Wasserstein Distributionally Robust Kalman Filtering (1) (1) (1) - - PowerPoint PPT Presentation

Wasserstein Distributionally Robust Kalman Filtering

Soroosh Shafieezadeh-Abadeh, Viet Anh Nguyen, Daniel Kuhn and Peyman Mohajerin Esfahani

(1) Risk Analytics and Optimization Chair, EPFL (2) Delft University of Technology

Poster: AB #14

(1) (1) (1) (2)

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Minimum mean square error estimation Zero-sum game against nature

Wasserstein distance

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

2 Image source: Jaggi, ICML (2013)

Classical Kalman filter

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update system predict

• bservation

state estimate nominal prior:

Distributionally robust Kalman filter

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update system predict

• bservation

state estimate nominal prior: Least favorable prior: solve SDP via Frank-Wolfe algorithm

Numerical results

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POSTER: AB #14 MMSE estimation Frank-Wolfe algorithm Kalman filtering

Robustness reduces regret Wasserstein filter displays: Lowest steady-state error Fastest convergence Empirical convergence speed