ABSTRACT
Based on the Kalman filtering and smoothing results above, the three required conditional expectations are computed as follows:
En[xn(k)] = En[xn(k)xn(k)11 =
En[xn(k)xn(k — 1)71 = En[xn(k)xn(k — 1)11 =
where E ,k-111tn,m is recursively calculated by x
En[xn(k)]En[xn(k)]Tr
En[xn(k)]En[xn(k — le , (10.74)
Updating w: To update c74, according to Eq. 10.53, p(onlm, 0) must be calculated. The calculation
proceeds as follows:
P(onlm,e) = p(o71m, 0)p(o21437, m, 6) • • • P(Ok 144-1, e) • • • P(01<n 107cn-1, —, 07, m,15),
where p(oz 1(4_1 , 07,m, G) is the PDF of the innovation sequence. This PDF has the Gaussian form of
(27) 5) lEgk,,„1 2 exP{— CO'kl,rn P.[V.5%,] —164} (10.75)
where the innovation sequence okfin is computed directly from the (forward) Kalman Filtering step Eq. 10.72.
