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doc: minor corrections
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franckgaga committed Aug 21, 2024
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Showing 1 changed file with 5 additions and 7 deletions.
12 changes: 5 additions & 7 deletions src/estimator/mhe/construct.jl
Original file line number Diff line number Diff line change
Expand Up @@ -929,9 +929,9 @@ the matrices for the estimation error at arrival:
```
in which ``\mathbf{e_x̄} = [\begin{smallmatrix} -\mathbf{I} & \mathbf{0} & \cdots & \mathbf{0} \end{smallmatrix}]``,
and ``\mathbf{f_x̄} = \mathbf{x̂_0^†}(k-N_k+K)``. The latter is the deviation vector of the
state at arrival ``\mathbf{x̂}_{k-N_k}(k-N_k+K) - \mathbf{x̂_{op}}`` (estimated at ``k-N_k``).
Lastly, the estimated states ``\mathbf{x̂_0}(k-j+K)`` from ``j=N_k-1`` to ``0``, also in
deviation form, are calculated with:
state at arrival estimated at ``k-N_k`` i.e. ``\mathbf{x̂_0^†}(k-N_k+K) =
\mathbf{x̂}_{k-N_k}(k-N_k+K) - \mathbf{x̂_{op}}``. Lastly, the estimated states
``\mathbf{x̂_0}(k-j+K)`` from ``j=N_k-1`` to ``0``, also in deviation form, are computed with:
```math
\begin{aligned}
\mathbf{X̂_0} &= \mathbf{E_x̂ Z + G_x̂ U_0 + J_x̂ D_0 + B_x̂} \\
Expand Down Expand Up @@ -968,7 +968,7 @@ deviation form, are calculated with:
\mathbf{Ĉ^m S}(H_e-1) \end{bmatrix} \mathbf{\big(f̂_{op} - x̂_{op}\big)}
\end{aligned}
```
and, for ``K=1``, the matrices are given by:
or, for ``K=1``, the matrices are given by:
```math
\begin{aligned}
\mathbf{E} &= - \begin{bmatrix}
Expand All @@ -993,9 +993,7 @@ deviation form, are calculated with:
\mathbf{Ĉ^m S}(H_e-2) \end{bmatrix} \mathbf{\big(f̂_{op} - x̂_{op}\big)}
\end{aligned}
```
The matrices for the estimated states does not depend on ``K``:
```math
and for the estimated states:
The matrices for the estimated states does not depend on the constant ``K``:
```math
\begin{aligned}
\mathbf{E_x̂} &= \begin{bmatrix}
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