Table 1 Fixed-horizon TV UFIR filtering algorithm

Given:

K, N, m=n−N+1⩾0, s=m+K−1,

m+K⩽l⩽n.

Set:

${\widehat{\mathbf{x}}}_s$ by (69) and G _s by (70).

Update:

${\mathbf{G}}_l={[{\mathbf{H}}_l^T{\mathbf{H}}_l+{\left({\mathbf{F}}_l{\mathbf{G}}_{l-1}{\mathbf{F}}_l^T\right)}^{-1}]}^{-1}$,

${\widehat{\mathbf{x}}}_l={\mathbf{F}}_l{\widehat{\mathbf{x}}}_{l-1}+{\mathbf{G}}_l{\mathbf{H}}_l^T({\mathbf{z}}_l-{\mathbf{H}}_l{\mathbf{F}}_l{\widehat{\mathbf{x}}}_{l-1})$.

Instruction:

Use the estimate when l=n.