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

AI Thread Summary
The discussion revolves around an orbit determination issue using the Method of Gauss as outlined in Escobal's text. The user is coding in MATLAB and has successfully implemented Vallado's code but is struggling with Escobal's equation due to the unknown altitude variable H_i, which is essential for calculating the X, Y, and Z vectors. The user seeks clarification on whether their interpretation of the altitude requirement is correct, given that they lack range data. The incorrect values for the position vectors are leading to an inaccurate slant range value. Assistance is requested to resolve these issues and improve the coding process.
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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