daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Trivial formating issues: removed extra blank line, added missed dots at the ending of sentences.

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Gluttton 2015-05-01 12:53:27 +03:00
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01_g-h_filter.ipynb
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@ -985,10 +985,10 @@
"\n",
"**Let me repeat the key points as they are so important**. If you do not understand these you will not understand the rest of the book. If you do understand them, then the rest of the book will unfold naturally for you as mathematically elaborations to various 'what if' questions we will ask about *g* and *h*.\n",
"\n",
"* Multiple data points are more accurate than one data point, so throw nothing away no matter how inaccurate it is\n",
"* Always choose a number part way between two data points to create a more accurate estimate\n",
"* Predict the next measurement and rate of change based on the current estimate and how much we think it will change\n",
"* The new estimate is then chosen as part way between the prediction and next measurement\n",
"* Multiple data points are more accurate than one data point, so throw nothing away no matter how inaccurate it is.\n",
"* Always choose a number part way between two data points to create a more accurate estimate.\n",
"* Predict the next measurement and rate of change based on the current estimate and how much we think it will change.\n",
"* The new estimate is then chosen as part way between the prediction and next measurement.\n",
"\n",
"Let's look at a visual depiction of the algorithm."
]
@ -1990,12 +1990,7 @@
"I encourage you to experiment with this filter to develop your understanding of how it reacts. It shouldn't take too many attempts to come to the realization that ad-hoc choices for $g$ and $h$ do not perform very well. A particular choice might perform well in one situation, but very poorly in another. Even when you understand the effect of $g$ and $h$ it can be difficult to choose proper values. In fact, it is extremely unlikely that you will choose values for $g$ and $h$ that is optimal for any given problem. Filters are *designed*, not selected *ad hoc*. \n",
"\n",
"In some ways I do not want to end the chapter here, as there is a significant amount that we can say about selecting $g$ and $h$. But the g-h filter in this form is not the purpose of this book. Designing the Kalman filter requires you to specify a number of parameters - indirectly they do relate to choosing $g$ and $h$, but you will never refer to them directly when designing Kalman filters. Furthermore, $g$ and $h$ will vary at every time step in a very non-obvious manner. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"There is another feature of these filters we have barely touched upon - Bayesian statistics. You will note that the term 'Bayesian' is in the title of this book; this is not a coincidence! For the time being we will leave $g$ and $h$ behind, largely unexplored, and develop a very powerful form of probabilistic reasoning about filtering. Yet suddenly this same g-h filter algorithm will appear, this time with a formal mathematical edifice that allows us to create filters from multiple sensors, to accurately estimate the amount of error in our solution, and to control robots."
]
},