Scalable marginalized particle filter to improve state estimation of one-way coupled PDE systems

Abstract

Particle filtering is a popular class of methods to estimate the state of non-linear non-Gaussian state-space models in an online manner. However, in practice, their application to systems described by partial differential equations is limited due to issues of particle degeneracy in arbitrarily high dimension spaces and the prohibitively high computational cost of evaluating posteriors with direct numerical solvers. Here we use smooth transformation of prior particles into posterior, localization in which spurious correlations over large distances are suppressed, marginalize out conditionally linear-Gaussian state variables, employ a Physics-informed neural network to predict PDE solution over large time steps, and implement a cheap operator for recursive projection onto affine subspace of physical constraints. Through hardware-in-the-loop simulation testing on benchmark problem of a one-way coupled PDE system, it is validated that such an integrated framework maintains higher accuracy of the state estimates over existing methods when degree of non-linearity is increased. The efficiency and scalability of proposed framework paves way for state estimation of coupled PDE systems on embedded systems and mobile platforms.