Linganisha mbinu

	Uelekezaji Sawia	Mwakilishi wa msimamo waQuaternion	Uenezaji wa SGP4 TLE
Nyanja	Sayansi ya Anga	Sayansi ya Anga	Sayansi ya Anga
Familia	Process / pipeline	Process / pipeline	Process / pipeline
Mwaka wa asili	1957	1843	1970s
Mwanzilishi	Lin-Hsiung Chu	William Hamilton (quaternions), aerospace engineers	NORAD, USAF
Aina	Guidance law	Mathematical framework	Propagation method
Chanzo asilia	Knox, W. P. (1971). On optimal proportional navigation. IEEE Transactions on Aerospace and Electronic Systems, AES-7(3), 417–426.	Shuster, M. D. (1993). A survey of attitude representations. Journal of the Astronautical Sciences, 41(4), 439–517.	Vallado, D. A., Crawford, P., Hujsa, R., & Kelso, T. S. (2006). Revisiting Spacetrack Report Number 3. In AIAA/AAS Astrodynamics Specialist Conference.
Majina mbadala	PN, PN law	quaternion representation, attitude kinematics, q-vector	SGP4, TLE propagation, simplified perturbations
Zinazohusiana	3	3	3
Muhtasari	Proportional Navigation (PN) is a guidance law that generates command accelerations proportional to the rate of change of the line-of-sight angle between a pursuer and target. Introduced by Lin-Hsiung Chu in the 1950s, it became the foundation of modern missile guidance systems. PN solves the pursuit-evasion problem by ensuring that the pursuer intercepts a moving target with minimal computational overhead.	Quaternion attitude representation is a mathematical framework for describing three-dimensional rotations using four-dimensional vectors (quaternions). Superior to Euler angles due to the absence of singularities (gimbal lock), quaternions are the standard representation in modern attitude estimation, spacecraft control, and 3D computer graphics. Quaternion kinematics elegantly expresses how attitude evolves under angular velocity measurements from gyroscopes.	SGP4 (Simplified General Perturbations 4) is a rapid orbital propagation method that predicts satellite position and velocity from Two-Line Element (TLE) sets published by NORAD. Developed in the 1970s, SGP4 accounts for atmospheric drag, gravitational perturbations, and solar radiation pressure using simplified analytical models. SGP4 is the de facto standard for space surveillance, conjunction assessment, and satellite tracking.