Modern 4DVarContent License: Creative Commons Attribution 4.0 International (CC-BY-4.0)Credit must be given to the creatorDownloadsBiLevel EstimationHow can I estimate the state AND the parameters?J. Emmanuel JohnsonCNRS MEOM In these examples, we willθ∗=argminθL(θ)x∗(θ)=argminθJ(x;θ)\begin{aligned} \boldsymbol{\theta}^* &= \underset{\boldsymbol{\theta}}{\text{argmin}} \hspace{2mm} \boldsymbol{L}(\boldsymbol{\theta})\\ \boldsymbol{x}^*(\boldsymbol{\theta}) &= \underset{\boldsymbol{\theta}}{\text{argmin}} \hspace{2mm} \boldsymbol{J}(\boldsymbol{x};\boldsymbol{\theta}) \end{aligned}θ∗x∗(θ)=θargminL(θ)=θargminJ(x;θ)(1)ExamplesParameter EstimationExamplesGradient Learning