  This work presents a distributionally robust Kalman filter to address
uncertainties in noise covariance matrices and predicted covariance estimates.
We adopt a distributionally robust formulation using bicausal optimal transport
to characterize a set of plausible alternative models. The optimization problem
is transformed into a convex nonlinear semi-definite programming problem and
solved using the trust-region interior point method with the aid of $LDL^\top$
decomposition. The empirical outperformance is demonstrated through target
tracking and pairs trading.
