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In this work, a distributionally robust Kalman filter is presented to addressuncertainty in noise covariance matrices and predicted covariance estimates. Weadopt a minimax formulation using bi-causal optimal transport to characterize aset of plausible alternative models. The optimization problem is transformedinto a convex nonlinear semi-definite programming problem and solved using thetrust-region interior point method with the aid of $LDL^\top$ decomposition.The empirical outperformance of our bi-causal framework is demonstrated throughtarget tracking and pairs trading.

Distributionally robust Kalman filtering with volatility uncertainty