Wheeled Mobile Robotics

$\begin{array}{l}\hfill \begin{array}{cc}{\mathit{P}}_{k|k}& ={\mathit{P}}_{k|k-1}-{\mathit{K}}_k\mathit{C}{\mathit{P}}_{k|k-1}-{\mathit{P}}_{k|k-1}{\mathit{C}}^T{\mathit{K}}_k^T+{\mathit{K}}_k{\mathit{S}}_k{\mathit{K}}_k^T\\ ={\mathit{P}}_{k|k-1}-{\mathit{K}}_k\mathit{C}{\mathit{P}}_{k|k-1}-{\mathit{P}}_{k|k-1}{\mathit{C}}^T{\mathit{K}}_k^T+{\mathit{P}}_{k|k-1}{\mathit{C}}^T{\mathit{K}}_k^T\\ ={\mathit{P}}_{k|k-1}-{\mathit{K}}_k\mathit{C}{\mathit{P}}_{k|k-1}\end{array}\end{array}$

Example 6.19

There is a mobile robot that drives around on a plane and measures its position with a GPS sensor 10 times in a second (sampling time T_s = 0.1 s). The position measurement is disturbed with zero-mean Gaussian noise with variance 10 m². The mobile robot drives with the speed of 1 m/s in the x direction and with the speed of 0 m/s in the y direction. The variance of Gaussian noise of the velocity is 0.1 m²/s². At the beginning of observation, the mobile robot is situated in the origin x = [0, 0]^T, but our initial estimate about the ...