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We propose and analyze a block coordinate descent proximal algorithm(BCD-prox) for simultaneous filtering and parameter estimation of ODE models.As we show on ODE systems with up to d=40 dimensions, as compared tostate-of-the-art methods, BCD-prox exhibits increased robustness (to noise,parameter initialization, and hyperparameters), decreased training times, andimproved accuracy of both filtered states and estimated parameters. We show howBCD-prox can be used with multistep numerical discretizations, and we establishconvergence of BCD-prox under hypotheses that include real systems of interest.

A Block Coordinate Descent Proximal Method for Simultaneous Filtering and Parameter Estimation