Probabilistic BMC4I Algorithms for Modeling BMD Uncertainties

A key component of any ballistic missile defense system is the decision architecture of what to intercept, where to intercept, when to intercept and which weapon system to use. The key pieces of information that drive the decision as to the "what", "where", and "when" are: (1) what is the threat (its lethality and what does it threaten); and (2) what is the probability of kill. To this end, a key building block is Probabilistic Battle Space Analysis (PBSA). The focus of this effort determines the shot opportunities for various firing doctrines, representing BMD errors into a mean and covariance of Single Shot Probability of Kill. Battle Space Analysis is a key component of MD C2BMC. In Phase I we developed a preliminary algorithmic architecture to determine Probabilistic Battle Space, including robust estimates of Pkill. Our algorithmic and software architecture is modular and designed to probabilistically accommodate constraints of various weapon systems. In Phase II we will develop the algorithmic detailed design and prototype software to Technology Readiness Level 5 (or 6). There are uncertainties and ambiguities in the knowledge, information and data used to plan a missile defense engagement, such as the treat state vector. Existing missile defense systems base their engagement decisions primarily on mean parameter values such as threat state vectors, without systematically taking into consideration the associated uncertainties. Decisions that do not consistently handle the stochastic nature of the engagement can be overly optimistic or overly pessimistic in their estimate of probability of kill. Based on significant lessons learned it was found that considering the effect of these uncertainties when planning engagements can significantly enhance the overall effectiveness of a BMD system. While the many-on-many engagement problem is key for real-time Battle Management, the proper formulation and solution of the one-on-one engagement problem is the core building block. Our study focused on the probabilistic formulation and solution of the one-on-one engagement problem, systematically taking into account uncertainties and errors. We are in the process of modeling knowledge representations and developing probabilistic behavior models that realistically represent the ballistic missile battle space for use in high performance and high effectiveness, global maximization of P-kill over all of battle space engagement decision algorithms. The representation of the one-on-one engagement problem is to roll up all uncertainties into Single Shot Probability of Kill (SSPK) with its `mean' and `distribution' in multi-dimensional space, and plan engagements in optimal P-kill `volumes' in this multi-dimensional space. The GMD and KEI POs have endorsed our study, and we intend to develop core and generic capabilities in Probabilistic Battle Space Analysis during the Phase II Basic Contract that can be modified and tailored for GMD and KEI specific issues. We propose an additional Option 1 Contract to address some of the key and generic PBSA issues in Midcourse MD, and an Option 2 Contract to address generic PBSA issues in Boost Phase MD, avoiding specific design issues of GMD and KEI. The Phase II implementation will focus on algorithmic methods that efficiently compute the effects of key MD uncertainties on potential engagements. Our objective is to develop detailed algorithms and tools in a spiral, evolutionary manner for potential insertion into BMDS block upgrades and for use in other domains, focusing on missile/air defense applications in Phase II. We intend to extend our approach to non-DoD government applications and to private sector commercial markets in Phase III.