and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of Q. The third element is altitude, which we assume is independent of $x$. That results in a block design for $\\mathbf Q$:\n",
     "\n",
@@ -1285,7 +1285,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Tracking Maneuevering Aircraft"
+    "### Tracking Maneuvering Aircraft"
    ]
   },
   {
@@ -2059,8 +2059,8 @@
     "$$\n",
     "\\begin{cases}\n",
     "\\mathcal{X}_0 = \\mu \\\\\n",
-    "\\mathcal{X}_i = \\mu +  \\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i, & \\texttt{for i=1..n} \\\\\n",
-    "\\mathcal{X}_i = \\mu - \\left[\\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} & \\texttt{for i=(n+1)..2n}\n",
+    "\\mathcal{X}_i = \\mu +  \\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i, & i=1..n \\\\\n",
+    "\\mathcal{X}_i = \\mu - \\left[\\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} & i=(n+1)..2n\n",
     "\\end{cases}\n",
     "$$\n",
     "\n",
@@ -2074,7 +2074,7 @@
     "\\Sigma = \\mathbf{SS}^\\mathsf T\n",
     "$$\n",
     "\n",
-    "This definition is favored because $\\mathbf S$ is computed using the [*Cholesky decomposition*](https://en.wikipedia.org/wiki/Cholesky_decomposition) [3]. It decomposes a Hermitian, positive-definite matrix into a triangular matrix and its conjugate transpose. The matrix can be either upper \n",
+    "This definition is favored because $\\mathbf S$ is computed using the [*Cholesky decomposition*](https://en.wikipedia.org/wiki/Cholesky_decomposition) [5]. It decomposes a Hermitian, positive-definite matrix into a triangular matrix and its conjugate transpose. The matrix can be either upper \n",
     "or lower triangular, like so:\n",
     "\n",
     "$$A=LL^{∗} \\\\ A=U^{∗}U$$\n",
@@ -3225,11 +3225,11 @@
     "\n",
     "- [2] Simon J. Julier. \"The Scaled Unscented Transformation\". Proceedings of the American Control Conference 6. IEEE. (2002)\n",
     "\n",
-    "- [1] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n",
+    "- [3] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n",
     "\n",
-    "- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman  Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
+    "- [4] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman  Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
     "\n",
-    "- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
+    "- [5] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
    ]
   }
  ],
@@ -3250,7 +3250,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.3"
   }
  },
  "nbformat": 4,