Distributionally robust Kalman filtering with volatility uncertainty

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 $LD{L}^{\mathrm{\top }}$ decomposition. The empirical outperformance is demonstrated through target tracking and pairs trading.