Sampled Observability and State Estimation of Linear Discrete Ensembles

State Tracking of Linear Ensembles via Optimal Mass Transport

“…An alternative approach would be testing all associations between measurements and particles, but this would require a combinatorial search which grows exponentially in T . Yet another possible approach for addressing this problem is to use heuristics along the lines of K-means clustering, as proposed in [21].…”

“…In particular we consider the tracking problems where we seek to estimate the states of several identical and indistinguishable systems from only their joint outputs. This is also known as state estimation of ensembles, see [22], [21]. One of the main obstacles is that it is not known which output that is generated by a certain subsystem, hence an association problem has to be solved.…”

Sample-based population observers

“…V. THE DISCRETE ENSEMBLE OBSERVABILITY PROBLEM Our proposed solution for the observer design of continuous ensembles in the foregoing sections also yields direct implications for the discrete version of the ensemble observability problem [14]. In this closely related, but significantly different discrete setup, we consider a fixed number of N systems and at each time step, the N corresponding outputs are measured, however, in an anonymized fashion, i.e.…”

“…In [14] we aimed to address the multitarget tracking problem from a more conceptual and theoretical point of view. In anticipation of a unification of the discrete and the continuous frameworks developed in [9], in [14], the problem was already formulated using the framework of discrete measures. This formulation will now indeed serve as a bridge by which different insights about the computational problem from the continuous case can be immediately applied to the discrete case as well.…”

“…The same line of thoughts centered around the questions of controllability and observability are recently being investigated in relation to a new class of systems, consisting of populations of dynamical systems of the same structure with a given distribution in their states [4], [5], [6], [7], [8], [9], [10]. While a classical system can be thought of as a single point particle evolving in state-space (following the combined effect of a drift and a control vector field), for a population comprised of a large number of dynamical system, the point describing the state of the system would be replaced by a (probability) distribution of points, as suggested in Figure 1.…”