A normalized weighted entropy measure for sensor allocation within simulations

Abstract

Information superiority is considered a critical capability for future joint forces. Sensor allocation and information processing are critical to achieving this information superiority but the value of information is difficult to assess. We develop a weighted entropy measure for sensor allocation within simulations by using the Dynamic Model of Situated Cognition as a framework in which to view the processing and flow of information in a complex technological-cognitive system. The entropy measure developed is normalized across each requirement and weighted according to the Commander's priorities within the phase of that operation. We develop a methodology for implementation for this normalized weighted entropy measure to allocate sensors within a combat simulation. INTRODUCTIONDecision-makers struggle with the value of information in almost all forms. Therefore, it is not surprising that the way information is valued and used within combat simulations is also difficult to represent. In this paper we propose a methodology that relies on Commander's Critical Information Requirements (CCIR) that are defined in the planning stage and are linked to phases of combat operations. We particularly do not rely on the notion of the expected value of information which requires calculation but, instead, rely on a measure of uncertainty as it relates to mission priorities, namely, the weighted entropy measure which we describe. Sensor allocation has increased in its importance as the use of sensors has increased with the proliferation of unmanned aerial vehicles, unmanned ground vehicles, unattended ground sensors and others. Methodologies such as the Assignment Scheduling Capability for Unmanned Aerial Vehicles (Ahner 2006) assigns sensors to demands but needs an external mechanism to assign the value received for a sensor-demand assignment. Sensor assets should be allocated based upon the extent that a sensor allocation reduces the uncertainty within this weighted entropy measure. Entropy, when used in the context of information, is often thought of in terms of Shannon's entropy measure which quantifies, in an expected value sense, the quality of long messages, usually in units such as bits. In this paper, we are not interested in the quality of the message but focus on the content of information as it applies to decision making. Nonetheless, we use a weighted entropy measure due to its excellent properties of measuring uncertainty of information. Barr and Sherrill (1996) explore "information gain" in a military context with the addressed primary objective appearing to be "to study relationships between information gained about the enemy disposition and various measures of combat effectiveness (Barr and Sherrill 1996)." A Bayesian update is used to update the probability of an event given the probability that a sensor detects a target. This new probability is used to calculate the new entropy. The difference in the old and new entropy is what is referred to as "information gain." Our paper improves upon this concept by normal...

Maximizing Approximately k-Submodular Functions

“…The work of [21] considered the problem of maximizing H(x x x) subject to individual size constraints for x x x, using H(x x x) to capture the uncertainty of measurements. Sensor measurements often have random noise due to hardware issues, environmental effects, and imprecision in measurement [10], and weighted entropy functions are used to capture such errors [2]. As such, we consider a noisy variant of the problem of [21], where the uncertainty of measurements is captured by a weighted function H(x x x) = ξ(x x x) • H(x x x) and ξ() is generated by our AG, MaxG, or MeanG generation method.…”

“…These applications include subset selection which is fundamental in areas such as (sequential) document summarization, sensor placement, and influence maximization [9,21]. For example, in sensor placement, the objective is to select a subset of good sensors and the approximation comes from sensors producing noisy values due to hardware issues, environmental effects, and imprecision in measurement [2,10]. In influence maximization, the objective is to select a subset of good users to start a viral marketing campaign over a social network and the approximation comes from our uncertainty about the level of influence of specific users in the social network [11,17,26].…”