iDANSE: Iterative Data-driven Nonlinear State Estimation of Model-free Hidden Sequences

Abstract

We introduce a model-free hidden sequence (MHS) estimation problem where the task is to estimate a long sequence of ‘model-free’ process hidden under additive Gaussian noise. To estimate the posterior of the hidden sequence from the noisy observation sequence, we have three main challenges: (a) the process is ‘model-free’, that means there is no underlying state-space-model (SSM), limiting the use of traditional SSM-informed model-based methods like Kalman filter (KF) and particle filter (PF); (b) only an unlabelled dataset comprised of noisy observation sequences is available as training data, and hence no supervised learning possible; and, (c) the use of sequential ancestral sampling based methods, like dynamical variational autoencoders (DVAEs), results in prohibitive complexity. To address the challenges we adopt a recently established recurrent neural network (RNN)-based method called DANSE (data-driven nonlinear state estimation). We develop an iterative DANSE (iDANSE) in unsupervised learning setup where a set of neural networks (NNs) are used iteratively. The set of NNs refines MHS estimation over the iterations. Using simulations, the performance of iDANSE is demonstrated for a benchmark Lorenz process (a chaotic attractor) and compared with SSM-informed extended KF (EKF) and unscented KF (UKF).