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Robust data association is critical for analysis of long-term motion trajectories in complex scenes. In its absence, trajectory precision suffers due to periods of kinematic ambiguity degrading the quality of follow-on analysis. Common optimization-based approaches often neglect uncertainty quantification arising from these events. Consequently, we propose the Joint Posterior Tracker (JPT), a Bayesian multi-object tracking algorithm that robustly reasons over the posterior of associations and trajectories. Novel, permutation-based proposals are crafted for exploration of posterior modes that correspond to plausible association hypotheses. JPT exhibits more accurate uncertainty representation of data associations with superior performance on standard metrics when compared to existing baselines. We also show the utility of JPT applied to automatic scheduling of user-in-the-loop annotations for improved trajectory quality.

The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem has a unique, sparse solution. Here each row of A comprises one experiment consisting of input/output measurements and cannot be freely chosen. We show that if experiments are poorly designed, the rank condition may never be satisfied, resulting in multiple solutions. We discuss experimental strategies for designing experiments such that the sensing matrix has the desired properties and the problem is therefore well posed. This formulation allows prior knowledge to be taken into account in the form of known nonzero entries of x, requiring fewer experiments to be performed. A number of simulated examples are given to illustrate the approach, which provides a useful strategy commensurate with the type of experiments and measurements available to biologists. We also confirm suggested limitations on the use of convex relaxations for the efficient solution of this problem., Comment: 10 pages, preprint submitted to Automatica