For perfectly known input values TR (k = 1,2,..) a function generator yields output values y. (k 1,2, ..). It is desired to model the function generator as a straight line using the pairs (The, yk), i.c., y& = mick + c + We, where in and c are the unknown constants (to be found), w. ~ /(0, R) and the value of R is known. (a) Formulate this straight line fitting problem as a Kalman filter and write all the key system model as well as Kalman filter equations. (b) Using the notation from the book, P(kjk) I can be calculated using P(kjk) SHER H. Find expressions for P(kjk) and the Kalman gain W(k) (hint: use alternative expressions for the gain). (c) If TR = k (i.c., uniformly spaced data points), find a simple expression for the Kalman gain