EnLLVM: Ensemble Based Nonlinear Bayesian Filtering Using Linear Latent Variable Models

TL;DR

EnLLVM introduces an ensemble-based nonlinear Bayesian filtering method that efficiently handles high-dimensional systems with intractable likelihoods by leveraging linear latent variable models for fast, accurate state estimation.

Contribution

It presents a novel filtering approach using linear latent projections and Gaussian mixtures, enabling efficient real-time Bayesian filtering in complex, high-dimensional systems.

Findings

Outperforms ensemble Kalman filter in high-dimensional Lorenz system

Requires fewer simulations for accurate filtering

Achieves fast implementation without high-dimensional covariance computations

Abstract

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.