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doc: MHE exetended help details on AD backends
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src/estimator/mhe/construct.jl

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@@ -357,10 +357,12 @@ MovingHorizonEstimator estimator with a sample time Ts = 10.0 s, Ipopt optimizer
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- If `model` is a [`LinModel`](@ref), the optimization is treated as a quadratic program
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with a time-varying Hessian, which is generally cheaper than nonlinear programming. By
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default, a [`KalmanFilter`](@ref) estimates the arrival covariance (customizable).
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- Else, a nonlinear program with automatic differentiation (AD) solves the optimization.
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Optimizers generally benefit from exact derivatives like AD. However, the `f` and `h`
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functions must be compatible with this feature. See the [`JuMP` documentation](@extref JuMP Common-mistakes-when-writing-a-user-defined-operator)
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for common mistakes when writing these functions. An [`UnscentedKalmanFilter`](@ref)
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- Else, a nonlinear program with dense [`ForwardDiff`](@extref ForwardDiff) automatic
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differentiation (AD) compute the objective and constraint derivatives by default
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(customizable). Optimizers generally benefit from exact derivatives like AD. However,
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the `f` and `h` functions must be compatible with this feature. See the
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[`JuMP` documentation](@extref JuMP Common-mistakes-when-writing-a-user-defined-operator)
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for common mistakes when writing these functions. Also, an [`UnscentedKalmanFilter`](@ref)
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estimates the arrival covariance by default.
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The slack variable ``ϵ`` relaxes the constraints if enabled, see [`setconstraint!`](@ref).

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