Spatial-Temporal Statistical Approaches to Problems in Command and Control

Spatial statistical research in Command and Control (C2) at The Ohio State University is currently focused on the estimation and prediction of danger. To facilitate this task, researchers began by modeling the battlespace, using the hierarchical design illustrated below. With this hierarchy in place, the types of available data and then the nature of danger was examined. Simultaneously, an object-oriented battle-simulation program was developed to provide test data for analysis.

Data for C2 Decisions

Observed data are almost certainly noisy and perhaps compromised due to temporal or spatial censoring, location-based error, or false data provided by the enemy. One source of data might include the observed locations of an enemy weapon, reported using several different sensors. It is assumed that the data are reported in Cartesian coordinates with statistical error distributed according to their relative polar coordinates.

Danger Potential

The Danger Potential, generated by a single weapon element at a fixed and known location, is the expected damage at any location. Though danger potential currently focuses on the potential damage posed by enemy weapons, additional hazards, such as terrain features, can be factored into more complicated versions of danger potential.

If the conditional distribution of the impact location given a specified target location and the location of the firing weapon element is known, the danger-potential field is well defined. If a closed-form representation for the danger-potential field cannot be found, Monte Carlo integration can be used to estimate the field. Usually the location of the firing weapon is unknown and has to be estimated. Given the observations, there are two approaches: ‘plug-in’ and Bayesian; we explore both.

Evolving danger potential posed by five tanks; animation sequence repeats. Based on Irwin, M.E., Cressie, N., and Johannesson, G. (2002). Spatial-temporal nonlinear filtering based on hierarchical statistical models. Test 11, 249-302.

General Spatial-Temporal Approach

Our spatial-temporal statistical approach allows flexibility of questions that might be answered using the data. One might consider the locations of a set of weapons, the danger potential posed by a particular battle space, or the answers to specific questions, such as, “How often are enemy weapons within 10 miles of the border?”, or “Does the danger posed to friendly regions appear to be increasing significantly over time?” All of these questions are non-linear and thus techniques such as Kalman filtering are non-optimal. That is, standard target tracking can give biased answers to these questions.

Object-Oriented Battle Simulation

In order to provide test data for our research, we developed a battle-simulation program in the interpreting, object-oriented language, R. The simulation consists of an outer loop, which loops through time, and an inner loop, which loops through the military constituents. The inner loop has steps that scan the battlespace, make decisions for the military constituents, move military constituents, evaluate any attacks made by military constituents, and update any attributes changed during the current time loop.

As illustrated above, the military constituents can be divided into multiple classes. Similarly, each class defined can have multiple elements. Some classes of elements include sensors that observe the location of constituents (within range) with error, weapons that shoot at a given target with error, and commanders that choose waypoints and weapon targets. Each of these elements has functions in the object-oriented code associated with them. These functions define how the particular tasks are completed.

Selected Papers:

• Wendt DA, Cressie N, and Johannesson G (2001). A spatial-temporal approach to Command and Control problems in battle-space digitization, in Battlepace Digitization and Network-Centric Warfare, ed. R. Suresh. Society of Photo-Optical Instrumentation Engineers (SPIE) Proceedings, Vol. 439, SPIE, Bellingham, WA, 232 - 243. Abstract
  
  
• Irwin ME, Cressie N, and Johannesson G (2002). Spatial-temporal nonlinear filtering based on hierarchical statistical models (with discussion). Test, 11:249-302.

This research is supported by the Computational Decision Making Program of the Office of Naval Research.

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Last modified: Monday, December 10, 2007 11:55 AM.