DNS: Data-driven Nonlinear Smoother for Complex Model-free Process

TL;DR

This paper introduces DNS, a data-driven nonlinear smoother that estimates hidden states in complex, model-free dynamical processes using a recurrent architecture, outperforming existing smoothers in simulations.

Contribution

The paper presents DNS, a novel unsupervised, data-driven nonlinear smoothing method that does not require knowledge of the process dynamics and provides a closed-form posterior.

Findings

DNS outperforms deep Kalman smoother (DKS) in simulations.

DNS surpasses iDANSE in accuracy for complex processes.

Effective in smoothing Lorenz and other stochastic systems.

Abstract

We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the nonlinear dynamics of the complex process. There is no state-transition model (STM) of the process available. The proposed DNS uses a recurrent architecture that helps to provide a closed-form posterior of the hidden state sequence given the measurement sequence. DNS learns in an unsupervised manner, meaning the training dataset consists of only measurement data and no state data. We demonstrate DNS using simulations for smoothing of several stochastic dynamical processes, including a benchmark Lorenz system. Experimental results show that the DNS is significantly better than a deep Kalman smoother (DKS) and an iterative data-driven nonlinear state estimation (iDANSE) smoother.