Particle-based Data-driven Nonlinear State Estimation of Model-free Process from Nonlinear Measurements

We consider the problem of causal filtering of a model-free process from (noisy) nonlinear measurements. The 'model-free process' means that we do not have a state-space model (SSM) of the process dynamics, limiting the use of traditional model-driven filters, such as unscented Kalman filter (UKF) and particle filter (PF). To address the problem we propose a particle-based data-driven nonlinear state estimation (pDANSE) method. In pDANSE, a recurrent neural network (RNN) provides the statistical parameters of a Gaussian prior of the underlying state, and particles are then drawn from the prior to compute the posterior moments. pDANSE is typically trained in a semi-supervised fashion. For our experiments we study the use of half-wave rectification as a nonlinear transformation of measurements. We first show that an unsupervised learning-based method under-performs, and subsequently the semi-supervised learning-based pDANSE performs satisfactorily. Using Lorenz-63 system as benchmark, pDANSE is found to be competitive against a model-driven PF that knows the exact SSM.