From: Family of state space least mean power of two-based algorithms
Step | Operation | Multiplication | Additions |
---|---|---|---|
Predict | \(\bar {\mathbf {x}}[k]_{n\times 1} = \mathbf {A}[k-1]_{n\times n}\hat {\mathbf {x}}[k-1]_{n\times 1}\) | n 2 | n 2−n |
\(\bar {\mathbf {P}}[k]_{n\times n} = \mathbf {A}[k-1]_{n\times n}\mathbf {P}[k-1]_{n\times n}\mathbf {A}^{T}[k-1]_{n\times n} + \mathbf {Q}[k]_{n\times n}\) | 2n 3 | 2n 3−n 2 | |
Update | \({\mathbf {\varepsilon }}[k]_{m\times 1} = \mathbf {y}[k]_{m\times 1} -\mathbf {C}[k]_{m\times n}\bar {\mathbf {x}}[k]_{n\times 1}\) | mn | nm |
\(\mathbf {S}[k]_{m\times m} =\mathbf {C}[k]_{m\times n}\bar {\mathbf {P}}[k]_{n\times n}\mathbf {C}^{T}[k]_{n\times m} + \mathbf {R}[k]_{m\times m}\) | m n 2+m 2 n | m 2 n+m n 2−m n | |
\(\mathbf {K}[k]_{n\times m} = \bar {\mathbf {P}}[k]_{n\times n}\mathbf {C}^{T}[k]_{n\times m}\mathbf {S}^{-1}[k]_{m\times m}\) | m 3+m 2 n+m n 2 | m 3+m 2 n | |
\(\hat {\mathbf {x}}[k]_{n\times 1} =\bar {\mathbf {x}}[k]_{n\times 1} + \mathbf {K}[k]_{n\times m}{\mathbf {\varepsilon }}[k]_{m\times 1}\) | mn | nm | |
\(\mathbf {P}[k]_{n\times n} = (\mathbf {I}_{n\times n}-\mathbf {K}[k]_{n\times m}\mathbf {C}[k]_{m\times n})\bar {\mathbf {P}}[k]_{n\times n}\) | m n 2+n 3 | m n 2+n 3−n 2 | |
Total for the KF algorithm | m 3+2m 2 n+3m n 2+2m n+3n 3+n 2 | m 3+2m 2 n+3m n 2−m n+3n 3+n 2−n |