2. Given the stochastic system with scalar measurement $k+1 = (1333*, 33;: E R\

2. Given the stochastic system with scalar measurement m, TkRn, xo) where N (O, V) and To, are all independent random variables for all k. (a) Determine the algorithm for the linear minimum-variance esti- mator, i.e., determine the filter gain and associated update and propagation of the variances variances. (b) Justify the algorithm using the Orthogonal Projection Lemma (OPL). (c) As k + oo i. to what value doe-s the second moment of the state and the error variance (Hint: propagate the inverse of the error vari- ance) converge when is a stable matrix? ii. to what value does the second moment of the state and the error variance converge when (t) is an unstable matrix?