tutorialpoint.org

Engg. tutorials

  • Instrumentation and Control Lab
  • Control systems assignment
  • Shape memory alloy SMA actuator
  • Dielectric elastomer
  • EM theory lecture notes
  • GATE question papers
  • JAM question papers
  • Kalman filter tutorial
  • Nonlinear estimation
  • Nonlinear Estimation

    Board

    2 Literature review on quadrature based nonlinear estimation (cont'd...)

    2.5 Generation of deterministic sampling points and weights

    Unscented Kalman filter (GHF)

    $\bullet$ Let $P_{x,h}$ denote the covariance of an $n$-dimensional random variable $x_{h}$, $P_{y,h}$ be the covariance of measurement vector $y_{h}$ and $P_{xy,h}$ be the covariance of state and measurement vectors.

    $\bullet$ A matrix $\Psi$ is generated using $2n+1$ weighted sigma points.

    $\bullet$ A scaling parameter $k$ is used such that $\sqrt{(n+k)P_{x,h}}_{i}$ gives the $ith$ row or column of matrix square root of $(n+k)P_{x,h}$. This can be done using cholesky decomposition.

    $\bullet$ Unscented transformation can be represented as

    1) Generation of sigma points \begin{equation*} \psi_{0,h}=x_{h} \end{equation*} for $i$=$1$ to $n$ \begin{equation*} \psi_{i,h}=x_{h}+(\sqrt{(n+k)P_{x,h}})_{i} \end{equation*} for $i$=$n+1$ to $2n$ \begin{equation*} \psi_{i,h}=x_{h}-(\sqrt{(n+k)P_{x,h}})_{i} \end{equation*}

    2) Generation of weights \begin{equation*} W_{0}=k/(n+k) \end{equation*} for $i$=$1$ to $2n$ \begin{equation*} W_{i}=\dfrac{1}{2(n+k)} \end{equation*}

    < Prev.Page 1   2   3   4  5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   Next page>