Robust State Space Filtering Under Incremental Model Perturbations Subject to a Relative Entropy Tolerance

• Published in: IEEE transactions on automatic control Vol. 58; no. 3; pp. 682 - 695
• Main Authors: Levy, B. C., Nikoukhah, R.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2013; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Commitment; Covariance matrix; dynamic minimax game; Dynamics; Entropy; Estimation; Filtering; Filtration; Games; Kalman filters; Least squares method; least-favorable model; Minimax technique; myopic strategy; relative entropy; risk-sensitive filtering; robust filtering; Robustness; Studies; Tolerances; Vectors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2012.2219952

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the maximizer adopts a myopic strategy. This game is shown to admit a saddle point whose structure is characterized by applying and extending results presented earlier in "Robust least-squares estimation with a relative entropy constraint" (B. C. Levy and R. Nikoukhah, IEEE Trans. Inf. Theory, vol. 50, no. 1, 89-104, Jan. 2004) for static least-squares estimation. The resulting minimax filter takes the form of a risk-sensitive filter with a time varying risk sensitivity parameter, which depends on the tolerance bound applied to the model dynamics and observations at the corresponding time index. The least-favorable model is constructed and used to evaluate the performance of alternative filters. Simulations comparing the proposed risk-sensitive filter to a standard Kalman filter show a significant performance advantage when applied to the least-favorable model, and only a small performance loss for the nominal model.