Merge pull request #97 from JuliaControl/doc_correction

minor doc correction

Author: franckgaga

src/estimator/kalman.jl

@@ -578,13 +578,14 @@ is based on the process model :
 \end{aligned}
 ```
 See [`SteadyKalmanFilter`](@ref) for details on ``\mathbf{v}(k), \mathbf{w}(k)`` noises and
-``\mathbf{R̂}, \mathbf{Q̂}`` covariances. The functions ``\mathbf{f̂, ĥ}`` are `model` 
-state-space functions augmented with the stochastic model of the unmeasured disturbances,
-which is specified by the numbers of integrator `nint_u` and `nint_ym` (see Extended Help).
-The ``\mathbf{ĥ^m}`` function represents the measured outputs of ``\mathbf{ĥ}`` function
-(and unmeasured ones, for ``\mathbf{ĥ^u}``). The matrix ``\mathbf{P̂}`` is the estimation
-error covariance of `model` state augmented with the stochastic ones. Three keyword
-arguments specify its initial value with ``\mathbf{P̂}_{-1}(0) = 
+``\mathbf{R̂}, \mathbf{Q̂}`` covariances. The two matrices are constructed from ``\mathbf{Q̂ =
+\text{diag}(Q, Q_{int_u}, Q_{int_{ym}})}`` and ``\mathbf{R̂ = R}``. The functions
+``\mathbf{f̂, ĥ}`` are `model` state-space functions augmented with the stochastic model of
+the unmeasured disturbances, which is specified by the numbers of integrator `nint_u` and
+`nint_ym` (see Extended Help). The ``\mathbf{ĥ^m}`` function represents the measured outputs
+of ``\mathbf{ĥ}`` function (and unmeasured ones, for ``\mathbf{ĥ^u}``). The matrix 
+``\mathbf{P̂}`` is the estimation error covariance of `model` state augmented with the 
+stochastic ones. Three keyword arguments specify its initial value with ``\mathbf{P̂}_{-1}(0) = 
 \mathrm{diag}\{ \mathbf{P}(0), \mathbf{P_{int_{u}}}(0), \mathbf{P_{int_{ym}}}(0) \}``. The 
 initial state estimate ``\mathbf{x̂}_{-1}(0)`` can be manually specified with [`setstate!`](@ref).
 

src/estimator/mhe/construct.jl

@@ -318,9 +318,9 @@ MovingHorizonEstimator estimator with a sample time Ts = 10.0 s, Ipopt optimizer
     ``\mathbf{x̂_i}`` can be manually specified with [`setstate!`](@ref), or automatically 
     with [`initstate!`](@ref) for [`LinModel`](@ref). Note the MHE with ``p=0`` is slightly
     inconsistent with all the other estimators here. It interprets the initial values as
-    ``\mathbf{x̂_i} = \mathbf{x̂}_{-1}(-1)`` and  ``\mathbf{P̂_i} = \mathbf{P̂}_{-1}(-1)``, that 
-    is, an *a posteriori* estimate[^2] from the last time step. The MHE with ``p=1`` is
-    consistent, interpreting them as  ``\mathbf{x̂_i} = \mathbf{x̂}_{-1}(0)`` and
+    ``\mathbf{x̂_i} = \mathbf{x̂}_{-1}(-1)`` and  ``\mathbf{P̂_i} = \mathbf{P̂}_{-1}(-1)``, an 
+    *a posteriori* estimate[^2] from the last time step. The MHE with ``p=1`` is consistent,
+    interpreting them as  ``\mathbf{x̂_i} = \mathbf{x̂}_{-1}(0)`` and
     ``\mathbf{P̂_i} = \mathbf{P̂}_{-1}(0)``.
 
     [^2]: M. Hovd (2012), "A Note On The Smoothing Formulation Of Moving Horizon Estimation",