State tracking of linear ensembles via optimal mass transport
This work addresses the problem of tracking indistinguishable agents for control systems researchers, offering a novel theoretical framework but with limited practical validation.
The paper tackles state estimation for linear ensembles of indistinguishable agents using optimal mass transport, formulating it as a convex optimization problem for general distributions and as semidefinite programming for Gaussian marginals, enabling efficient tracking for large state dimensions.
We consider the problems of tracking an ensemble of indistinguishable agents with linear dynamics based only on output measurements. In this setting, the dynamics of the agents can be modeled by distribution flows in the state space and the measurements correspond to distributions in the output space. In this paper we formulate the corresponding state estimation problem using optimal mass transport theory with prior linear dynamics, and the optimal solution gives an estimate of the state trajectories of the ensemble. For general distributions of systems this can be formulated as a convex optimization problem which is computationally feasible with when the number of state dimensions is low. In the case where the marginal distributions are Gaussian, the problem is reformulated as a semidefinite programming and can be efficiently solved for tracking systems with a large number of states.