answe all 3 questions with explanation

In mobile robotics, it is important to determine the robot poses (states) using robot control information and measurement information. To obtain an accurate estimation of the robot pose, Particle Filter (PF) is commonly used. For a particular range sensor used on the robot, the measurement noise can be described by a Gaussian distribution: p(x) = - exp (x - 1) ? 202 where mean, /= 0 (m) and the standard deviation, o= 0.05 (m). 1. At a particular robot location, the sensor had measured a distance of d = 2.0 (m). If a particle i has an estimated measurement of d = 2.05 (m) what is the likelihood of this particle representing the actual position of the robot? (3 marks) 2. Hypothetically, there are 10 particles used in the PF process. The normalised weights of 9 such particles are listed in the table, what is Was? P particle 2 3 5 6 7 8 9 10 Particle position (m) 2.05 2.02 1.90 1.89 2.10 2.15 2.00 2.08 1.95 1.85 Normalised weight 0.160 0.243 0.036 0.023 Wn5 0.003 0.263 0.073 0.160 0.003 (2 marks) 3. From the above table Which particle has the highest probability of being re-sampled? (1 mark)