I have an objective function for finding out the signal estimate say $\parallel X_{cap}-X\parallel_2^2 +$ denoising term. Can someone suggest me any techniques on how to incorporate a filter such as Kalman filter as an addend to this objective function in place of denoising term since the output of the filter is vector and the objective function has all scalar terms (since we are taking norm).
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$\begingroup$ The question isn't clear. What's the model, what's the input and what are yo after? $\endgroup$– RoyiFeb 26, 2022 at 7:55
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$\begingroup$ The model is for estimating X_cap (signal to be reconstructed). Say we have an optimization problem L such that the error is minimised. I want to incorporate the filtering (Kalman filter) in that objective function itself. I have tried using the filter after the optimization. Is there any way to apply the Kalman filter like total variation (norm 1 ) $\endgroup$– budding_scholarFeb 26, 2022 at 9:46
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$\begingroup$ Are you after the formulation of the optimization problem the Kalman Filter solves? $\endgroup$– RoyiFeb 26, 2022 at 12:14
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$\begingroup$ I want to include kalman filter as a optimization problem $\endgroup$– budding_scholarFeb 27, 2022 at 4:27
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$\begingroup$ What do you mean? The Kalman Filter has only a single formulation as optimization problem. $\endgroup$– RoyiFeb 27, 2022 at 4:29
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