From 32861cac1eba88ee8863d0ae1ef0151c19606d4b Mon Sep 17 00:00:00 2001 From: Paul Kulchenko Date: Fri, 15 May 2015 13:22:41 -0700 Subject: [PATCH] Fixed small typo in Extended Kalman chapter. --- 11_Extended_Kalman_Filters.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/11_Extended_Kalman_Filters.ipynb b/11_Extended_Kalman_Filters.ipynb index f575a67..1cdebc7 100644 --- a/11_Extended_Kalman_Filters.ipynb +++ b/11_Extended_Kalman_Filters.ipynb @@ -509,7 +509,7 @@ "source": [ "As we can see there are two minor changes to the Kalman filter equations, which I have underlined. The first change replaces the equation $\\mathbf{x} = \\mathbf{Fx}$ with $\\mathbf{x} = f(\\mathbf{x})$. In the Kalman filter, $\\mathbf{Fx}$ is how we compute the new state based on the old state. However, in a nonlinear system we cannot use linear algebra to compute this transition. So instead we hypothesize a nonlinear function $f()$ which performs this function. Likewise, in the Kalman filter we convert the state to a measurement with the linear function $\\mathbf{Hx}$. For the extended Kalman filter we replace this with a nonlinear function $h()$, giving $\\mathbf{z}_x = h(\\mathbf{x})$.\n", "\n", - "The only question left is how do we implement use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system. For example, consider the function $f(x) = x^2 -2x$.\n", + "The only question left is how do we implement and use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system. For example, consider the function $f(x) = x^2 -2x$.\n", "\n", "The rest of the equations are unchanged, so $f()$ and $h()$ must produce a matrix that approximates the values of the matrices $\\mathbf{F}$ and $\\mathbf{H}$ at the current value for $\\mathbf{x}$. We do this by computing the partial derivatives of the state and measurements functions:" ]