The robot's state is represented by an integer $110$ corresponding to its location in the map at time $.$ We will approximate our belief over this state with $=8$ particles.

You have no control over the robot's actions. At each timestep, the robot either stays in place, or moves to any one of its neighboring locations, all with equal probability. For example, if the robot starts in state

$=7,$ it will move to state $$

$=6$ with probability $1$ or $=7$ with probability $1.$ Similarly, if the

$+1$

$2+12$

robot starts in state $=2,$ the next state $+1$ can be any element of $\{1,2,3,10\},$ and each occurs with

probability $1.$

$4$

At each time step, a sensor on the robot gives a reading $$ in $\{,,,\}$ corresponding to the $\_$type$\_$ of state the robot is in$.$ The possible types are:

Hallway $($H$)$ for states bordered by two parallel walls $(4,9).$

Corner $($C$)$ for states bordered by two orthogonal walls $(3,5,8,10).$

Tee $($T$)$ for states bordered by one wall $(2,6).$

Dead End $($D$)$ for states bordered by three walls $(1,7).$

The sensor is not very reliable: it reports the correct type with probability $1,$ but gives erroneous readings

$2$

the rest of the time, with probability $1$ for each of the three other possible readings.