DNS: Data-driven Nonlinear Smoother for Complex Model-free Process
This addresses the challenge of state estimation in complex systems without known dynamics, which is incremental as it builds on prior data-driven smoothers.
The authors tackled the problem of estimating hidden state sequences from noisy linear measurements in complex model-free dynamical processes, achieving significantly better performance than existing methods like deep Kalman smoother and iDANSE smoother in simulations, including on a benchmark Lorenz system.
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.