You have sampled from the probability distribution you created and have officially moved through one iteration of particle filtering using your 5 friends as particles! Amazing!
Now, we will go through a motion update, which is important because it helps your algorithm be more robust and efficient.
Below, the locations of the particles for iteration 0 are given.
Particle 1 (Susan): (1, 3, 0)
Particle 2 (Connie): (4, 5, 2.12)
Particle 3 (Kevin): (5, 4, 1.31)
Particle 4 (Penelope): (1, 4, 3.22)
Particle 5 (Egg): (3, 2, 5.44)
You are gradually moving across the room (increasing your x coordinate by 1 each iteration). What locations should the particles be at for iteration 1?
Add cos(theta) to x and sin(theta) to y to project the motion into the particle's frame.