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Github Issue #80 Invalid use of kappa

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I used kappa in a couple of places for the square root, when I should
have been using lambda.
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Roger Labbe 2016-02-05 07:51:43 -08:00
parent f64aec3693
commit f6c83812a1
1 changed files with 2 additions and 2 deletions
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10-Unscented-Kalman-Filter.ipynb
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@ -2231,7 +2231,7 @@
"\n",
"The Python is not difficult once we understand the $\\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i$ term.\n",
"\n",
"The term $\\sqrt{(n+\\kappa)\\Sigma}$ is a matrix because $\\Sigma$ is a matrix. The subscript $i$ in $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ is choosing the column vector of the matrix. What is the square root of a matrix? There is no unique definition. One definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$: if $\\Sigma = SS$ then $S = \\sqrt{\\Sigma}$.\n",
"The term $\\sqrt{(n+\\lambda)\\Sigma}$ is a matrix because $\\Sigma$ is a matrix. The subscript $i$ in $[\\sqrt{(n+\\lambda)\\Sigma}]_i$ is choosing the column vector of the matrix. What is the square root of a matrix? There is no unique definition. One definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$: if $\\Sigma = SS$ then $S = \\sqrt{\\Sigma}$.\n",
"\n",
"We will choose an alternative definition that has numerical properties which make it easier to compute. We can define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n",
"\n",
@ -2276,7 +2276,7 @@
"source": [
"```python\n",
"sigmas = np.zeros((2*n+1, n))\n",
"U = scipy.linalg.cholesky((n+kappa)*P)\n",
"U = scipy.linalg.cholesky((n+lambda_)*P) # sqrt\n",
"\n",
"sigmas[0] = X\n",
"for k in range (n):\n",