Numerical Gaussian process Kalman filtering
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Numerical Gaussian processes have recently been developed to handle spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the well established recursive Kalman filter equations. This enables us to do Kalman filtering for infinite-dimensional systems with Gaussian processes. This is possible because i) we are obtaining a linear model from numerical Gaussian processes, and ii) the states of which are by definition Gaussian distributed random variables. Convenient properties of the numerical GPKF are that no spatial discretization is necessary, and setting up of the Kalman filter, namely the process and measurement noise levels, need not be fine-tuned by hand, as they are hyper-parameters of the Gaussian process and learned online on the data stream. We showcase the capability of the numerical GPKF in a simulation study of a heterogeneous cell population displaying cell-to-cell variability in cell size.
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