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Roger Labbe 2014-12-01 10:45:38 -08:00
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Preface.ipynb
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"\n",
"A word on variable names. I am an advocate for descriptive variable names. `R` is not, normally, descriptive. `R` is the measurement noise covaraiance matrix, so I could reasonably call it `measurement_noise_covariance`, and I've seen libraries do that. I've chosen not to do that. Why? In the end, Kalman filtering is math. To write a Kalman filter you are going to have to start by sitting down with a piece of paper and doing some math. You will be writing normal algrebric equations. Also, every Kalman filter text and source on the web uses the same linear algebra equations. You cannot read about the Kalman filter without seeing\n",
"\n",
"$$ \\dot{\\mathbf{x}} = \\mathbf{Fx} + \\mathbf{Gu}$$\n",
"$$\\dot{\\mathbf{x}} = \\mathbf{Fx} + \\mathbf{Gu}$$\n",
"\n",
"in every source (a few sources use A and B instead of F and G). One of my goals in this book is to bring you to the point where you can read the original literature on Kalman filtering. I take an optimistic tone in this book - that Kalman filtering is easy to learn - and in many ways it is. However, for nontrivial problems the difficulty is not the implementation of the equations, but learning how to set up the equations so they solve your problem. In other words, every Kalman filter will implement $ \\dot{\\mathbf{x}} = \\mathbf{Fx} + \\mathbf{Gu}$; the difficult part is figuring out what to put in the matrices $\\mathbf{F}$ and $\\mathbf{G}$ to make your filter work for your problem. Vast amounts of work have been done to figure out how to apply Kalman filters in various domains, and it would be tragic to not be able to read the literature and avail yourself of this research. \n",
"in every source (a few sources use A and B instead of F and G). One of my goals in this book is to bring you to the point where you can read the original literature on Kalman filtering. I take an optimistic tone in this book - that Kalman filtering is easy to learn - and in many ways it is. However, for nontrivial problems the difficulty is not the implementation of the equations, but learning how to set up the equations so they solve your problem. In other words, every Kalman filter will implement $\\dot{\\mathbf{x}} = \\mathbf{Fx} + \\mathbf{Gu}$; the difficult part is figuring out what to put in the matrices $\\mathbf{F}$ and $\\mathbf{G}$ to make your filter work for your problem. Vast amounts of work have been done to figure out how to apply Kalman filters in various domains, and it would be tragic to not be able to read the literature and avail yourself of this research. \n",
"\n",
"So, like it or not you will need to learn that $\\mathbf{F}$ is the *state transition matrix* and that $\\mathbf{R}$ is the *measurement noise covariance*. Once you know that the code will become readable, and until you know that all publications and web articles on Kalman filters will be inaccessible to you. \n",
"\n",