doc: minor corrections

Author: franckgaga

src/estimator/execute.jl

@@ -86,7 +86,7 @@ end
 
 Init `estim.x̂0` states from current inputs `u`, measured outputs `ym` and disturbances `d`.
 
-The method tries to find a good steady-state for the initial estimate ``\mathbf{x̂}(0)``. It
+The method tries to find a good steady-state for the initial estimate ``\mathbf{x̂}``. It
 removes the operating points with [`remove_op!`](@ref) and call [`init_estimate!`](@ref):
 
 - If `estim.model` is a [`LinModel`](@ref), it finds the steady-state of the augmented model

src/estimator/kalman.jl

@@ -96,7 +96,7 @@ Q_{int_u}, Q_{int_{ym}})}`` and ``\mathbf{R̂ = R}``. The matrices ``\mathbf{Ĉ
 the rows of ``\mathbf{Ĉ, D̂_d}`` that correspond to measured outputs ``\mathbf{y^m}`` (and 
 unmeasured ones, for ``\mathbf{Ĉ^u, D̂_d^u}``). The Kalman filter will estimate the current
 state with the newest measurements ``\mathbf{x̂}_k(k)`` if `direct == true`, else it will
-predict the the state of the next time step ``\mathbf{x̂}_k(k+1)``.
+predict the state of the next time step ``\mathbf{x̂}_k(k+1)``.
 
 # Arguments
 !!! info

src/sim_model.jl

@@ -189,7 +189,8 @@ detailstr(model::SimModel) = ""
 
 Init `model.x0` with manipulated inputs `u` and measured disturbances `d` steady-state.
 
-It removes the operating points on `u` and `d` and calls [`steadystate!`](@ref):
+The method tries to initialize the model state ``\mathbf{x}`` at steady-state. It removes
+the operating points on `u` and `d` and calls [`steadystate!`](@ref):
 
 - If `model` is a [`LinModel`](@ref), the method computes the steady-state of current
   inputs `u` and measured disturbances `d`.