Exciting times lie ahead in the world of satellite navigation systems.
A vastly improved Global Positioning System will soon be available to the civil community, GLONASS is becoming more reliable with each passing year, and Galileo and Compass are on their way not far behind. Thus, in the near future navigation systems engineers will have more pseudorange measurements to work with than any of us would have dreamed of a decade ago.
Exciting times lie ahead in the world of satellite navigation systems.
A vastly improved Global Positioning System will soon be available to the civil community, GLONASS is becoming more reliable with each passing year, and Galileo and Compass are on their way not far behind. Thus, in the near future navigation systems engineers will have more pseudorange measurements to work with than any of us would have dreamed of a decade ago.
Given this situation, the obvious question then arises: “What shall we do with this wealth of range data?” Irrespective of accuracy considerations, this bounty of measurement redundancy can make receiver autonomous integrity monitoring — or RAIM — a more robust means of assuring system integrity — that is, of ensuring that only “healthy” GNSS signals are used in navigation and positioning solutions.
This article will address how we might most effectively accomplish this end.
Background
How could anybody write a learned technical article on something as simple as cross-comparing two independent GNSS solutions? In safety critical situations, prudent navigators have been comparing the readings of two similar instruments against each other since antiquity.
This is, of course, a qualitative concept, and a good one!
Only when we attempt to quantify the concept in terms of strict statistical requirements and instrument accuracies does the problem becomes interesting mathematically. RAIM does exactly that. It quantifies the concept of using a self-consistency check of redundant measurements to assure navigational integrity.
In this article, we describe a new variant of RAIM called Novel Integrity Optimized RAIM or NIORAIM (pronounced “nee-oh-raim”) that can be applied to enhance the availability of the consistency check. We will discuss the NIORAIM concept in detail a little later, but first let’s consider the practical considerations of working with multiple GNSS signals in the integrity domain.
The availability of alternative GNSS constellations, both in the present and future, has stirred a great deal of interest towards combining measurement information for enhanced performance. In general, the more measurements there are, the better the positioning, navigation, or timing solution. For integrity monitoring, however, other subtle considerations arise over how to combine these diverse signals and pseudoranges.
From an optimal performance standpoint, one would be inclined to simply expand the standard form of RAIM (or NIORAIM) to include all satellite measurements from multiple constellations in a centralized manner. This probably affords the best results in terms of lowest integrity limits, but this approach is also limiting in that it assumes only one satellite failure at a time; multiple failures will require special accommodation that greatly increases the complexity of the solution and degrades the performance accordingly.
In an ION GNSS 2005 paper titled “GPS and Galileo with RAIM or WAAS for Vertically Guided Approaches,” (see Additional Resources section in the full PDF version of the article, downloadable above) Y. C. Lee of Mitre and co-authors suggested that a more conservative — albeit less optimal — approach would be to do the self-consistency check at the solution level.
In describing a GPS/Galileo joint constellation, Lee proposed what is essentially a cross-compare of two independent solutions, one from GPS and the other from Galileo. In contrast to the standard, more centralized RAIM solution, Lee’s proposal is a decentralized (or federated) solution. His approach allows for multiple satellite failures to occur within one system, but only one system can have a failure or failures at any one time.
Tight accuracy/integrity applications have raised concerns about the multitude of failure types that might occur, however rarely, under seemingly “normal” conditions. The decentralized approach provides a clearer and stronger partitioning between the solutions independently derived from GPS and from Galileo.
This philosophy is not without precedent. Most aircraft systems achieve high integrity by means of producing multiple independent solutions from clearly partitioned sensors. Often, this is done with some compromise in accepting the decentralized solution as compared to the centralized one.
The purpose of this article is to pursue this decentralized approach to RAIM and analyze its performance, especially from the viewpoint of NIORAIM. In the remaining discussion, we will be using vertical position during precision approach as an example application. The numerical values used for the false alarm and missed detection rate specifications are taken from a more recent (2007) paper by Lee and M. P. McLoughlin, which is also listed in the Additional Resources section.
In our discussion, we do not intend to promote numerical values for any particular application. Rather, we consider the methodology presented here to be the important contribution of the article.
It is, however, worth mentioning that this methodology can also be applied to any two-system combination where the position parameter of interest is a scalar. For example, it would apply equally well to the along-track or cross-track integrity assurance problem (with different numerical values, of course) . . .
. . .Conclusions
A rigorous methodology has been presented for analyzing the effectiveness of NIORAIM when applied to the two-system problem, along with results comparing NIORAIM with conventional RAIM. These show that a significant reduction in VIL is obtainable for typical civil avionics integrity specifications. The improvement in VIL comes with a modest loss in rms accuracy during normal no-failure conditions, which may or may not be acceptable, depending on the situation at hand.
The authors do not mean to recommend NIORAIM for any specific application. The methodology presented here is simply offered for fair consideration along with other alternatives in any particular application. No attempt has been made here to evaluate the availability rates. This is obviously an important facet in any integrity assurance application, but we will leave it to others to address this problem.
In this article, we have explained multi-GNSS NIORAIM in terms of a two-system combination. However, the same methodology can be readily extended to situations involving even more systems, and this may prove to be of greater importance as additional systems become operational.
In such cases, the computational effort turns out to be more intensive; so, the use of a lookup table certainly becomes even more valuable. A three-system lookup table, for example, would become two-dimensional (in λ) instead of the one-dimensional lookup table shown in this paper for the two-system case.
Even though the preparation of this lookup table will be considerably more involved, the real-time operation of deriving the VIL given the associated sigmas of the three systems is expected to be quick and efficient.
(For the complete article, including figures, graphs, and additional resources, please download the PDF version at the link above. )
