# On Nonlinearity Measuring Aspects of Stochastic Integration Filter

### Jindřich Havlík, Ondřej Straka, Jindřich Duník, Jiří Ajgl

#### Abstract

The paper deals with Bayesian state estimation of nonlinear stochastic dynamic systems. The focus is aimed at the stochastic integration filter, which is based on a stochastic integration rule. It is shown that the covariance matrix of the integration error calculated as a byproduct of the rule can be used as a measure of nonlinearity. The measure informs the user about validity of the assumptions of Gaussianity, which is adopted by the stochastic integration filter. It is also demonstrated how to use this information for a prediction of the number of remaining iterations of the rule. The paper also focuses on utilization of the integration error covariance matrix for improving estimates of the mean square error of the estimates, which is produced by the filter.

#### References

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#### Paper Citation

#### in Harvard Style

Havlík J., Straka O., Duník J. and Ajgl J. (2016). **On Nonlinearity Measuring Aspects of Stochastic Integration Filter** . In *Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-198-4, pages 353-361. DOI: 10.5220/0005983903530361

#### in Bibtex Style

@conference{icinco16,

author={Jindřich Havlík and Ondřej Straka and Jindřich Duník and Jiří Ajgl},

title={On Nonlinearity Measuring Aspects of Stochastic Integration Filter},

booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2016},

pages={353-361},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005983903530361},

isbn={978-989-758-198-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - On Nonlinearity Measuring Aspects of Stochastic Integration Filter

SN - 978-989-758-198-4

AU - Havlík J.

AU - Straka O.

AU - Duník J.

AU - Ajgl J.

PY - 2016

SP - 353

EP - 361

DO - 10.5220/0005983903530361