Robotics Asked by Astghik Hakobyan on October 3, 2021

Consider a nonlinear system $x(k+1)=f(x(k),u(k))$, where $x(k)inmathbb{R}^{n}$ is the state, $u(k)inmathbb{R}^m$ is the control input. Here $u(k)$ is normally distributed RV with mean $mu_u(k)$ and variance $Sigma_u(k)$. I want to find the distribution of $x(k)$ starting from some deterministic $x(0)$ for some horizon $K$.

Then can the ordinary EKF update equation be used for the prediction in the below way?

begin{align*}

mu_x(k+1)&=f(mu_x(k),mu_u(k)),\

Sigma_x(k+1)&=nabla_x f(mu_x(k),mu_u(k))Sigma_x(k)nabla_x f(mu_x(k),mu_u(k))^top+nabla_u f(mu_x(k),mu_u(k))Sigma_u(k)nabla_u f(mu_x(k),mu_u(k))^top

end{align*}

Yes. This approach is commonly used when IMUs are present because they measure the rate of state change with some uncertainty.

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