State and parameter estimation using Monte Carlo evaluation of path integrals

TL;DR

This paper introduces a Monte Carlo approach to evaluate path integrals for estimating unobserved states and parameters in dynamical systems, leveraging observations to guide the estimation process.

Contribution

It presents a novel Monte Carlo method for direct numerical evaluation of conditional paths and moments in state space, incorporating observational data as guiding potentials.

Findings

Demonstrates explicit influence of observational data on state estimation

Analyzes the number of observations needed for accurate unobserved state estimation

Examines the Gaussianity assumption in the conditional probability distribution

Abstract

Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the model to direct system orbits in state space. The path integral representation permits direct numerical evaluation of the conditional mean path through the state space as well as conditional moments about this mean. Using a Monte Carlo method for selecting paths through state space we show how these moments can be evaluated and demonstrate in an interesting model system the explicit influence of the role of transfer of information from the observations. We address the question of how many observations are required to estimate the unobserved state variables, and we examine the assumptions of Gaussianity of the underlying conditional probability.