Analytical Trajectory Prediction for Intercepting Aerial Vehicles Using Proportional Navigation Guidance Law

Accurate trajectory prediction constitutes a fundamental requirement for real-time interception of incoming aerial vehicles. Conventional numerical prediction methods based on integration techniques exhibit computational inefficiency due to iterative processes and demonstrate sensitivity to uncertainties in the guidance parameter. This paper proposes an adaptive framework integrating online guidance parameter identification with analytical trajectory prediction. The investigated scenario is that an incoming aerial vehicle implementing a Proportional Navigation Guidance (PNG) law attempts to attack a stationary target. The methodology employs a hybrid architecture integrating Multiple Model Adaptive estimation (MMAE) with Extended Kalman Filter (EKF). This integrated system dynamically estimates guidance parameters through Bayesian fusion of real-time relative motion measurements, where the MMAE probabilistically weights multiple dynamic models to address target maneuver uncertainties while the EKF suppresses nonlinear measurement noise via linearization techniques. Closed-form solutions for lateral motion characteristics are derived through collision triangle simplification, enabling explicit correlation between guidance parameters and trajectory features without numerical integration. A feedback loop continuously updates trajectory predictions by incorporating optimized parameter estimates. Numerical simulations under representative engagement scenarios demonstrate significantly enhanced computational efficiency compared to conventional integration methods, while maintaining prediction accuracy across diverse maneuvering conditions and noise levels, thereby validating consistent performance against initial state variations. This research establishes theoretical foundations and delivers practical solutions for next-generation interception systems demanding real-time adaptability.