📝 Fixed duplicated of of in 07-Kalman-Filter-Math.ipynb

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Guillaume Jacquenot 2021-03-19 21:58:49 +01:00
parent 24b9fb3cf7
commit 5be6417523

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@ -170,7 +170,7 @@
"\n",
"We can do that only because $\\dot x = v$ is simplest differential equation possible. Almost all other in physical systems result in more complicated differential equation which do not yield to this approach. \n",
"\n",
"*State-space* methods became popular around the time of the Apollo missions, largely due to the work of Dr. Kalman. The idea is simple. Model a system with a set of $n^{th}$-order differential equations. Convert them into an equivalent set of first-order differential equations. Put them into the vector-matrix form used in the previous section: $\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{Bu}$. Once in this form we use of of several techniques to convert these linear differential equations into the recursive equation:\n",
"*State-space* methods became popular around the time of the Apollo missions, largely due to the work of Dr. Kalman. The idea is simple. Model a system with a set of $n^{th}$-order differential equations. Convert them into an equivalent set of first-order differential equations. Put them into the vector-matrix form used in the previous section: $\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{Bu}$. Once in this form we use of several techniques to convert these linear differential equations into the recursive equation:\n",
"\n",
"$$ \\mathbf x_k = \\mathbf{Fx}_{k-1} + \\mathbf B_k\\mathbf u_k$$\n",
"\n",