Linear Covariance Analysis for Head-On Target Engagements

A linear covariance simulation framework is developed and validated for a two-dimensional target engagement scenario. The scenario comprises a single interceptor equipped with an inertial navigation system aided by absolute position measurements, as well as range, angle, and range rate measurements relative to the incoming target. The interceptor uses a proportional navigation guidance law to engage the target, modeled as nominally constant velocity perturbed by Singer motion accelerations. The linear covariance framework is developed by linearizing the differential and measurement equations about the nominal trajectory, and forming an augmented system comprising truth and navigation state dispersions. In contrast with sample-based methods, the developed linear covariance framework can calculate the truth state dispersion covariance and the estimation error covariance throughout the engagement in a single run. It also provides several advantages over analysis methods such as the adjoint technique or traditional covariance analysis. The linear covariance computational efficiency is exploited to rapidly analyze a head-on target engagement problem.