Effects of Full Order Geopotential Hessian on Precision Orbit Determination of Geodetic Satellites

Successful satellite operations often depend on the ability to precisely determine the satellite’s position throughout it’s operational lifetime. Often, simplified models are used to reduce the computational complexity when producing an orbit determination solution. One example is the use of lower order gravitational terms when computing the state transition matrix. The US Naval Research Laboratory’s Orbit Covariance Estimation and Analysis software is used to characterize the affects of using the full order geopotential terms when calculating the state transition matrix. Orbit solutions are calculated for several geodetic satellite using satellite laser ranging data. The RMS of the error residual and number of iterations needed for convergence are used as metric to evaluate the difference of using the full order geopotential to calculate the state transition matrix. It is found that typically the RMS error is the same when the higher order gravitational terms are used; however, the number of iterations needed for convergence are often lower. Additionally, the difference in the orbit solution between both methods is examined. Surprisingly, these orbit solutions may differ by up to several meters. This indicates that the higher order gravitational terms should always be considered when calculating the state transition matrix. Because fewer iterations are often needed, this can result in an overall decrease in computational time required.