From 4671efef15f11f3b580db57ddfd64fdaaac2e7c7 Mon Sep 17 00:00:00 2001 From: Saurav Date: Wed, 30 Nov 2016 12:25:52 -0500 Subject: [PATCH] Fix LTI system theory equation for phi(t) --- 07-Kalman-Filter-Math.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/07-Kalman-Filter-Math.ipynb b/07-Kalman-Filter-Math.ipynb index 2255d45..b81d667 100644 --- a/07-Kalman-Filter-Math.ipynb +++ b/07-Kalman-Filter-Math.ipynb @@ -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 @@ "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python 3", + "display_name": "Python [default]", "language": "python", "name": "python3" },