If there is a temperature sensor mounted on a mobile robot. The sensor reading, z(k), is linearly related to the temperature of the environment, T(k): z(k) = 0.2T(k) It is also assumed that the temperature sensor is subject to a zero-mean Gaussian noise with a standard deviation of: = 0.5C It is assumed that the environmental temperature is constant with no process noise at the time. If the initial estimate of the temperature T(0) = 30, with an initial system covariance of P(0) = 10. If there is a measurement taken at time step 1, z(1) = 5.017, answer the following: 1. Establish the system model of temperature T(k+1) 2. What is the measurement model? Using Kalman filter to calculate the following: 3. Estimated temperature covariance at time step 1, P(1|0) 4. Kalman gain, K(1) 5. Innovation r(1) 6. Updated Temperature estimate, T(1) 7. Updated temperature covariance P(1)