The SGP4 analytical satellite theory continues to play a key role in distributing space-object ephemeris information from generators to their users.  This is due to the very large number of space objects and the bandwidth limitations associated with transmitting precision numerical ephemeris.  The current paper explores the limitations of the SGP4 satellite theory for LEO orbits and suggests an approach that will allow end users to improve the quality of the ephemeris information that is obtained from the currently distributed SGP4 element sets.

The SGP4 satellite theory, developed by Lane and Cranford (1969), is based on the work of Brouwer (1959) on drag-free motion and that of Brouwer and Hori (1961) for the coupled motion due to the geopotential and atmospheric drag. The SGP4 theory is consistent with the knowledge of the Earth's gravitational field available at the time of Brouwer's development (O'Keefe, Eckels, and Squires, 1959).

The following decade saw several developments relevant to space operations:

Improvements in digital computing
The number of space objects
Special Perturbation orbit propagators (e.g., TRACE, GTDS, GEODYN, etc) with comprehensive perturbation models
A variety of radar and optical sensors
Algorithms and computer programs for the construction of the tesseral terms in the geopotential

In response to this situation, two approaches evolved:
Approaches that use several-day sequences of SGP4 element sets for an individual space object to improve the orbit predictions for that object
Improvements to the core satellite theory algorithms

The first approach has evolved to include hybrid, machine-learning, and neural-network approaches.

The development of improved core satellite theory algorithms is illustrated by the Draper Semi-analytical Satellite Theory (DSST). The DSST was intended to include comprehensive force models with accuracy approaching that of Special Perturbations and computational speed approaching that of General Perturbations. The DSST was based on the Generalized Method of Averaging and included separate sets of models for the mean element and short-period motions. The DSST was formulated entirely in terms of the nonsingular equinoctial orbital elements.

The GTDS Orbit Determination Program, which served as the development platform for the DSST effort, was also modified to include the Air Force Space Command General Perturbation solutions: SGP, GP4, HANDE, and SALT.  Subsequently, GTDS was further modified to include the Naval Space Command PPT2 satellite theory. Together with the existing GTDS numerical orbit propagator and the GTDS DSST semianalytical options, this gave GTDS a comprehensive set of orbit determination capabilities.

Comparisons of DSST and SGP4 led to an understanding of the errors introduced by applying SGP4 satellite theory to LEO orbit determination. Position predictions made with individual SGP4 element sets were shown to exhibit errors on the order of 1 km (Small, 1978; Herriges, 1988) due to neglecting the geopotential tesseral m-daily perturbations.

Testing of the Naval Space Command PPT2 model of satellite motion was of particular interest. Comparison testing of the DSST and PPT2 satellite theories demonstrated that the tesseral m-daily terms are the major source of unmodeled periodic motion in PPT2 for LEO (several hundred meters). This realization led the DSST developers to consider whether the DSST tesseral m-daily model could be included in a modified form of PPT2.

Numerical comparisons of the resulting PPT2-MDAILY algorithm with the DSST demonstrated that the additional errors of commission are negligible. Very high-precision, externally generated reference orbits for TOPEX and TAOS were used to demonstrate the accuracy improvement associated with PPT2-MDAILY (Cefola and Fonte, 1996).

The current paper focuses on a detailed error analysis of SGP4 performance for LEO orbits, including detailed graphical representations for the tesseral m-daily terms.  The paper also considers opportunities for the enhancement of the SGP4 theory:

inclusion of tesseral m-daily terms
inclusion of tesseral linear combination short periodic terms
inclusion of secular and long periodic terms due to the zonal harmonics that are presently unmodeled (J6 and above)

For the tesseral linear-combination short-period motion, a recursive model is already available from the DSST development. The interface between SGP4 and the tesseral terms will employ much of the capability already developed for the PPT2 tesseral m-daily theory. Inclusion of the zonal terms will be aided by the availability of a recursive form of Brouwer's core algorithms for the secular and long-periodic motion.