A particle filter is used to localize a differential-drive robot within an indoor environment. The robot's state is defined by [x y 0]. a) Consider the 3 particles below, determine the robot's position [xy]. x (m) 5.4 5.2 1.1 y (m) 7.5 7.7 4.4 0 (rad) 0.31 0.28 0.99 W 0.399 0.399 0.002 b) Consider the 3 particles below, determine the robot's orientation [ 0 ]. You can assume that = 3.14. x (m) y (m) 0 (rad) W 5.4 7.7 3.13 0.333 5.2 7.7 -3.10 0.333 5.5 7.6 3.11 0.333