16.322 Stochastic Estimation and Control, Fall 2004 Prof vander Velde X System states only System and filter states System and filter states Filter states only X(0,0) 0X,,(∞) The System states v Shaping filter states With this initialization X.(t) will remain constant- which it should do if we think of x(t) as a member of a stationary process16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 3 of 3 , System states only System and filter states System and filter states Filter states only 0 0 (0,0) 0 ( ) T T s s s T T s v v X x x x v vx vv X X ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ ∞ where System states Shaping filter states s x x v ⎡ ⎤ ⎡ ⎤ = = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ With this initialization, , ( ) Xv v t will remain constant – which it should do if we think of x( )t as a member of a stationary process