Wasserstein Distributionally Robust Kalman Filtering (1) (1) (1) Soroosh Shafieezadeh-Abadeh, Viet Anh Nguyen, Daniel Kuhn (2) and Peyman Mohajerin Esfahani (1) Risk Analytics and Optimization Chair, EPFL (2) Delft University of Technology Poster: AB #14
Minimum mean square error estimation Zero-sum game against nature Wasserstein distance 1
Optimal estimator Least favorable prior Structural results Result 1. Result 2. Frank-Wolfe algorithm Result 3. Analytically solvable oracle subproblem Result 4. Guaranteed convergence speed Image source: Jaggi, ICML (2013) 2
Classical Kalman filter state estimate observation system update predict nominal prior: 3
Distributionally robust Kalman filter state estimate observation system update predict Least favorable prior: nominal prior: solve SDP via Frank-Wolfe algorithm 4
Numerical results MMSE estimation Frank-Wolfe algorithm Kalman filtering Robustness reduces regret Empirical convergence speed Wasserstein filter displays: Lowest steady-state error Fastest convergence POSTER: AB #14 5
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