Let x = [pr. Py] the x and y component of the position of a robot. Consider the following sensor model: m2 m 123 m 0 P 0.5 P 1 0.5 -0.5 0.5] = From the measurement devices, you obtain the following values [mi, m2, m3, ms] = [0.8961118,-0.04937679, 0.29680553, 0.982085]. 1. Assuming that each sensor has a uniform measurement-error statistic, obtain the following: a. The mathematical expression of the criterion to be optimized. (2 points) b. The estimate of the position of the robot x that optimises the criterion in a. (3 points) 2. If it turns out that the sensors have different measurement errors statistics, where the variances for sensors i= 1,...,4 are 10-,2 x 10-,3 x 10-, and 4 x 10-, respectively, then obtain the following: a. The mathematical expression of the criterion to be optimized taking into account the different sensor's measurement noise variances. (2 points) b. The estimate of the position of the robot x that optimises the criterion in a. (3 points)