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.