Vertical Protection Level Equations for Dual Frequency SBAS

The L1-only Satellite-Based Augmentation System (SBAS) Minimum Operational Performance Standards (MOPS) were developed long before any SBASs were certified for operation. During the development and certification of the Wide Area Augmentation System (WAAS), it was discovered that the zero-mean Gaussian basis of the Vertical Protection Level (VPL) equation was not strictly true for some error sources, and very difficult to sufficiently demonstrate for others. The actual data collected in support of system performance demonstrated non-Gaussian behavior. Further, sources of small uncorrectable biases were discovered after the original MOPS development. These biases can arise from consistent, minor differences in the signal structure from one satellite to another. Antenna biases at the satellite, at the reference stations, and at the user are other possible sources of these biases. Because the MOPS VPL equation is based upon zero-mean Gaussian error combination, much additional work was required to demonstrate that the actual errors could be sufficiently protected safely. Some performance is lost because the system has to implement conservative approaches to account for these discrepancies. The advent of dual frequency SBAS affords the opportunity to revisit the MOPS and use different approaches for this new class of user. Lessons learned from the L1-only system certification and operation can be leveraged to both ease development of the future dual frequency system and improve user performance. This paper examines the VPL equations and proposes changes to directly address these lessons. The handling of nonGaussian behavior and small biases directly address both goals. The VPL can be further changed to directly address the threats that most limit availability. Without the corrupting influence of the ionosphere, satellite faults become the dominant source of significant error. New VPL equations are proposed to specifically account for individual satellite fault modes. This paper will demonstrate that by avoiding overly conservative steps required to handle all possible cases, the users will see reduced protection levels and higher availability. INTRODUCTION The Global Positioning System (GPS) is in the process of adding new civil signals [1] [2] [3]. These new civil signals include a second frequency in a protected Aeronautical Radio Navigation Services (ARNS) band that may be used to guide aircraft. The incorporation of this new signal into Satellite-Based Augmentation Systems (SBAS), such as the Federal Aviation Administration’s (FAA) Wide Area Augmentation System (WAAS) [4] [5], allows for greatly expanded service and capabilities. Most importantly, the largest source of uncertainty affecting the accuracy and integrity of the system can be directly observed and eliminated in the aircraft. This allows for better levels of service within the existing coverage region and expansion of coverage beyond where the reference station network can adequately monitor the ionosphere. The addition of a new frequency also provides an opportunity to broadcast a new set of SBAS corrections that can take a different approach than was used on the legacy L1 correction signal. Thus, lessons learned from implementation of the L1-only SBASs can be applied to the development of the L5 correction signal to support L1/L5 signals. The original integrity approach was based upon a simple notion that the actual error distributions would be close to Gaussian and that as they were convolved together the resulting positioning errors would also be close to Gaussian. Although this notion is correct, the small departures from ideal behavior led to challenges in following this approach precisely. In order to protect against non-Gaussian behavior, new approaches were developed to create safe confidence bounding terms to broadcast to the user [6] [7]. However, these approaches usually impose conservative constraints that restrict availability more than necessary. In addition, some of the analyses are cumbersome and time-consuming. A more direct approach could improve availability and simplify the certification of the system. Previously, it has been suggested to incorporate small nominal bias terms into the computation of the positioning bound [8] [9]. This paper goes even further, changing the protection level computation to specifically model the known fault modes. The resulting proposal has similarities to other satellite navigation integrity schemes, borrowing elements from the Ground-Based Augmentation System (GBAS) [10], Advanced Receiver Autonomous Integrity Monitoring (ARAIM) [11] [12] [13], and the Galileo Safety-of-Life (SoL) approach [14]. The paper begins by discussing the relative merits of an L1/L5 solution in the aircraft compared to the existing L1-only method. Next we review the L1-only integrity equation and the benefit of adding nominal biases. We then develop the new protection level approach based upon the expected fault modes. The paper then examines a previous study on the accuracy of the existing L1-only system to develop models for the expected accuracy of the future L1/L5 system. These models are used to compare the improvement offered by the proposed changes relative to a more conventional L1/L5 implementation of the existing scheme. Finally conclusions and recommendations are provided. THE UTILITY OF L1/L5 IN THE AIRCRAFT GPS satellites originally only offered one civil signal at the GPS L1 frequency (1575.42 MHz). Fortunately this falls in an ARNS band and may be used for civil aviation. It has already been incorporated into several systems to provide guidance to aircraft [15] [5] [10]. Two additional civil frequencies are starting to be added to the GPS satellites. L2 (1227 MHz) is further along, but is not in an ARNS band and may not be used for aviation. L5 has only just started to be implemented but is in an ARNS band and may be used for aircraft guidance. The main advantage of having two signals at two distinct frequencies is that the range error caused by the ionosphere may now be directly estimated and removed. The ionosphere is the largest source of uncertainty for single-frequency GPS-based aircraft navigation. Often, the ionospheric delay is small and smoothly varying. However there can be disturbances that create significant variations over time and/or space. L1-only systems must account for this risk as they assess the potential bounds on position errors. L1/L5 systems are not vulnerable to this uncertainty and can form smaller bounds around the possible positioning error. Table 1 highlights this advantage. The table also identifies a disadvantage with this approach. The ionosphere-free combination of signals increases the dependency on both the L1 and L5 signal errors. Although the combination eliminates dependence on ionospheric delay error and keeps the same dependence on tropospheric and satellite clock and ephemeris errors, other L1 only errors such as multipath are multiplied by 2.26 and L5 only errors are multiplied by 1.26. Thus, if the same level of multipath exists on L1 and L5 the overall contribution is increased to 2.6 times that of L1only. We will show this to be a poor trade most of the time, in that the nominal ionosphere accuracy of the WAAS Iono error Clock / ephemeris Tropo error L1 error L5 error RSS