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Table 3 Direct fixed-interval TV OUFIR smoothing algorithm

From: Iterative unbiased FIR state estimation: a review of algorithms

Stage

 

Given:

K, N=constant, q, m=nN+10,

 

s=m+K−1, m+Kln.

Set:

x ̂ s by (75) and G s by (76).

Update:

G l = [ H l T H l + ( F l G l 1 F l T ) 1 ] 1 ,

 

K l = i = 0 q 1 F l i 1 G l H l T ,

 

x ̂ l q = F l q x ̂ l q 1 + K l z l H l i = 0 q F l i x ̂ l q 1 .

Instruction:

The algorithm is valid for any nN−1+q. Use the

 

smoothed estimate when l=n. The fixed interval

 

of M=N=N opt points is from time index m to n.