Orbit Determination and Satellite Navigation

The Maui Space Surveillance Site, located at the summit of Mount Haleakala, Hawaii, is a state-of-the-art electro-optical facility supporting both the Air Force Maui Optical Station and a Ground-based Electro-optical Deep Space Surveillance (GEODSS) sensor suite. Data from this and other sites are used to compute the orbits of objects of foreign or unknown origin. (U.S. Air Force)

Orbit Determination and Satellite Navigation

John Langer, Thomas Powell, and John Cox

The Global Positioning System is remarkably precise in determining a user's location. But before these satellites can help anyone else, they first need to know their own positions and movements. Orbit determination is the branch of space science that makes such knowledge possible.

For centuries, astronomers, physicists, and mathematicians have sought to predict the motion of celestial bodies. It was not until the late 1950s, however, with the launches of the Sputnik and Vanguard satellites, that the modern discipline of orbit determination was born. This new field differed from traditional astronomy in three essential ways. First, it typically tracked satellites via radiometric techniques, rather than via telescopes. Second, it focused on Earth-centered orbits, rather than orbits around the sun or distant planets. Third, it relied on intensive numerical calculations, rather than estimates and heuristics.

The science progressed quickly in its formative years, thanks to the rapid advances in computing technology that accompanied the early space race. Such developments finally made it possible to solve (in a reasonable amount of time) the computationally intensive equations that govern orbital motion. Much of the early work focused on generating better ephemerides—timetables of satellite speed and trajectory. Large computers would calculate the complex equations of motion to generate these tables, and the results would be compared with actual radio measurements from tracking stations. The comparison would reveal ways to improve the underlying algorithms, gradually increasing the precision of the orbital predictions (see sidebar, Sensor Systems for Satellite Tracking).

Today, The Aerospace Corporation plays a prominent role in the science of orbit determination, along with the related fields of orbit reconstruction and orbit prediction. Techniques developed by the company continue to set the standard for researchers across the globe, and new advances promise to keep Aerospace at the forefront of the field.

TRACE

Aerospace involvement in orbit determination extends back to 1961. The U.S. military space effort was well underway by this time, and the Air Force Satellite Control Network (AFSCN) already included a master control station in Sunnyvale, California, and nine S-band (1.7–2.3 gigahertz) tracking stations positioned across the globe. It was at this time that Aerospace engineers began developing an orbit determination and analysis program called TRACE.

Aerospace used a TRACE-based analysis tool to develop an optimal orbit-determination strategy for Radcal. The tool enabled analysts to simulate the effects of various measurement and force model errors. Aerospace used the same tool to develop the operational GPS-based orbit-determination system. (View larger image.)

TRACE was unique in that it was not designed for any one mission or application; rather, it provided a configurable, general scheme for modeling a wide array of orbits, orbital missions, and tracking networks—including AFSCN. It also possessed an error-analysis capability that enabled orbit planners to evaluate hypothetical scenarios and optimize tracking schedules accordingly.

TRACE became a standard tool in the industry and was used to prototype many early operational systems. In fact, TRACE-based analysis contributed to the orbit-determination design for most major U.S. military and intelligence satellite systems (see sidebar, Precision Modeling for Orbit Determination). The software has been under continuous development and enhancement for more than 40 years, and is still one of the few standards employed industrywide.

Traditional Approaches

Aerospace used its TRACE software to develop key concepts for the Defense Satellite Program (DSP), which provides military surveillance, and Milstar, which provides secure communications. The nature of these two constellations presented various challenges for planners and operators alike.

For example, researchers found that the accuracy of the DSP ephemeris could be enhanced by a reduction in the latency period of its distributed orbit-vector estimates. They achieved this by processing the tracking data and estimating the orbit in real time. In that way, the current orbit elements can be distributed at a frequency driven by the frequency of tracking data collection—nominally four to six times per day. Of course, a real-time orbit estimator presents a more difficult technical problem than the standard "least-squares" estimator. Noise and other unpredictable error sources can derail a real-time orbit estimator, and these need to be filtered out.

Aerospace developed a sequential filter that estimates the orbit of DSP satellites in real time. It's a prototype of a system that can provide accurate short-term predictive ephemerides on demand while also allowing autonomous orbit determination—meaning it can respond to changes in orbits or orbital measurements without human intervention. When proven, it will significantly reduce the operational cost of systems for generating highly accurate orbit estimations and ephemerides. The technology is also used to support launches of geosynchronous satellites, providing real-time estimates of launch-vehicle trajectory.

Milstar navigation requirements are based on the need for antenna maneuverability, signal timing accuracy, and system autonomy. To achieve system autonomy, Milstar uses its communication links to measure both range and satellite clock-time offsets relative to a master clock. The measured ranges from ground terminals and from other satellites are used to estimate a satellite's orbit using software based on TRACE.

Milstar's innovative use of communication links for orbit estimation and timekeeping required numerous analyses and continuous evaluation by Aerospace. The system performs well, and assuming a successful test of the recently launched Flight 5, will achieve global communications coverage.

Determining GPS Orbits

Navigation around the world has been dramatically changed by the Global Positioning System (GPS), and the power of this system is derived first and foremost from the orbit-determination process that drives it. After all, without a way to pinpoint the locations of the GPS satellites, users—who determine their positions relative to the GPS satellites—would quite literally be lost.

Tracking data from Air Force stations are used to compute GPS orbits

Tracking data from six Air Force monitoring stations are used to compute GPS orbits. Additional NIMA tracking stations may be added to the GPS ground network in the future.

The GPS operational control segment collects tracking measurements at five (soon to be six) monitoring stations around the world. This information is transferred to a central processing facility in Colorado Springs. There, the data are processed via a Kalman filter, a device that estimates the GPS orbits and biases in the onboard atomic clocks. These estimates are then used to form "navigation messages," which are uploaded to the appropriate GPS satellites, which in turn transmit them to every GPS receiver in range. The navigation messages indicate where the satellites are so users can determine their position relative to them.

Aerospace was involved in the initial design, acquisition, and deployment of the GPS operational control segment, prototyping many of the algorithms in TRACE. Aerospace modeling and simulation led to a better understanding of GPS, and to numerous improvements.

For example, the fundamental performance metric for GPS is called user range error—a numerical value that describes errors in the estimates of GPS satellite position and onboard clock biases. Combined with information about the relative arrangement or geometry of the GPS satellites in view, user range error can help predict the accuracy of a GPS receiver's position, velocity, and time computation. In 1990, the specification for user range error was set at 6 meters. Continuous improvements to the GPS satellites and the operational control segment—made possible in part by Aerospace simulations—have effectively reduced the user range error from the initial target of 6 meters to approximately 2 meters today.

Improving GPS Orbits

The GPS operational control segment monitors the performance of the system, but has few resources for investigating and proposing improvements. This task is left to various GPS-related working groups. Acting in concert with these groups, Aerospace has played a key role in several initiatives:

Reduced Age-Of-Data. A major error source in the user range error is the "age" of the navigation message. Errors caused by orbital deviations tend to accumulate over time, so the GPS user will experience the greatest accuracy just after a navigation message upload, and the least accuracy just before. Originally, navigation messages were uploaded once per day, with additional uploads made whenever user range error was found to exceed its maximum allowable value. Over the years, however, error requirements have grown more stringent, necessitating better performance monitoring and more frequent uploads, particularly for "problem" GPS satellites deemed to have a higher risk or history of error. More frequent uploads, in turn, have significantly reduced the extent of user range errors.

Improved Satellite Clock Management. Aerospace has years of operational experience developing and managing atomic clocks for GPS satellites. Aerospace data helped show that it is better to decommission an anomalous GPS clock and activate a spare than to attempt to regulate the wayward clock.

Upgraded Station Surveys. Analysis at Aerospace showed that reducing the uncertainty in the GPS tracking station locations from 1.5 to 0.1 meters would significantly improve orbit and clock estimation. New surveys were performed to describe the locations more accurately, and the updated values were installed in 1994, enhancing overall performance.

Improved "Tuning" of the Kalman Filter. Aerospace and other research groups suggested a number of slight adjustments to some of the parameters used by the Kalman filter in the operational control segment. These adjustments were made in 1997, first to the parameters that control the estimation of the onboard clock biases, then to the parameters that control the estimation of the effect of solar wind on the GPS satellite trajectories. These enhancements, once validated by the various working groups, were implemented in the operational control segment and produced immediate and significant improvements in performance (see sidebar, The Kalman Filter: Applying the Scientific Method).

Aerospace continues to analyze the operational control segment with an eye toward improvement. Aerospace is also pushing to accelerate the Accuracy Improvement Initiative, a multipronged scheme that includes a major restructuring of the operational control segment estimation software, the addition of tracking data from a number of stations provided by the National Imaging and Mapping Agency, and other updates. Aerospace analysis indicates that these improvements will bring the user range error down to about 1.3 meters.

Continued Innovation

Aerospace was among the early proponents of the Wide Area GPS Enhancement (WAGE) initiative. This scheme, currently in operational testing, exploits the fact that a number of bits in the GPS navigation message broadcast are unused. These bits could be used to provide update information not only for the GPS satellite seen by the user, but for the entire GPS constellation. This clever trick of telemetry could reduce the user range error by 15–20 percent for a suitably equipped user.

The Wide-Area GPS Enhancement initiative seeks to utilize unused bits in the GPS navigation message to provide update information for the GPS satellites. This technique of telemetry could reduce user range error by 15–20 percent for a suitably equipped user. The left graph shows user range error without enhancement, and the right graph shows the performance improvements possible through enhancement.

Aerospace prototyped a system survivability mode for GPS, called Autonav, that enables the system to perform autonomously in case a disaster or other event renders the operational control segment unusable. The GPS satellites will perform intraconstellation ranging measurements via special crosslinks. Then, using onboard processing, each satellite will compute its own orbit and clock offsets. Not only does this approach provide security against catastrophes, but it could also help improve the performance of the constellation during normal operation. As the actual Autonav capability gets phased in, Aerospace will test the system to determine its potential benefits for regular performance.

GPS-Based Orbit Determination

Until the early 1990s, all orbit determination—even for GPS—relied on Earth-based tracking and processing. Typically, a network of tracking stations would monitor a constellation and transfer the tracking information to one or more "central" processing sites, where the actual orbits would be computed. With the maturation of GPS, certain satellites—particularly those in low Earth orbit—could carry GPS receivers and compute their own positions directly. The potential cost savings makes this approach very attractive: Ground stations might still be needed for tracking, telemetry, and control, but the resource-intensive processes of scheduling, collecting, and transferring ground-based tracking data could be avoided. In addition, the Department of Defense will dramatically reduce the use of S-band for satellite tracking, potentially freeing up a significant portion of this valuable spectrum band for other uses.

Radcal demonstrated that GPS equipment can be used to generate precise orbital data

Radcal demonstrated that low-cost GPS equipment can be used to generate highly precise orbital data.

Aerospace helped develop the GPS-based orbit-determination scheme for Radcal, a radar calibration satellite deployed by the Air Force Space Test and Small Launch Vehicle program in 1993. Commissioned under an aggressive one-year contract-to-launch schedule, the satellite was chiefly designed to support calibration of the C-band radars used by the U.S. Space Launch Range. Unlike previous low-cost space missions, Radcal required precise orbit determination—accurate to 5 meters or less during radar calibration. To meet this requirement, Radcal carried a special Doppler beacon that could be tracked by a global network of tracking stations. It also carried two commercial-grade GPS receivers. These inexpensive devices were not equipped to decode the high-precision military signal known as the P(Y) code; rather, they were designed to receive the GPS Standard Positioning Service, which provided positioning accuracy on the order of 100 meters (because the signal was intentionally degraded at the time through a protocol known as selective availability).

Data from the Standard Positioning Service can be augmented in various ways to obtain greater accuracy. To determine what methods would be both sufficient and cost-effective, Aerospace researchers built a complex simulation. At the heart of the simulation was Aerospace's TRACE program, used in one mode to generate the reference trajectories and orbital conditions and in another mode to support various estimation strategies.

The simulation showed that as the GPS data-collection interval expanded, the overall orbit error decreased. Still, the effects of selective availability remained too high to ensure the necessary precision. Thus, with the assent of the GPS Joint Program Office (JPO), the Radcal researchers asked a team from the Applied Research Laboratories at the University of Texas to develop a PC-based system that would remove the effects of selective availability. The output of this system was then fed into a TRACE-based estimator built by Aerospace to produce a final orbit.

A key factor in Radcal processing was the "fit span," the length of the data interval used to compute the orbit. The effects of measurement errors decrease with a greater fit span, but the effects of force model errors increase. TRACE allowed analysts to select the optimal fit span. (View larger image)

After Radcal was launched, the GPS data were collected and processed using TRACE. Orbits derived from these data were compared to orbits derived from the accurate but substantially more expensive Doppler scheme. The on-orbit results confirmed the earlier simulation analyses: with some additional processing, GPS measurements from an inexpensive commercial receiver could be used to produce precision orbits.

Radcal was significant as Aerospace's first involvement in precise low Earth orbit reconstruction via GPS data. The analysis tools and operational experience gained from this small program have subsequently provided significant benefit to a number of major low Earth orbit programs.

Geosynchronous Altitudes

Although GPS was designed primarily for users at or near Earth's surface, a new group of users have learned how to exploit the technology in ways that its early users probably didn't imagine. These new users take advantage of the fact that GPS satellite signals are directed toward Earth in a broadcast pattern that is slightly wider than the planet. Thus, a geosynchronous spacecraft on the opposite side of Earth can, with the proper equipment, receive and process the "spillover" GPS signals (see sidebar, Tracking Geosynchronous Satellites with GPS). Spacecraft operators recognized the potential to improve their navigation accuracy at a very early stage; however, the particulars of geosynchronous orbits present some unique challenges.

For example, geosynchronous spacecraft have historically been controlled from ground stations, as have most other spacecraft; however, a geosynchronous satellite has little or no relative motion with respect to Earth's surface, making the problem of geosynchronous orbit determination somewhat more difficult. Also, a single ground station can't always be located in the best spot for tracking a geosynchronous spacecraft, and this poor observation geometry adds another level of difficulty. GPS offers the potential for both improved geometry through multiple observation points and autonomous navigation of the satellite, without ground-based tracking.

Aerospace analysts began publishing studies on the problem of navigating geosynchronous satellites with GPS in the 1970s. Key issues included requirements for link closure, advantages over ground systems, autonomous navigation and control, and even formation flying at geosynchronous altitude.

While these studies and others were based on theoretical predictions and numerical simulations, there was little actual flight experience using GPS at geosynchronous altitudes until the Falcon Gold experiment of 1997. Sponsored by the U.S. Air Force Academy, the experiment captured GPS signals in a geosynchronous transfer orbit, which reaches geosynchronous altitude at its highest point. The Falcon Gold experiment consisted of a battery-powered sensor mounted on a Centaur upper stage, which captured small snapshots of radio energy around the GPS carrier frequencies and transmitted them to the ground. Aerospace assisted the Academy by processing this raw data with a special "software GPS receiver." The detection and characterization of several GPS signals in the Falcon Gold data both validated the low-cost hardware approach and verified that GPS signals could be used by spacecraft flying above the GPS constellation.

GPS satellite signals are directed toward Earth in a broadcast pattern that is slightly wider than the planet. Thus, a geosynchronous spacecraft on the opposite side of Earth can, with the proper equipment, receive and process the "spillover" GPS signals. (View larger image.)

Introducing "Space Service"

In the past, spacecraft users of GPS—especially high-altitude spacecraft users—were not formally recognized as a class of GPS users. While the JPO was aware that many spacecraft were in fact using GPS in experimental or even operational capacities, it was unable to convince the operators of those systems to establish formal requirements like those identified for terrestrial and airborne users. Without this formal recognition from the JPO, spacecraft operators ran the risk that the JPO would modify the GPS signal in ways that would benefit terrestrial users but degrade the service to spacecraft users.

The volume of Aerospace analysis on spacecraft users of GPS, combined with the Falcon Gold results, led to the first formal recognition of spacecraft users in the Joint Requirements Oversight Council Operational Requirements Document for GPS, published in 1999. This formal recognition came with the addition of a "Space Service Volume" to the Operational Requirements Document, dedicated to high-altitude spacecraft users of GPS, which includes the region between low Earth and geosynchronous orbits.

Orbit Determination in the Future

The science of orbit determination has come a long way in 40 years. Starting from an offshoot of astronomy, it has developed into a robust, independent discipline that underlies today's most critical satellite and navigation technologies. Advances in orbit determination led to one of the most successful space programs of all time: the Global Positioning System. Interestingly, GPS itself is becoming the basis of orbit determination for a growing number of space systems—starting with the low Earth orbiting systems and extending even to the geosynchronous regime. With GPS receivers becoming ever more affordable, the odds are increasing that a GPS-based orbit-determination scheme will come along to rival or even supplant the traditional AFSCN-based approach. A global interest in freeing up portions of the valuable S-band spectrum further encourages a migration from AFSCN to GPS.

GPS isn't the only up-and-coming technology for orbit-determination. Laser tracking and optical schemes specifically for higher-altitude orbits are also drawing interest in the scientific community. These approaches promise higher accuracy, reliability, and autonomy for future space systems. Aerospace engineers continually track these emerging technologies, and the TRACE-led suite of Aerospace tools is continuously upgraded to model and analyze them. Thus, as the science of orbit determination continues to evolve, Aerospace will help set the pace and direction of further advances in the field.