Consider a robot with its centre of mass located at x = [P, Py). The robot is equipped with sensors that can measure the squared distance between $\mathbf{x}$ and four landmarks located in the following coordinates: Pz. Pyl Pr2 Py.2 4 4 Pr.3 Py.3 PA PyA] The measurement models for sensor $i=1,\ldots,4$, is given by: m,= (p. - Ps.) + (Py - Pr.) + ei a. Write the measurement model above in vector form for all sensors. (1 points) b. Obtain the Jacobian related to the measurement model in the vector form in point a. (2 points) c. If the measurements obtained from the sensors are [49.93427503, 34.02551511, 18.03571293, 33.97350448], and the measurement noise ei, i = 1,...,4 is zero mean with variance 2.5 x 10-3, calculate two iteration of the estimate of x, using an initial guess (0) = [0,0] and gradient descent step size = 10-5. (7 points)