Orbit Determination Issue (Method of Gauss, in Escobal's text)

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SUMMARY

The discussion centers on orbit determination using MATLAB, specifically referencing the "Methods of Orbit Determination" by Escobal. The user encounters difficulties with the altitude variable H_i, which is essential for calculating the satellite's position but remains unknown due to a lack of range data. The equations provided, including G1, G2, X, Y, and Z, illustrate the user's approach to solving the problem. The user seeks clarification on the interpretation of H_i and its impact on the accuracy of the calculated vectors.

PREREQUISITES
  • Understanding of orbit determination methods, particularly angles-only techniques.
  • Familiarity with MATLAB programming and its mathematical functions.
  • Knowledge of satellite altitude measurement relative to an ellipsoid.
  • Basic grasp of spherical coordinates and their conversion to Cartesian coordinates.
NEXT STEPS
  • Research the implications of unknown altitude in orbit determination methods.
  • Learn about the Method of Gauss for orbit determination.
  • Explore Vallado's code for orbit determination and its implementation in MATLAB.
  • Investigate techniques for estimating satellite altitude without range data.
USEFUL FOR

Aerospace engineers, MATLAB programmers, and students studying orbital mechanics who are interested in practical applications of orbit determination techniques.

tjcafitz
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So I'm coding up some initial orbit determination stuff in MATLAB (for personal education; I love this stuff), and I am using 'Methods of Orbit Determination' by Escobal as a guide. I already got Vallado's code to work, now I'm just comparing other methods. I'm having an issue with one of his equations, though. Obviously, the method is angles-only, but one of the givens Escobal requires is H_i, and in his nomenclature section he says that H is the "Altitude of satellite measured normal to adopted ellipsoid". So its the altitude, which is an unknown since we don't have the orbit. I don't even have range data. Am I interpreting this part wrong? The reason I care about that variable is that my values for the X, Y, and Z vectors are off, which gives me a small slatn range value, which gives me the incorrect final value. the set of equations is:
G1(i) = a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
G2(i) = (1-f)^2*a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
X(i) = -G1(i)*cosd(phi)*cosd(theta(i)) ;
Y(i) = -G1(i)*cosd(phi)*sind(theta(i)) ;
Z(i) = -G2(i)*sind(phi) ;

Any ideas/help would be greatly appreciated.
 
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tjcafitz said:
So I'm coding up some initial orbit determination stuff in MATLAB (for personal education; I love this stuff), and I am using 'Methods of Orbit Determination' by Escobal as a guide. I already got Vallado's code to work, now I'm just comparing other methods. I'm having an issue with one of his equations, though. Obviously, the method is angles-only, but one of the givens Escobal requires is H_i, and in his nomenclature section he says that H is the "Altitude of satellite measured normal to adopted ellipsoid". So its the altitude, which is an unknown since we don't have the orbit. I don't even have range data. Am I interpreting this part wrong? The reason I care about that variable is that my values for the X, Y, and Z vectors are off, which gives me a small slatn range value, which gives me the incorrect final value. the set of equations is:
G1(i) = a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
G2(i) = (1-f)^2*a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
X(i) = -G1(i)*cosd(phi)*cosd(theta(i)) ;
Y(i) = -G1(i)*cosd(phi)*sind(theta(i)) ;
Z(i) = -G2(i)*sind(phi) ;

Any ideas/help would be greatly appreciated.
Hi!

Do you have Vallado's code maybe? I would really like to take a look at it :)
Thanks!
 

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