diff --git a/10-Unscented-Kalman-Filter.ipynb b/10-Unscented-Kalman-Filter.ipynb index 744798a..ce48391 100644 --- a/10-Unscented-Kalman-Filter.ipynb +++ b/10-Unscented-Kalman-Filter.ipynb @@ -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",