Estimation of potential field environments from heterogeneous behaviour of sensing agents

This paper proposes a novel modelling framework for estimating the global potential field from trajectories of multiple sensing agents whose perception of the unknown field is subject to abrupt changes. We derive a parametrised formulation of the estimation problem by combining the jump Markov non-linear system (JMNLS) model of agent dynamics with a basis function decomposition of the environmental field. An approximate expectation-maximisation algorithm is employed for joint estimation of the global field and of the agent behavioural modes from observed agent trajectories. To avoid prohibitive computational costs associated with the state estimation of JMNLS, we utilise two approximation steps. First, an interacting multiple model smoother is used to account for the hybrid structure that emerges in this problem. Second, we propose two approaches to approximating the non-linear sufficient statistics during the expectation step. This results in the maximization step being exact. The performance of the developed framework is tested on simulation examples and demonstrated on an application study in which the observed movement patterns of immune cells are utilised in quantifying the underlying chemical concentration field that governs their migration. The results showcase that the proposed framework can be readily applied to problems where agents assume several behavioural modes.