Batch filtering and RTS additions.

Added descriptions on using batch filtering to produce results,
and how to call the RTS smoother algorithms.

10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:ce14fff7e0ef1785ba83a455e926d8748b9cbd6b084e913d3580ea41d79d0221"
+  "signature": "sha256:69a64babdd622c8d8baa2d202fe7e15207c4b74ceb33e933c23742815922808f"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -261,7 +261,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f578bd5d4e0>"
+        "<IPython.core.display.HTML at 0x7fd8c0d15128>"
        ]
       }
      ],
@@ -309,9 +309,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f8e82e8>"
+        "<matplotlib.figure.Figure at 0x7fd8a48af278>"
        ]
       }
      ],
@@ -347,9 +347,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f8c9048>"
+        "<matplotlib.figure.Figure at 0x7fd8a488d8d0>"
        ]
       }
      ],
@@ -396,7 +396,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f8c3978>"
+        "<matplotlib.figure.Figure at 0x7fd8a487ab00>"
        ]
       }
      ],
@@ -494,16 +494,16 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576af89358>"
+        "<matplotlib.figure.Figure at 0x7fd89ff99160>"
        ]
       },
       {
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "Difference in mean x=-0.167, y=44.040\n"
+        "Difference in mean x=0.192, y=43.977\n"
        ]
       }
      ],
@@ -542,7 +542,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f8c92e8>"
+        "<matplotlib.figure.Figure at 0x7fd8a4554128>"
        ]
       }
      ],
@@ -582,7 +582,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576aff1d68>"
+        "<matplotlib.figure.Figure at 0x7fd89ffb8400>"
        ]
       }
      ],
@@ -637,7 +637,7 @@
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        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576af206a0>"
+        "<matplotlib.figure.Figure at 0x7fd89fd809e8>"
        ]
       }
      ],
@@ -978,9 +978,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576af20048>"
+        "<matplotlib.figure.Figure at 0x7fd8a007ee48>"
        ]
       }
      ],
@@ -1010,9 +1010,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576b012fd0>"
+        "<matplotlib.figure.Figure at 0x7fd89ffd65f8>"
        ]
       }
      ],
@@ -1059,7 +1059,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576af6b438>"
+        "<matplotlib.figure.Figure at 0x7fd89ff61320>"
        ]
       }
      ],
@@ -1182,7 +1182,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f32b2b0>"
+        "<matplotlib.figure.Figure at 0x7fd8a431a128>"
        ]
       }
      ],
@@ -1214,7 +1214,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f2db4a8>"
+        "<matplotlib.figure.Figure at 0x7fd89ff68048>"
        ]
       }
      ],
@@ -1302,7 +1302,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576b0c5198>"
+        "<matplotlib.figure.Figure at 0x7fd8a45edbe0>"
        ]
       }
      ],
@@ -1347,7 +1347,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f8c94e0>"
+        "<matplotlib.figure.Figure at 0x7fd8a436e5f8>"
        ]
       }
      ],
@@ -1405,7 +1405,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f33a358>"
+        "<matplotlib.figure.Figure at 0x7fd8a42db9e8>"
        ]
       }
      ],
@@ -1504,7 +1504,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576aeed630>"
+        "<matplotlib.figure.Figure at 0x7fd8a006c6d8>"
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        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f576b0de198>"
+        "<matplotlib.figure.Figure at 0x7fd8a4316e10>"
        ]
       }
      ],
@@ -1663,7 +1663,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576f36d7f0>"
+        "<matplotlib.figure.Figure at 0x7fd8a43a8ac8>"
        ]
       }
      ],
@@ -1698,7 +1698,7 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAJPCAYAAABo2UApAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f576aefbfd0>"
+        "<matplotlib.figure.Figure at 0x7fd8a005d400>"
        ]
       }
      ],
@@ -1779,7 +1779,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 42
+     "prompt_number": 28
     },
     {
      "cell_type": "markdown",
@@ -1866,13 +1866,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 28,
+       "prompt_number": 29,
        "text": [
         "array([410, 520, 630])"
        ]
       }
      ],
-     "prompt_number": 28
+     "prompt_number": 29
     },
     {
      "cell_type": "markdown",
@@ -1957,7 +1957,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 43
+     "prompt_number": 30
     },
     {
      "cell_type": "markdown",
@@ -1997,7 +1997,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 44
+     "prompt_number": 31
     },
     {
      "cell_type": "markdown",
@@ -2056,7 +2056,7 @@
       "    Pxz = zeros((self._dim_x, self._dim_z))\n",
       "    for i in range(self._num_sigmas):\n",
       "        Pxz += self.W[i] * np.outer(sigmas_f[i] - self.xp,\n",
-      "                                    sigmas_h[i] - zp))\n",
+      "                                    sigmas_h[i] - zp)\n",
       "\n",
       "    K = dot(Pxz, inv(Pz)) # Kalman gain\n",
       "\n",
@@ -2066,7 +2066,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 45
+     "prompt_number": 32
     },
     {
      "cell_type": "markdown",
@@ -2074,7 +2074,9 @@
      "source": [
       "### Full Source from FilterPy\n",
       "\n",
-      "Without further explanation, here is the full source from FilterPy."
+      "Without further explanation, here is the full source from FilterPy.\n",
+      "\n",
+      "** author's note ** this is somewhat dated, but I am not going to update this section every time I make a minor change to the filterpy code."
      ]
     },
     {
@@ -2373,7 +2375,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 50
+     "prompt_number": 33
     },
     {
      "cell_type": "markdown",