- Capability based TE Model - these models rank targets according to their capability index, where capability index defines the ability of the target to inflict damage to a DA. 

- Intent based TE Model - these models estimate intent of a target to calculate threat index. Intent refers to the will of a target to inflict damage to a DA. 

According to the literature, different parameters can be used to estimate the capability and intent of an identified threat for example target type, speed, direction, weapon type and envelope etcetera can be used to estimate capability of a threat while, heading (bearing and course), velocity, altitude and speed etcetera, can help predict intent of an identified threat 
[7]. Combining these two we have opportunity based threat evaluation. 

## B. Weapon Allocation (Wa)

Primitive battlefield modeling can be done using basic mathematical functions and rules. In reality, there can be N 
number of Defended Assets (DAs) having M number of Weapon systems (WSs) of different types. Each WS usually has its own lethality index, priority, rate of fire, field of fire, elevation angle and other parameters. Not all WSs have ability to neutralize every kind of threat. So, while selecting best WS 
to encounter a threat, there is a need to consider capability and suitability of each WS as applicable to each scenario. DAs too have important parameters associated with them for example each DA may have its own priority and vulnerability index. 

Based on these values different parametric values and WSs are assigned to each DA. WA corresponds to selecting the best available weapon system to neutralize a particular target i.e. 

selecting which WSs to be used to neutralize a particular target in a multi-threat scenario. [8] - [14] provide a good literature on WA problem. TEWA, being a real time system is subject to uncertainties and hard set of external constraints. Due to dynamic ever-changing environment, assignment problems might need to be re-solved, this makes scheduling problem even more complex to design and implement [7]. 

Design of WA algorithm depends on defensive strategy to be implemented i.e. the defense may either want to maximize the total expected value of the DAs, or the defense may want to minimize the total expected surviving value of the targets that survive all weapon engagements. The first approach using max function is known as preferential defense strategy while the later one is known as subtractive defense strategy [15]. According to Hosein [15], subtractive defense strategy can be seen as a special case of preferential defense strategy when numbers of threats per DA are small. If we increase the number of threats directed to each DA, subtractive defense fails. On the contrary preferential strategy is highly sensitive to uncertainty level of input data [15]. 

Execution models for WA can fall into two categories, the ones that take into account notion of time i.e. dynamic execution model and the models without the notion of time i.e. 

static models that include processes defined over a single time horizon [16]. Using dynamic approach we can make multiple engagements in stages by observing the outcomes of previous engagement before making any further engagements [17]. 

From implementation point of view each of this stage can 

![0_image_0.png](0_image_0.png)

iterate through Boyd's Observe-Orient-Decide-Act (OODA) loop [6]. Figure4 shows OODA loop for WA. 

In this section, a new two staged model of Threat Evaluation and Weapon Assignment is proposed. The assignment problem is formulated as an optimization problem with constraints and then solved by a variant of many-to-many Stable Marriage Algorithm (SMA). 

## A. Preprocessing Phase

We present a Decision Support based system, consisting of correlated threat and weapon libraries. To formulate the TEWA problem, we need the information about the kill probabilities and lethality index for each weapon-target pair. This information comes from threat and weapon libraries. Our solution is based on two way correlation between weapon and threat library. Kill probabilities and lethality index are dependent not only on threats but also on WSs and load on WSs. Threat library holds data for all possible type of threats like Ground-attack aircrafts, Fighter aircrafts, Helicopters, Interceptors, Reconnaissance, Trainer and Transport aircrafts etcetera. Weapon library on the other hand, holds data for different type of weapons in hand like Cannons, Rockets, Ground Missiles, Smart Bombs, Free Fall Bombs, and Low Level Attack Bombs etcetera. To make TE process optimal we use weapon effectiveness based threat/weapon correlation database, that defines the highest priority, most effective, weapon to counter expected threats, thus ensuring that the selected weapons have the capability to neutralize particular target, improving the cost and value of the assignment. TE and WA processes use different parameters. All these parameters have their own significance and thus can be used to make different weighted parametric equations in TE and WA 
process. To get optimal weight value for each parameter; weights can be kept configurable to see their impact in different offline scenarios. To assign values to these parameters fuzzy logic is used restricting values of parameters between 0 and 1. The solution considers one or more type of WSs possessed by a 