Validation of the Unfaulted Error Bounds for ARAIM

Abstract

This paper examines how to evaluate observed instantaneous signal-in-space errors and determine suitable upper bounds on their likely distribution. We compare this performance against the commitments and broadcast values from the satellites to determine whether the provided values are sufficient or not. An important aspect is to characterize the errors in light of known or predictable characteristics. Oftentimes, errors are grouped together to create a single averaged distribution. However, there may be times and conditions where performance is notably worse. We need to separate out such conditions and evaluate the distributions individually so as not to form overly optimistic estimates of the error bounds. Further, we must ensure that these parameters will continue to bound future fault-free behavior. We will describe the conservative steps taken in the estimation process and the validation effort, both with the real data and versus the stated commitments from the constellation service providers.

Impact of sample correlation on SISRE overbound for ARAIM

“…Consequently, it can be stated that core distribution parameters reach fixed values for monitoring periods of 6-8 months. As pointed out in Perea et al 6 and Walter et al, 7 note that the largest RMS values correspond to the two Cs-equipped block IIF GPS satellites (SVN65 and SVN72) which show particularly less temporal variability with respect to the rest of the Rb-equipped satellites. As can be inferred, the onboard clock type has a pivotal role in the error correlation and sample independence for GPS satellites.…”

“…In addition, the work in Perea et al indicated that GPS clock errors presented a correlation time of 10‐12 hours whereas orbit errors show longer correlation time with 12‐h periodic components. Those findings were later corroborated by Stanford University in Walter et al Given the high correlation of the data, it becomes clear that SISRE characterization based on service history gets more cumbersome for new constellations where less data is available. The work presented in this paper takes a step forward and analyzes the effect of error correlation in SISRE bounding for GPS and Galileo.…”

“…As the monitoring period increases, mean errors reduce to values on the order of reference products accuracy. As pointed out in both Perea et al 6 and Walter et al, 7 during the first weeks of operations, some GPS satellites show abnormally large errors that are not representative of the satellite's performance after that period. To also illustrate the variability on SISRE dispersion, Figure 2 includes the SISRE worst user location root mean square (RMS) values on a monthly basis.…”

“…This statement has also been supported by Walter et al in his previous study. 7 In case permanent biases are observed in the range error due to clock and ephemeris error, it can be attributed to a misalignment in the reference APC between Broadcast Ephemeris and reference data ( Table 1). Our allegations are based on the findings in our previous work 6 and the prior section:…”

Gaussian‐Pareto overbounding of DGNSS pseudoranges from CORS

“…EVT can mitigate these problems by separating the modeling of the core of an error distribution (which is often approximately Gaussian) from the tails (which are often heavy‐tailed). For example, this type of error data was observed recently in bounding certain error models in advanced receiver autonomous integrity monitoring (ARAIM) . The idea of separating the core and tails was first proposed in Rife et al The authors' prior research into EVT was primarily concerned with assessing the ability of current EVT methods to compute tail overbounds that are truly conservative.…”