Ballistic Missile Boost Phase Acceleration Reconstruction using Wavelet Multi-resolution Analysis

In recent years, the accurate characterization of the boost phase of a missile's flight has become a more challenging and prominent research topic as the noise level is extremely large relative to the quantity of interest. Reconstructing the boost phase acceleration profile of a ballistic missile from state observation is of interest to the technical intelligence community, ballistic missile defense, as well as the missile warning community. There are methods available such as Tikhonov regularization if the noise level is not too large. However, if the noise environment is very high most algorithms will perform poorly. In this paper, we explore the problem of estimating the thrust of a missile from very noisy estimates of its position over time by using wavelet techniques. Several wavelet basis functions and multi-resolution methods are explored to yield the most effective solution to this problem. These techniques have been successfully used on actual rocket-launch data in the past. Our method can be applied to US boost-phase missile defense such as protection of US homeland against nuclear attacks, other weapons of mass destructions or conventional ballistic missile attacks, military bases, and protecting US allies and partners.