Path integration
= Path integration
{title2=$\dot\theta=\omega,\quad\dot p=v(\cos\theta,\sin\theta)^{\mathsf T}$}
Updating an internal position or heading estimate from self-motion signals, such as angular velocity and translation. In an ideal planar case, $\dot\theta=\omega$ and $\dot p=v(\cos\theta,\sin\theta)^{\mathsf T}$. Integrating biased or noisy inputs accumulates errors, motivating correction by landmarks and other external cues.