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Skew-t Filter and Smoother with Improved Covariance Matrix Approximation

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Original languageEnglish
Pages (from-to)5618-5633
JournalIEEE Transactions on Signal Processing
Issue number21
Early online date13 Aug 2018
Publication statusPublished - Nov 2018
Publication typeA1 Journal article-refereed


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 GPS 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, the paper presents a study of theoretical performance bounds for the proposed algorithms.


  • Approximation algorithms, Biological system modeling, Covariance matrices, Cramer-Rao lower bound, expectation propagation, Gaussian distribution, Kalman filter, Noise measurement, robust filtering, RTS smoother, Signal processing algorithms, skew t, Smoothing methods, t-distribution, truncated normal distribution, variational Bayes

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