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Skew-t Filter and Smoother With Improved Covariance Matrix Approximation
Tampere Univ Technol, Finland; HERE Technol, Finland.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Univ Cambridge, England.
Tampere Univ Technol, Finland.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2018 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 21, p. 5618-5633Article in journal (Refereed) Published
Abstract [en]

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation. Although the variational update is done suboptimally using an expectation propagation algorithm, our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm. Consequently, the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low-complexity alternatives in accuracy and speed. We present both simulations and tests based on real-world navigation data, in particular the global positioning system data in an urban area, to demonstrate the performance of the novel methods. Moreover, the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew-t is outlined. Finally, this paper presents a study of theoretical performance bounds for the proposed algorithms.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 66, no 21, p. 5618-5633
Keywords [en]
Skew t; t-distribution; robust filtering; Kalman filter; RTS smoother; variational Bayes; expectation propagation; truncated normal distribution; Cramer-Rao lower bound
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-152048DOI: 10.1109/TSP.2018.2865434ISI: 000446159800009OAI: oai:DiVA.org:liu-152048DiVA, id: diva2:1259452
Note

Funding Agencies|TUT Graduate School; Foundation of Nokia Corporation; Tekniikan edistamissaatio; Emil Aaltonen Foundation; Swedish research council (VR), project scalable Kalman filters

Available from: 2018-10-29 Created: 2018-10-29 Last updated: 2019-03-18

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