Engineering topics

Schiesser, Emil R.

Publications and source records attributed to Schiesser, Emil R..

3 records

NASA NTRS2000

Semi-Major Axis Knowledge and GPS Orbit Determination

In recent years spacecraft designers have increasingly sought to use onboard Global Positioning System receivers for orbit determination. The superb positioning accuracy of GPS has tended to focus more attention on the system's capability to determine the spacecraft's location at a particular epoch than on accurate orbit determination, per se. The determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. It is necessary to address semi-major axis mission requirements and the GPS receiver capability for orbital maneuver targeting and other operations that require trajectory prediction. Failure to determine semi-major axis accurately can result in a solution that may not be usable for targeting the execution of orbit adjustment and rendezvous maneuvers. Simple formulas, charts, and rules of thumb relating position, velocity, and semi-major axis are useful in design and analysis of GPS receivers for near circular orbit operations, including rendezvous and formation flying missions. Space Shuttle flights of a number of different GPS receivers, including a mix of unfiltered and filtered solution data and Standard and Precise Positioning Service modes, have been accomplished. These results indicate that semi-major axis is often not determined very accurately, due to a poor velocity solution and a lack of proper filtering to provide good radial and speed error correlation.

Carpenter, J. Russell↗

NASA NTRS2000

Semi-Major Axis Knowledge and GPS Orbit Determination

In recent years spacecraft designers have increasingly sought to use onboard Global Positioning System receivers for orbit determination. The superb positioning accuracy of GPS has tended to focus more attention on the system's capability to determine the spacecraft's location at a particular epoch than on accurate orbit determination, per se. The determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. It is necessary to address semi-major axis mission requirements and the GPS receiver capability for orbital maneuver targeting and other operations that require trajectory prediction. Failure to determine semi-major axis accurately can result in a solution that may not be usable for targeting the execution of orbit adjustment and rendezvous maneuvers. Simple formulas, charts, and rules of thumb relating position, velocity, and semi-major axis are useful in design and analysis of GPS receivers for near circular orbit operations, including rendezvous and formation flying missions. Space Shuttle flights of a number of different GPS receivers, including a mix of unfiltered and filtered solution data and Standard and Precise Positioning, Service modes, have been accomplished. These results indicate that semi-major axis is often not determined very accurately, due to a poor velocity solution and a lack of proper filtering to provide good radial and speed error correlation.

Carpenter, J. Russell↗

NASA NTRS1998

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Carpenter, J. Russell↗