diff --git a/src/estimator/mhe/construct.jl b/src/estimator/mhe/construct.jl
index a01208d66..176f8a19b 100644
--- a/src/estimator/mhe/construct.jl
+++ b/src/estimator/mhe/construct.jl
@@ -2,11 +2,7 @@ const DEFAULT_LINMHE_OPTIMIZER    = OSQP.MathOptInterfaceOSQP.Optimizer
 const DEFAULT_NONLINMHE_OPTIMIZER = optimizer_with_attributes(Ipopt.Optimizer,"sb"=>"yes")
 const DEFAULT_NONLINMHE_GRADIENT  = AutoForwardDiff()
 const DEFAULT_NONLINMHE_JACOBIAN  = AutoForwardDiff()
-const DEFAULT_NONLINMHE_HESSIAN   = AutoSparse(
-    AutoForwardDiff();
-    sparsity_detector=TracerSparsityDetector(),
-    coloring_algorithm=GreedyColoringAlgorithm(ALL_COLORING_ORDERS, postprocessing=true),
-) 
+const DEFAULT_NONLINMHE_HESSIAN   = AutoForwardDiff()
 
 @doc raw"""
 Include all the data for the constraints of [`MovingHorizonEstimator`](@ref).
@@ -449,27 +445,6 @@ MovingHorizonEstimator estimator with a sample time Ts = 10.0 s:
       for common mistakes when writing these functions. Also, an [`UnscentedKalmanFilter`](@ref)
       estimates the arrival covariance by default.
 
-    One exception about AD: the selected backend for the Hessian of the Lagrangian function
-    with `hessian=true` options is sparse:
-    ```julia
-    AutoSparse(
-        AutoForwardDiff(); 
-        sparsity_detector  = TracerSparsityDetector(), 
-        coloring_algorithm = GreedyColoringAlgorithm(
-            (
-                NaturalOrder(),
-                LargestFirst(),
-                SmallestLast(),
-                IncidenceDegree(),
-                DynamicLargestFirst(),
-                RandomOrder(StableRNG(0), 0)
-            ), 
-        postprocessing = true
-        )
-    )
-    ```
-    that is, it will test many coloring orders at preparation and keep the best. 
-
     Note that if `Cwt≠Inf`, the attribute `nlp_scaling_max_gradient` of `Ipopt` is set to 
     `10/Cwt` (if not already set), to scale the small values of ``ε``. Use the second
     constructor to specify the arrival covariance estimation method.