Optimal state estimation with measurements corrupted by Laplace noise

F Farokhi; J Milosevic; H Sandberg

Conference Proceedings

Optimal state estimation with measurements corrupted by Laplace noise

F Farokhi, J Milosevic, H Sandberg

2016 IEEE 55th Conference on Decision and Control (CDC) | IEEE | Published : 2016

DOI: 10.1109/CDC.2016.7798286

Abstract

Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, ..

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University of Melbourne Researchers

Farhad Farokhi Author

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Grants

Awarded by McKenzie Fellowship, ARC

Funding Acknowledgements

[ "The work of F. Farokhi was supported by a McKenzie Fellowship, ARC grant LP130100605, an early career grant from the Melbourne School of Engineering.", "The work of H. Sandberg and J. Milosevic was supported by the Swedish Civil Contingencies Agency through the CERCES project." ]