I'm a Ph.D. student working under supervision of Ondřej Straka in the Identification and Decision Making research group, Department of Cybernetics, University of West Bohemia. My research focuses on improvement of the sigma-point filtering algorithms. I work with Bayesian quadrature, which is a conceptually alternative approach to numerical integration and an instance of probabilistic numerics algorithm.

**Nonlinear filtering** is a problem of inferring an underlying signal from noisy measurements, which permeates the field of signal processing. Filters are useful for aircraft navigation, multiple target tracking, financial time series analysis, audio processing and numerous other applications.

I focus on a particular class of local filters, known as **sigma-point filters**, which are heavily reliant on the approximate numerical integration schemes, known as quadratures.

**Bayesian quadrature** treats numerical integration as statistical inference. The result of integration is not a single value, but a distribution over all possible results given the known function values. Along with the result we are also given integral variance, which is an additional piece of information having no counterpart in the classical treatment of quadrature. I aim to use this additional information for improvement of the overall filter performance. Since the integral variance depends on the covariance function parameters, the main challenge now is finding suitable parameters which provide well-calibrated uncertainties.

- [PDF] Prüher, J., Tronarp, F., Karvonen, T., Särkkä, S. & Straka, 0. (2017). Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise. (Submitted to FUSION 2017)
- [PDF] Prüher, J., & Straka, 0. (2017). Gaussian Process Quadrature Moment Transform. IEEE Transactions on Automatic Control (Submitted)
- [PDF] Prüher, J., & Särkkä, S. (2016). On the Use of Gradient Information in Gaussian Process Quadratures. Machine Learning for Signal Processing (MLSP), 2016 IEEE International Workshop on. (Best Student Paper Award)
- [DOI] Prüher, J., & Šimandl, M. (2016). Bayesian Quadrature Variance in Sigma-Point Filtering. In J. Filipe, K. Madani, O. Gusikhin, & J. Sasiadek (Eds.), Informatics in Control, Automation and Robotics 12th International Conference, ICINCO 2015 Colmar, France, July 21-23, 2015 Revised Selected Papers (pp. 355–370). Springer International Publishing.
- [URL] Prüher, J., & Šimandl, M. (2015). Bayesian Quadrature in Nonlinear Filtering. In ICINCO 2015 - 12th International Conference on Informatics in Control, Automation and Robotics (pp. 380–387).
- [DOI] Prüher, J. and Král, L. (2015). Functional Dual Adaptive Control with Recursive Gaussian Process Model, Journal of Physics: Conference Series, vol. 659, p. 12006, 2015.
- [DOI] Prüher, J., & Šimandl, M. (2014). Gaussian process based recursive system identification. In 11th European Workshop on Advanced Control and Diagnosis 2014, ACD 2014 (Vol. 570, pp. 1–9).
- [DOI] Král, L., Prüher, J., & Šimandl, M. (2014). Gaussian Process Based Dual Adaptive Control of Nonlinear Stochastic Systems. In Control and Automation (MED), 2014 22nd Mediterranean Conference on (pp. 1074–1079).