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{{short description|Solution to the spacecraft attitude determination problem}}{{Tone|date=June 2022}}
The '''TRIAD method''' is the earliest published algorithm for determining spacecraft attitude, which was first introduced by Harold Black in 1964.<ref>{{cite journal|last=Black|first=Harold|title=A Passive System for Determining the Attitude of a Satellite|journal=AIAA Journal|date=July 1964|volume=2|issue=7|pages=1350–1351|doi=10.2514/3.2555|bibcode = 1964AIAAJ...2.1350. }}</ref><ref>{{cite journal|last=Black|first=Harold|title=Early Developments of Transit, the Navy Navigation Satellite System|journal=Journal of Guidance, Control and Dynamics|date=July–August 1990|volume=13|issue=4|pages=577–585|doi=10.2514/3.25373|bibcode = 1990JGCD...13..577B }}</ref><ref>{{Cite journal |last=Markley |first=F. Landis |date=1999 |title=Attitude Determination Using Two Vector Measurements |url=https://www.researchgate.net/publication/4706531_Attitude_Determination_Using_Two_Vector_Measurements |journal=1999 Flight Mechanics Symposium |pages=2 |via=ResearchGate}}</ref> Given the knowledge of two vectors in the reference and body coordinates of a satellite, the TRIAD algorithm obtains the direction cosine matrix relating to both frames. Harold Black played a key role in the development of the guidance, navigation, and control of the U.S. Navy's Transit satellite system at Johns Hopkins Applied Physics Laboratories. TRIAD represented the state of practice in spacecraft attitude determination before the advent of [[Wahba's problem]].<ref>{{cite journal|last=Wahba|first=Grace|title=A Least Squares Estimate of Satellite Attitude, Problem 65.1|journal=SIAM Review|date=July 1966|pages=385–386|doi=10.1137/1008080|volume=8}}</ref> and its several optimal solutions. Covariance analysis for Black's solution was subsequently provided by Markley.<ref>{{cite journal|last=Markley|first=Landis|title=Attitude Determination Using Vector Observations: A Fast Optimal Matrix Algorithm|journal=The Journal of Astronautical Sciences|date=April–June 1993|volume=41|issue=2|pages=261–280|url=http://www.malcolmdshuster.com/FC_Markley_1993_J_FOAM_JAS_MDSscan.pdf|accessdate=April 18, 2012}}</ref>
We consider the linearly independent reference vectors <math>\vec{R}_{1}</math> and <math>\vec{R}_2 </math>. Let <math> \vec{r}_1, \vec{r}_2</math> be the corresponding measured directions of the reference unit vectors as resolved in a body fixed frame of reference. Following that, they are then related by the equations,goo goo GA Ga you little bich why are you reading Wikipedia ▼
==Summary==
▲We consider the linearly independent reference vectors <math>\vec{R}_{1}</math> and <math>\vec{R}_2 </math>. Let <math> \vec{r}_1, \vec{r}_2</math> be the corresponding measured directions of the reference unit vectors as resolved in a body fixed frame of reference. Following that, they are then related by the equations,
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