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Added link to Wikipedia for Cholesky decomposition.

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Roger Labbe 2014-12-01 07:17:56 -08:00
parent e76698dd33
commit f6537d34a8
1 changed files with 5 additions and 3 deletions
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10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb
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@ -1815,7 +1815,7 @@
"\\Sigma = SS^\\mathsf{T} \\\\\n",
"$$\n",
"\n",
"This latter method is typically chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition*. \n",
"This latter method is typically chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition* [3]. \n",
"Numpy provides this with the `numpy.linalg.cholesky()` method. If your language of choice is Fortran, C, C++, or the like standard libraries such as LAPACK also provide this routine. And, of course, matlab provides `chol()`, which does the same thing.\n",
"\n",
"This method returns a lower triangular matrix, so we will take the transpose of it so that in our for loop we can access it row-wise as `U[i]`, rather than the more cumbersome column-wise notation `U[i,:]`.\n",
@ -2401,7 +2401,9 @@
"\n",
"- [1] Simon, Dan. *Optimal State Estimation*, John Wiley & Sons, 2006.\n",
"\n",
"- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)"
"- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
"\n",
"- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
]
}
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