  Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data
volume, velocity and increasing complexity of computational models. In this
paper, we propose a novel ensemble based nonlinear Bayesian filtering approach
which only requires a small number of simulations and can be applied to
high-dimensional systems in the presence of intractable likelihood functions.
The proposed approach uses linear latent projections to estimate the joint
probability distribution between states, parameters, and observables using a
mixture of Gaussian components generated by the reconstruction error for each
ensemble member. Since it leverages the computational machinery behind linear
latent variable models, it can achieve fast implementations without the need to
compute high-dimensional sample covariance matrices. The performance of the
proposed approach is compared with the performance of ensemble Kalman filter on
a high-dimensional Lorenz nonlinear dynamical system.
