Sensor Footprint Approximation in HLA DDM
The High Level Architecture (HLA) is a set of architecture and infrastructure standards for distributed simulation. The HLA Data Distribution Management (DDM) services filter the simulation data received by the federates in a federation based on the federates' data subscriptions. Those subscriptions are declared as axis-parallel rectangular regions in a multi-dimensional coordinate space. A common scheme for using DDM is to define a coordinate space corresponding to the geographical area of the scenario wherein subscription regions are axis-parallel rectangles enclosing the simulated entities' sensor footprints. Because sensor footprints are typically shapes other than axis-parallel rectangles, subscription rectangles enclosing them will likely include areas not in the sensor footprint. That extra area can result in unwanted data being delivered to the federate, in an amount proportional to the amount of additional area.
CMSA analyzed the extra area that results when a sensor footprint is approximated by an axis-parallel subscription rectangle for nine sensor footprint shapes. For all but one of the sensor footprint shapes, the area of the smallest possible enclosing subscription rectangle depends on the orientation of the sensor footprint, so their areas were calculated as averages over all orientations. The ratio of the area enclosed by the subscription rectangle to the area of the sensor footprint ranged approximately from 1 to 8 for typical sensor footprint size parameters and could be much larger.
Defining the enclosing DDM subscription rectangle to be as small as possible so as to minimize its area, and thus the unwanted data, has the consequence that the location, shape, and area of the subscription rectangle are dependent on the orientation of the sensor footprint. A change to the orientation of the sensor may necessitate changing the corresponding subscription rectangle, even if the footprint shape does not change. To avoid this overhead associated with the "minimum" approach, some federates instead use a "maximum" approach, wherein the subscription rectangle is defined so as to be large enough to enclose the sensor footprint at all orientations. Of course, such maximum rectangles are larger than minimum rectangles, which are themselves larger than the sensor footprints. This extra area could result in additional unwanted data being delivered to the federate. CMSA compared the areas of the minimum and maximum subscription rectangles for nine two-dimensional sensor footprint shapes, where the areas of the minimum rectangles are averaged over all orientations. The maximum rectangle is typically around 4 times larger than the minimum rectangle and 8 times larger than the sensor footprint.
M. D. Petty, "Approximating Sensor Footprints with DDM Rectangles: Circles, Sectors, and Non-Axis Parallel Rectangles", Proceedings of the Spring 2005 Simulation Interoperability Workshop, San Diego CA, April 3-8 2005, pp. 419-430.
M. D. Petty, "Approximating Sensor Footprints with HLA DDM Rectangles: Ellipses, Sectors with Semicircular Ends, and Rectangles with Semicircular Ends", Proceedings of the Fall 2005 Simulation Interoperability Workshop, Orlando FL, September 18-23 2005, pp. 151-163.
M. D. Petty, "Approximating Sensor Footprints with HLA DDM Rectangles: Lines, Quadrilaterals, and Multi-Sectors", Proceedings of the Spring 2006 Simulation Interoperability Workshop, Huntsville AL, April 2-7 2006, pp. 155-177.
M. D. Petty, "Approximating Sensor Footprints with HLA DDM Rectangles: Comparing the Maximum and Minimum Approaches", Proceedings of the Fall 2006 Simulation Interoperability Workshop, Orlando FL, September 10-15 2006, pp. 475-488.
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