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Chapter 7 Fix LTI system theory equation for phi(t)
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Roger Labbe 2017-01-14 09:01:38 -08:00 committed by GitHub
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07-Kalman-Filter-Math.ipynb
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@ -718,7 +718,7 @@
"\n",
"[*Linear Time Invariant Theory*](https://en.wikipedia.org/wiki/LTI_system_theory), also known as LTI System Theory, gives us a way to find $\\Phi$ using the inverse Laplace transform. You are either nodding your head now, or completely lost. I will not be using the Laplace transform in this book. LTI system theory tells us that \n",
"\n",
"$$ \\Phi(t) = \\mathcal{L}^{-1}[(s\\mathbf{I} - \\mathbf{F})^{-1}]$$\n",
"$$ \\Phi(t) = \\mathcal{L}^{-1}[(s\\mathbf{I} - \\mathbf{A})^{-1}]$$\n",
"\n",
"I have no intention of going into this other than to say that the Laplace transform $\\mathcal{L}$ converts a signal into a space $s$ that excludes time, but finding a solution to the equation above is non-trivial. If you are interested, the Wikipedia article on LTI system theory provides an introduction. I mention LTI because you will find some literature using it to design the Kalman filter matrices for difficult problems. "
]
@ -1758,7 +1758,7 @@
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