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Skew-t Filter and Smoother with Improved Covariance Matrix Approximation

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Skew-t Filter and Smoother with Improved Covariance Matrix Approximation. / Nurminen, Henri; Ardeshiri, Tohid; Piche, Robert; Gustafsson, Fredrik.

In: IEEE Transactions on Signal Processing, Vol. 66, No. 21, 11.2018, p. 5618-5633.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Nurminen, H, Ardeshiri, T, Piche, R & Gustafsson, F 2018, 'Skew-t Filter and Smoother with Improved Covariance Matrix Approximation', IEEE Transactions on Signal Processing, vol. 66, no. 21, pp. 5618-5633. https://doi.org/10.1109/TSP.2018.2865434

APA

Nurminen, H., Ardeshiri, T., Piche, R., & Gustafsson, F. (2018). Skew-t Filter and Smoother with Improved Covariance Matrix Approximation. IEEE Transactions on Signal Processing, 66(21), 5618-5633. https://doi.org/10.1109/TSP.2018.2865434

Vancouver

Nurminen H, Ardeshiri T, Piche R, Gustafsson F. Skew-t Filter and Smoother with Improved Covariance Matrix Approximation. IEEE Transactions on Signal Processing. 2018 Nov;66(21):5618-5633. https://doi.org/10.1109/TSP.2018.2865434

Author

Nurminen, Henri ; Ardeshiri, Tohid ; Piche, Robert ; Gustafsson, Fredrik. / Skew-t Filter and Smoother with Improved Covariance Matrix Approximation. In: IEEE Transactions on Signal Processing. 2018 ; Vol. 66, No. 21. pp. 5618-5633.

Bibtex - Download

@article{b4a1dcaee08e41f9b5397028af323094,
title = "Skew-t Filter and Smoother with Improved Covariance Matrix Approximation",
abstract = "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.",
keywords = "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",
author = "Henri Nurminen and Tohid Ardeshiri and Robert Piche and Fredrik Gustafsson",
year = "2018",
month = "11",
doi = "10.1109/TSP.2018.2865434",
language = "English",
volume = "66",
pages = "5618--5633",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC",
number = "21",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Skew-t Filter and Smoother with Improved Covariance Matrix Approximation

AU - Nurminen, Henri

AU - Ardeshiri, Tohid

AU - Piche, Robert

AU - Gustafsson, Fredrik

PY - 2018/11

Y1 - 2018/11

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Biological system modeling

KW - Covariance matrices

KW - Cramer-Rao lower bound

KW - expectation propagation

KW - Gaussian distribution

KW - Kalman filter

KW - Noise measurement

KW - robust filtering

KW - RTS smoother

KW - Signal processing algorithms

KW - skew t

KW - Smoothing methods

KW - t-distribution

KW - truncated normal distribution

KW - variational Bayes

U2 - 10.1109/TSP.2018.2865434

DO - 10.1109/TSP.2018.2865434

M3 - Article

VL - 66

SP - 5618

EP - 5633

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 21

ER -