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Fix unambiguous typos with codespell
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00-Preface.ipynb

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"\n",
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"<b>nbviewer</b>\n",
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"\n",
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"The nbviewer website will render any Notebook in a static format. I find it does a slightly better job than the GitHub renderer, but it is slighty harder to use. It accesses GitHub directly; whatever I have checked into GitHub will be rendered by nbviewer.\n",
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"The nbviewer website will render any Notebook in a static format. I find it does a slightly better job than the GitHub renderer, but it is slightly harder to use. It accesses GitHub directly; whatever I have checked into GitHub will be rendered by nbviewer.\n",
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"\n",
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"You may access this book via nbviewer here:\n",
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"\n",
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"\n",
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"A possible downside is that the equations that perform the filtering are hidden behind functions, which we could argue is a loss in a pedagogical text. I argue the converse. I want you to learn how to use Kalman filters in the real world, for real projects, and you shouldn't be cutting and pasting established algorithms all over the place.\n",
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"\n",
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"I use Python classes. I mostly use classes as a way to organize the data that the filters require, not to implement object oriented (OO) features such as inheritence. For example, the `KalmanFilter` class stores matrices and vectors called `x`, `P`, `R`, `Q`, `S`, `y`, `K`. I've seen procedural libraries for Kalman filters, and they require the programmer to maintain all of those matrices. This perhaps isn't so bad for a toy program, but program a bank of Kalman filters and you will not enjoy having to manage all of those matrices and other associated data. I have derived from these classes occasionally in my own work, and find it handy, but I don't want to force OO on people as I know many do not like it."
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"I use Python classes. I mostly use classes as a way to organize the data that the filters require, not to implement object oriented (OO) features such as inheritance. For example, the `KalmanFilter` class stores matrices and vectors called `x`, `P`, `R`, `Q`, `S`, `y`, `K`. I've seen procedural libraries for Kalman filters, and they require the programmer to maintain all of those matrices. This perhaps isn't so bad for a toy program, but program a bank of Kalman filters and you will not enjoy having to manage all of those matrices and other associated data. I have derived from these classes occasionally in my own work, and find it handy, but I don't want to force OO on people as I know many do not like it."
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Appendix-E-Ensemble-Kalman-Filters.ipynb

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"source": [
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"- [1] Mackenzie, Dana. *Ensemble Kalman Filters Bring Weather Models Up to Date* Siam News, Volume 36, Number 8, October 2003. http://www.siam.org/pdf/news/362.pdf\n",
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"\n",
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"- [2] Brown, Robert Grover, and Patrick Y.C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering, With MATLAB® excercises and solutions.* Wiley, 2012.\n",
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"- [2] Brown, Robert Grover, and Patrick Y.C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering, With MATLAB® exercises and solutions.* Wiley, 2012.\n",
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"\n",
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"- [3] Crassidis, John L., and John L. Junkins. *Optimal estimation of dynamic systems*. CRC press, 2011."
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]

Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb

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"\n",
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"We (well I) want to do this sort of thing because I want to use monte carlo simulations to compute distributions. It is easy to compute Gaussians when they pass through linear functions, but difficult to impossible to compute them analytically when passed through nonlinear functions. Techniques like particle filtering handle this by taking a large sample of points, passing them through a nonlinear function, and then computing statistics on the transformed points. Let's do that.\n",
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"\n",
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"We will start with the linear function $f(x) = 2x + 12$ just to prove to ourselves that the code is working. I will alter the mean and std of the data we are working with to help ensure the numbers that are output are unique It is easy to be fooled, for example, if the formula multipies x by 2, the mean is 2, and the std is 2. If the output of something is 4, is that due to the multication factor, the mean, the std, or a bug? It's hard to tell. "
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"We will start with the linear function $f(x) = 2x + 12$ just to prove to ourselves that the code is working. I will alter the mean and std of the data we are working with to help ensure the numbers that are output are unique It is easy to be fooled, for example, if the formula multiplies x by 2, the mean is 2, and the std is 2. If the output of something is 4, is that due to the multication factor, the mean, the std, or a bug? It's hard to tell. "
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{

Supporting_Notebooks/Iterative-Least-Squares-for-Sensor-Fusion.ipynb

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"\n",
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"$$\\delta \\mathbf z^+=\\delta \\mathbf z^- - \\mathbf H\\delta \\mathbf x.$$\n",
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"\n",
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"Here I have switched to using the matrix $\\mathbf H$ as the measurement function. We want to use linear algebra to peform the ILS, so for each step we will have to compute the matrix $\\mathbf H$ which corresponds to $h(\\mathbf{x^-})$ during each iteration. $h(\\bullet)$ is usually nonlinear for these types of problems so you will have to linearize it at each step (more about this soon).\n",
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"Here I have switched to using the matrix $\\mathbf H$ as the measurement function. We want to use linear algebra to perform the ILS, so for each step we will have to compute the matrix $\\mathbf H$ which corresponds to $h(\\mathbf{x^-})$ during each iteration. $h(\\bullet)$ is usually nonlinear for these types of problems so you will have to linearize it at each step (more about this soon).\n",
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"\n",
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"For various reasons you may want to weigh some measurement more than others. For example, the geometry of the problem might favor orthogonal measurements, or some measurements may be more noisy than others. We can do that with the equation\n",
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"\n",
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"$${\\delta \\mathbf x} = {{(\\mathbf H^\\mathsf{T}\\mathbf{WH})^{-1}}\\mathbf H^\\mathsf{T}\\mathbf{W} \\delta \\mathbf z^-}\n",
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"$$\n",
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"\n",
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"Since the equations are overdetermined we cannot solve these equations exactly so we use an iterative approach. An initial guess for the position is made, and this guess is used to compute for $\\delta \\mathbf x$ via the equation above. $\\delta \\mathbf x$ is added to the intial guess, and this new state is fed back into the equation to produce another $\\delta \\mathbf x$. We iterate in this manner until the difference in the measurement residuals is suitably small."
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"Since the equations are overdetermined we cannot solve these equations exactly so we use an iterative approach. An initial guess for the position is made, and this guess is used to compute for $\\delta \\mathbf x$ via the equation above. $\\delta \\mathbf x$ is added to the initial guess, and this new state is fed back into the equation to produce another $\\delta \\mathbf x$. We iterate in this manner until the difference in the measurement residuals is suitably small."
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animations/Gaussians_Animations.ipynb

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"sys.path.insert(0,'..') # allow us to format the book\n",
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"\n",
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"# use same formatting as rest of book so that the plots are\n",
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"# consistant with that look and feel.\n",
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"# consistent with that look and feel.\n",
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"import book_format\n",
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"book_format.set_style()"
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]

animations/Kalman_Filters_Animations.ipynb

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"sys.path.insert(0,'..') # allow us to format the book\n",
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"\n",
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"# use same formatting as rest of book so that the plots are\n",
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"# consistant with that look and feel.\n",
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"# consistent with that look and feel.\n",
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"import book_format\n",
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"book_format.set_style()"
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]

animations/multivariate_animations.ipynb

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"sys.path.insert(0,'..') # allow us to format the book\n",
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"\n",
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"# use same formatting as rest of book so that the plots are\n",
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"# consistant with that look and feel.\n",
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"# consistent with that look and feel.\n",
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"import book_format\n",
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"book_format.set_style()"
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]

animations/particle_animate.ipynb

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"sys.path.insert(0,'..') # allow us to format the book\n",
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"\n",
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"# use same formatting as rest of book so that the plots are\n",
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"# consistant with that look and feel.\n",
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"# consistent with that look and feel.\n",
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"import book_format\n",
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"book_format.set_style()"
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]

experiments/Untitled2.ipynb

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" // Register the callback with on_msg.\n",
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" comm.on_msg(function(msg) {\n",
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" //console.log('receiving', msg['content']['data'], msg);\n",
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" // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
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" // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
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" ws.onmessage(msg['content']['data'])\n",
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" });\n",
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" return ws;\n",

experiments/ball.py

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x0,y0 initial position
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launch_angle_deg angle ball is travelling respective to ground plane
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velocity_ms speeed of ball in meters/second
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velocity_ms speed of ball in meters/second
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noise amount of noise to add to each reported position in (x,y)
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"""
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experiments/baseball.py

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velocity_ms speeed of ball in meters/second
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velocity_ms speed of ball in meters/second
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noise amount of noise to add to each reported position in (x,y)
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"""
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experiments/satellite.ipynb

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"s1 = (0., 2.) # satellite 1\n",
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"s2 = (1., 2.) # satellite 2\n",
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"p = (-0.5, 1.) # platform postion\n",
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"p = (-0.5, 1.) # platform position\n",
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"\n",
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"s1 = (0., 200.) # satellite 1\n",
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"s2 = (100., 220.) # satellite 2\n",
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"p = (10, 1.) # platform postion\n",
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"p = (10, 1.) # platform position\n",
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"r1 = range_to(s1, p)\n",
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"r2 = range_to(s2, p)\n",

experiments/ukf_baseball.py

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in (x,y)
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kf_book/ekf_internal.py

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velocity_ms speed of ball in meters/second
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"""
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