VSE: Variational state estimation of complex model-free process

TL;DR

This paper introduces a variational state estimation method using RNNs to estimate the states of complex, model-free dynamical processes from noisy measurements, demonstrated on a Lorenz system.

Contribution

The paper presents a novel variational RNN-based approach for state estimation of complex, model-free processes with closed-form Gaussian posteriors, improving computational efficiency.

Findings

VSE provides accurate state estimates for the Lorenz system.

VSE is competitive with particle filters and data-driven methods.

The method is computationally simple during inference.

Abstract

We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have a suitable physics-based model characterizing the temporal evolution of the process state. The closed-form Gaussian posterior is provided by a recurrent neural network (RNN). The use of RNN is computationally simple in the inference phase. For learning the RNN, an additional RNN is used in the learning phase. Both RNNs help each other learn better based on variational inference principles. The VSE is demonstrated for a tracking application - state estimation of a stochastic Lorenz system (a benchmark process) using a 2-D camera measurement model. The VSE is shown to be competitive against a particle filter that knows the Lorenz system model and a recently proposed data-driven state estimation method that does not know the Lorenz system model.