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Initial Orbit Determination (Least Squares Method)

version (17.4 MB) by Meysam Mahooti
Initial orbit determination applying Least Squares method


Updated 16 Mar 2020

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For computation of orbital elements at the epoch, a large number of measurements including azimuth,elevation and range are gathered at tracking stations.
Here, I have used 46 sets of GEOS3 satellite measurements for initial orbit determination. First of all, initial guess of satellite's state vector is computed from three sets of azimuth and elevation applying Double-R-Iteration/Gauss method. Then, the state vector is propagated from epoch to the times of all measurements in an iterative procedure and the epoch's state vector is corrected at each stage.

Cite As

Meysam Mahooti (2020). Initial Orbit Determination (Least Squares Method) (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (9)

Murat Bulut

It is interesting that Gauss first used his method of least squares for determining the orbit of Ceres.


Hello Mr. Mahooti,
I would like to know why are you integrating VarEqn from [0 t] which corresponds to [Mjd_UTC, 2*Mjd_UTC - Mjd0]. (Line 221 of test_LSQ_GEOS3.m).


Hello Mr. Meysam Mahooti

Did you compare the accuracy of the results to the Orbit Determination Toolbox (ODTBX)?

thank you

Demi Moore


Revised on March 16, 2020.

Documentation is added.

ECI to ECEF transformation is updated based on IAU 2006 Resolution.

Revised on 2016-11-21.

The image is added.

MATLAB Release Compatibility
Created with R2019b
Compatible with any release
Platform Compatibility
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