Optimizing Performance Through Constellation Management
Paul Massatt and Wayne Brady
Deciding where to put the GPS satellites is no easy task. Research at Aerospace has been instrumental in answering the fundamental questions of constellation management: how many, how high, how close, and how long.
The configuration of the Global Positioning System (GPS) has always represented a compromise between user needs, budgetary constraints, and technical feasibility. The constellation has evolved to reflect changing requirements and program support, but the overriding management goal has never changed: to provide the most functional system for the broadest class of users, given a limited amount of resources. In pursuit of this goal, the GPS community must continually ask where to place satellites to best meet current and future needs. Research at The Aerospace Corporation has been essential in helping to answer that question.
Initial Proposals
The 24 primary satellites in the GPS constellation orbit Earth at an altitude of roughly 20,000 kilometers, circling the planet twice a day with precisely repeating ground tracks. Each of the six orbital planes, inclined 55 degrees relative to the equator and evenly spaced around Earth, contains at least four satellites, and some contain an additional spare satellite.
A 24-satellite baseline constellation was first proposed in the late 1970s. Various studies indicated that three orbital planes each containing eight satellites uniformly spaced 45 degrees apart would meet initial requirements most efficiently. The inclination was set at 55 degrees, and the orbital period was set at 11 hours, 58 minutes (to support repeating ground tracks). The three orbital planes would be perpendicular to one another and equally spaced around the equator. The in-orbit phasing between adjacent planes would be offset by 30 degrees as measured from the point where they crossed the equator.
The baseline GPS constellation consists of 24 satellites in six inclined planes, providing continuous fourfold (or better) coverage across the globe. |
Highly symmetrical configurations such as this are known as uniform constellations. The satellites are evenly distributed within the orbital planes, and the orbital planes are equally offset from each other. Early GPS models focused on uniform constellations because they provide the most satellite visibility on a global scale; however, uniform constellations do not always provide the best geometry, which ultimately determines receiver accuracy.
Nonuniform constellations were also considered—particularly after funding cuts forced the GPS program to move from 24 planned satellites down to 18. Aerospace conducted extensive analyses of satellite failure effects and determined that a three-plane constellation would achieve the broadest coverage possible with the 18 budgeted satellites. In fact, this nonuniform three-plane constellation could provide greater coverage than a uniform three-plane constellation.
Nonetheless, concern over the impact of satellite failures prompted a decision to support an 18-satellite, six-plane uniform constellation. Even this configuration, though, would result in a band of degraded accuracy that could last as long as one hour per day in the latitudes 30–40 degrees north and south of the equator.
Early Launches
Despite these planning efforts, no satellites were launched into any of these constellations. The first satellites were actually launched into two orbital planes with 120-degree separation at the equator. This arrangement was chosen because it could serve as the basis for either a three-plane or a six-plane constellation. Seven more Block I satellites were ultimately launched into a nonuniform constellation. The goal was to provide maximum coverage over Yuma, Arizona, where most of the early testing took place. The Block I satellites had a 63-degree inclination, which would provide better global coverage than a 55-degree inclination in case a six-plane constellation was adopted.
In the early 1980s, the United States decided to use the space shuttle as its principal launch source, and GPS was reconfigured for launch on this new platform. To accommodate new launch constraints, the inclination of the constellation was decreased to 55 degrees.
In early 1986, the space shuttle Challenger's solid rocket booster exploded during liftoff, prompting the GPS program to reassess its launch strategy. Consequently, the decision was made to switch from shuttle launches to Delta booster launches, and this switch caused a three-year delay in launching Block II satellites.
Shortly after the Challenger explosion, one of the Block I satellites failed. The Air Force was concerned that another satellite—the oldest on orbit—might also fail, eliminating any testing coverage at Yuma. Aerospace analysts examined the potential for moving different satellites to improve coverage. Researchers developed optimization techniques to determine the best arrangement for all satellites and the benefits that could be attained by moving only one or a few satellites.
The analysis revealed that one large maneuver would ensure three hours of daily testing coverage over Yuma even if the oldest satellite failed and five hours if it survived until the next block of satellites could be launched. This one large maneuver was coupled with a delay of station-keeping maneuvers for several other satellites to let them drift naturally into better locations. This event shows why simulations of coverage are often pessimistic: Most simulations assume that spares will only be moved within their existing slots when primary satellites fail. In actuality, if failures occur that are likely to have a long-term impact on GPS coverage, satellites will probably be moved wherever they're needed to improve the situation.
Spares and Pairs
While the GPS program office was transitioning to the initial 18-satellite target, Aerospace performed optimization studies to determine whether the three planned spares could be integrated more fully into the overall design to provide global coverage. Researchers began by studying the nature of the bands of degraded accuracy experienced with the 18-satellite, six-plane uniform constellation. Analysis showed that the degraded accuracy was produced at locations and times when only four satellites were visible. Moreover, it appeared that the high degree of symmetry inherent in the uniform constellation was in fact part of the problem. By carefully characterizing all of the regions of degraded accuracy, Aerospace determined that nonuniform fivefold coverage could be provided over the affected regions by substituting three satellites with three pairs of satellites. A small movement of two additional satellites enhanced the coverage even more.
While this strategy would prevent complete outages, it did not improve accuracy as much as desired; in fact, several regions would still experience substandard performance. Hence, Aerospace began searching for a way to optimize local performance.
Several obstacles had to be overcome before an optimization algorithm could be developed. For example, the methods generally used to evaluate coverage over the whole Earth throughout the course of a day relied on point-by-point evaluation over an extensive space-time grid. In addition, GPS receivers only locked onto four satellites at a time, so every combination of four satellites had to be examined individually. This method was cumbersome and slow. To optimize performance, one had to evaluate coverage over the large grid while also trying to determine how much to move the satellites, methodically repositioning each one and assessing its impact on performance. Moreover, the procedure required multiple iterations.
Researchers quickly realized that an optimum could not be achieved through traditional point-by-point grid evaluations. A breakthrough came when they applied new analytical methods using newly improved software. These changes considerably increased the efficiency of each objective function evaluation. They also allowed researchers to compute the effect of changing satellite locations more quickly. Rather than look at the effect of moving the satellites one at a time, they could track the satellites involved at the start and end of each period of degraded accuracy and analyze the effect of changing just those satellites. With these software efficiencies in place, optimization became much more feasible.
Gearing Up
The Aerospace analysis generated a nonuniform 21-satellite, six-plane constellation that had practically no degraded accuracy or severe drops in performance. The new constellation was also deemed more robust than the existing one, meaning it would perform better in case any satellites unexpectedly failed. Raising the inclination angle to 60 degrees or higher did not seem to impart any significant advantage, and considering that launch constraints made such a change difficult anyway, the inclination was preserved at 55 degrees. The Air Force approved the 21-satellite constellation as the new baseline and instructed the GPS Joint Program Office to implement it as soon as possible.
At the same time, the Air Force made clear that the ultimate goal for GPS was a 24-satellite constellation, and this was to be implemented as soon as funding permitted. Therefore, the program office needed to develop a 24-satellite constellation based on the 21-satellite plan. Fortunately, the program office had anticipated this need, and even before the Air Force authorized the 21-satellite constellation, Aerospace was already investigating the optimal 24-satellite constellation and developing a transition plan.
Computationally, this was not an easy task. The objective for the 24-satellite constellation was to maintain as much coverage as possible in the event of unexpected satellite failures. To find a local optimum, researchers would have to consider the failure of each of the 24 satellites individually. In addition, the larger constellation presented two to three times as many satellite combinations for each function evaluation.
Researchers tried to narrow their options as much as possible. For example, they decided to stick with the six-plane constellation because moving individual satellites from one orbital plane to another would require an extremely large amount of fuel. Also, they decided to focus on uniform constellations because the high degree of symmetry for such constellations favors strong global coverage. Still, these initial studies failed to provide a useful result. The best six-plane uniform constellation suffered significant losses of accuracy whenever a single satellite failed. In fact, coverage with a single satellite failure was not much better than that afforded by the 21-satellite constellation.
Aerospace analyzed the conditions that produced the poor accuracy and discovered that they all occurred with six satellites visible; however, the extremely regular and symmetric arrangement of the satellites actually prevented accurate ranging. It became clear that a uniform constellation might not be the best bet. While uniform constellations are effective at maximizing the number of satellites in view to users, they are not always effective at providing the best geometry to minimize position-estimate errors. Thus, unable to find a good six-plane uniform constellation, researchers began looking for a nonuniform alternative.
Several nonuniform arrangements were evaluated to see which one would provide the best coverage in case a number of satellites (up to three) failed. The best was a constellation based on the 18-satellite, six-plane uniform constellation—but in this case, certain satellites were replaced by pairs of satellites located close to each other (roughly 30 degrees apart on the same orbital plane). Once a robust initial configuration was found, Aerospace analysts migrated its modeling software to a Cray supercomputer, with modifications to take advantage of the Cray's pipeline processing capabilities.
Through this intensive modeling, the 24-satellite six-plane constellation was optimized to provide as much coverage as possible in the event of a single satellite failure. But although the optimization reduced the outages experienced with failures, it did not eliminate them all. The Air Force considered availability more important than small improvements in accuracy, so the constellation was optimized again to emphasize assured service over ultimate precision. With the redesigned constellation, the degradation in accuracy experienced during satellite failures was less severe. Moreover, overall performance after a satellite failure would not be significantly worse than with previous optimizations. As a matter of fact, the ranging error for the Block I satellites was less than half the initial specification, so the net accuracy provided by the new constellation was still better than the accuracy for which the system was originally built. In addition, the constellation showed little sensitivity to satellite drift.
Launch and Management
The GPS program office targeted initial Block II launches to enhance coverage over Yuma (to facilitate testing). After the success of the first few launches, remaining launches were targeted to improve global coverage as quickly as possible, with the exception that after Iraq invaded Kuwait, one launch was altered to provide better coverage over the Persian Gulf.
Midway through the buildup of the 21-satellite constellation, the Defense Department determined that GPS had the resources to support a 24-satellite constellation. This decision was based upon the strong performance shown by the Block I satellites (exceeding lifetime expectations by a factor of two) and the strong performance of the Delta launch booster. Realizing that many more satellites would have to be moved if the transition were conducted after full deployment, the program office began the transition to the 24-satellite constellation midway through the launch schedule. This action fulfilled the Air Force directive to implement a 24-satellite constellation as soon as funding permitted. The Pentagon reviewed the decision and consequently decided to support not only the 24-satellite constellation but also enough spares to ensure that the constellation size never fell below 24.
The GPS constellation has grown more robust over time (see sidebar). |
Spare satellites were not launched until the primary satellites had aged enough to present a strong probability of failure. When the risk of failure was deemed great enough, spares were launched into whichever orbital plane held the greatest risk of not maintaining four satellites. Each spare was positioned within the orbital plane in the location that provided the greatest increase to the robustness of the constellation. The availability of a large and robust constellation, coupled with the rarity of any satellite failure, allowed GPS to provide nearly continuous global coverage from the completion of the constellation in 1994 until the present.
When the initial GPS constellation was deployed, it was managed without a specific coverage requirement. Consequently, all constellation design and management decisions were based on the need to achieve optimal performance within reasonable operational loads and cost constraints. Eventually, a requirement was imposed for global coverage 98 percent of the time with a reasonable level of accuracy. The requirement was based on the amount of coverage that could be maintained if a worst-case failure of two satellites occurred during conditions of the worst potential satellite drift. In actuality, most users would regard this coverage as unacceptable, so the requirement therefore did not change the management philosophy of striving to achieve the best coverage and robustness at all times within the stipulated budgetary constraints.
To date, users of GPS have not experienced the significant loss of coverage that was predicted in early failure and replacement models. Few failures have occurred, and the satellites have lasted much longer than originally expected. Still, the longevity of the GPS satellites has produced some unique problems. For example, in a few instances, when aging satellites failed, spare satellites were relocated to replace them. Afterward, engineers successfully revitalized the failed satellites, so the repositioned spares no longer contributed to the robustness of the constellation as strongly as they had earlier. In addition, the orbits of the aging satellites have migrated significantly from their ideal positions, which further erodes robustness.
Such migration within the orbital planes was expected, but the predicted impact was considered small compared to the predicted impact of complete satellite failures. In actuality, with satellites lasting much longer than expected, the impact has been greater than originally expected. Finally, the lack of satellite failures has created an unrealistic expectation by users that global coverage will continue at the same level that it has in the past—although this is like expecting an old car to experience no more mechanical problems than a new car.
Requirements and Demands
Recently, the aging of the constellation did permit a small outage lasting 15–20 minutes that repeated daily over portions of Texas and Oklahoma. While this outage was small compared to what one would expect under steady-state operation of the constellation (when failures and launches occur at roughly the same rate), the region that was affected did not consider it small at all. Concern over the outage and its impact on civil transportation systems prompted officials to reposition one of the older satellites and retarget a launch to ensure uninterrupted service over the affected area.
This incident clearly demonstrates the dichotomy that has developed between user expectations and design objectives. GPS was not designed to provide continuous, uninterrupted global coverage. While global coverage has always been an objective, it has been pursued only within the limits of budgetary constraints.
For example, the size of the constellation was adopted to balance user demands for maximum coverage against government demands to constrain cost. If global coverage were the only goal, then a larger constellation could have been built. The difference in expectations between the users and builders of GPS stems from the shift in the predominant user community from military to civilian. When GPS is tied to civilian requirements, any outages quickly become intolerable. The mushrooming demand for GPS is rapidly placing greater priority on the desire for guaranteed uninterrupted service; it remains to be seen whether future funding and improvements in constellation replenishment and management strategies will satisfy this desire.
The GPS satellites are growing old and more prone to failure. User expectations have been built upon the service provided by a very robust constellation of relatively young satellites. As satellites age, failures should occur roughly in proportion to their replenishment rate, approximately two to three times per year. Failures will also occur at nonuniform rates, with some years seeing no failures and some years seeing several. Maintaining coverage during the replenishment cycle will be challenging.
Consequently, Aerospace conducted a new study to determine whether a larger constellation with greater robustness could be implemented, using allocated spare satellites directly in its structure to decrease dependence upon replacements. From this study, Aerospace devised a 27-satellite constellation, and the program office has since repositioned certain satellites to facilitate the transition. The 27-satellite constellation has five satellites in every other orbital plane—two paired and one isolated. The constellation can be maintained so that the most critical slot in each orbital plane always contains a strong healthy satellite with low risk of failure.
This strategy should alleviate the need for quick replacement of satellite failures via on-orbit spares. It should also reduce the desire to deal with every potential failure by launching a spare, and thus help minimize replenishment costs. The new constellation was optimized for best coverage with failures using the same criteria applied to the existing constellation. It was also examined carefully for its performance with two failed satellites. The new constellation is not expected to redress all the issues regarding the imbalance between user expectations and program funding, but it should alleviate some of the problems.
New Studies and New Capabilities
GPS is currently reviewing all requirements, satellite designs, constellation designs, and constellation management strategies with the intent of providing a better system that can be launched between 2009 and 2020. Constellation management issues are especially important when one starts to compare different numbers of orbit planes. For example, in a six-plane constellation, it is better to fly a large constellation without spares rather than a small constellation with spares because failures are unpredictable and the number of spares required to cover all orbit planes is costly. Spares can be used to advantage in a three-plane constellation, however, if they can be equipped with the ability to rapidly replace failed satellites. A large constellation without spares reduces the sudden impact of failed satellites, while a small constellation with spares can restore full constellation service faster.
Comparisons of three- and six-plane constellations are difficult because they are managed differently. In addition, the likely cost of the long transition between constellations (roughly 12–15 years, or the lifetime of the satellites) must be carefully weighed along with an assessment of the transition's impact on performance. Many other issues need to be examined, such as the ability to expand the constellation to meet increasing user demands and the ability to defend against hostile threats. These analyses will require computation several orders of magnitude greater than before.
Aerospace is exploring other constellation management issues as well (see sidebar, How High Should They Fly?). For example, when is it better to preemptively reposition satellites to maintain healthy units in critical constellation slots? If a satellite fails and cannot be replaced quickly, does it make sense to move another satellite to improve the constellation's coverage or robustness? Should satellite drift be controlled by keeping satellites within specified tolerances, by assessing the impact to coverage, or by changing the altitude of the constellation? How do different constellations compare when appropriate management strategies for each are considered?
While increases in user requirements are likely to spur the demand for more satellites, the ability to meet that demand in a cost-constrained environment will require careful engineering. Fortunately, new hardware and software efficiencies are permitting Aerospace to achieve computational efficiency significantly better than before. This will greatly boost the ability to analyze new requirements and compare both constellations and constellation management schemes. Thus, the confluence of governmental budgetary constraints, user demand, and engineering capability should continue to determine the optimal configuration of the GPS constellation.
To Summer 2002 Table of Contents
