Minimalist multiple target tracking using directional sensor beams

Abstract

Abstract-We consider the problem of determining the paths of multiple, unpredictable moving bodies in a cluttered environment using weak detection sensors that provide simple crossing information. Each sensor is a beam that, when broken, provides the direction of the crossing (one bit) and nothing else. Using a simple network of beams, the individual paths are separated and reconstructed as well as possible, up to combinatorial information about the route taken. In this setup, simple filtering algorithms are introduced, and a low-cost hardware implementation that demonstrates the practicality of the approach is shown. The results may apply in settings such as verification of multirobot system execution, surveillance and security, and unobtrusive behavioral monitoring for wildlife and the elderly.

Observability of Lattice Graphs

“…, j t are t distinct roots of the equation P i 1 (x) − P i 2 (x) (mod σ), which is not possible since this polynomial has degree t − 1 and at most t − 1 distinct roots. 2 Therefore, the rows i 1 and i 2 are not identical over the chosen t columns, proving that A is an orthogonal array.…”

“…Namely, an edge-colored graph is observable if the current node of an arbitrary but sufficiently long walk in the graph can be uniquely determined simply from the color sequence of the edges in the walk [7]. A fundamental problem in its own right, graph observability also models the "localization" problem in a variety of applications including monitoring, tracking, dynamical systems and control, where only partial or local information is available for tracking [1,2,4,6,9,10,11,12]. This is often the case in networks with hidden states, anonymized nodes, or information networks with minimalistic sensing: for instance, observability quantifies how little information leakage (link types) can enable precise tracking of users in anonymized networks.…”

Combinatorial filter reduction: Special cases, approximation, and fixed-parameter tractability

“…Because the sensor data and the processing are discrete, the computation power required by a robot to execute a combinatorial filter, measured both by time and by space, is generally very small. Combinatorial filters have been designed for several tasks such as navigation [9,10], target tracking [11,12], exploration [13], planning under topological constraints [14], and story validation [15,16]. Tovar, Cohen, Bobadilla,…”

Predictive Assessment and Proactive Monitoring of Struck-By Safety Hazards in Construction Sites: An Information Space Approach

“…This idea followed the concept presented in (Bobadilla et al 2011). Similar to the previous case, we represent the workspace of the construction site as ⊂ ℝ 2 with obstacles, .…”

“…We adopt a minimalist philosophy to understand information requirements to solve tasks involving moving bodies in the construction site. An example of this philosophy can be found in a system that tracks and counts moving bodies in the workspace (Bobadilla et al 2011). Instead of attempting to estimate the full physical state of the system, a smaller information space is defined where the task can be solved (LaValle 2009).…”