Consider a robot navigating in a rectangular hallway as shown in figure below with built $-$ in

encoders and laser sensor measuring distance to the front wall. Assume the robot motion to be one

dimensional along the line. The position shown in figure is the initial position of the robot,

$x_0=[x_t,y_t,{}_t{]}^T=[1\mathrm{.}5,3\mathrm{.}0,0\mathrm{.}35{]}^T$ with covariance $P_0=\left[\begin{array}{ccc}100& 0& 0\\ 0& 100& 0\\ 0& 0& 150\end{array}\right].$

You are required to implement Kalman filter localization algorithm. Use following data.