For perfectly known input values .11. (k = 1.2,...) a function generator yields output values 31;, (I: = 1, 2, . ...) It. is desired to model the function generator as a straight line using the pairs (#91112). i.e., ya = mm.- -| c + wk, where m and onto the unknown constants (to he found), wk NJ'WO, R) and the value of R is known. (a) Fonnulate this straight line tting problem as a Kalman filter and write all the key system model as well as Kalman Iter equations. (b) Using the notation from the hook, 13011115)\"1 can be calculated using k P(klk)\"1 = Z Hf R\" H. i=1 Find expressions [or F'(k|k)"" and the Kalman gain W09) (hint: use alternative expressions for the gain). (as) If 1:15: I: (Len, uniformly spaced data points), nd a simple expression for the Kalman gain