Semi-analytic progressive Gaussian filtering

As an alternative to Kalman filters and particle filters, recently the progressive Gaussian filter (PGF) was proposed for estimating the state of discrete-time stochastic nonlinear dynamic systems. Like Kalman filters, the estimate of the PGF is a Gaussian distribution, but like particle filters, its measurement update works directly with the likelihood function in order to avoid the inherent linearization of the Kalman filters. However, compared to particle filters, the PGF allows for much faster state estimation and circumvents the severe problem of particle degeneracy by gradually transforming its prior Gaussian distribution into a posterior one. In this paper, we further enhance the estimation quality and runtime of the PGF by proposing a semi-analytic measurement update applicable to likelihood functions that only depend on a subspace of the system state. In fact, the proposed semi-analytic measurement update is not limited to the PGF and can be used by any nonlinear state estimator as long as its state estimate is Gaussian, e.g., the Gaussian particle filter.