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# RAIM Algorithms

Fundamentals | |
---|---|

Title | RAIM Algorithms |

Edited by | GMV |

Level | Basic |

Year of Publication | 2011 |

Although conventional RAIM approaches highly improve the receiver’s capacity to detect large errors, their protection levels are not able to cover all user requirements. As an example, the civil aviation community imposes more stringent alert limits whereas Liability Critical Applications rather focus on higher availabilities. Dedicated RAIM algorithms need to be considered according to the application at hand.

## Contents

## RAIM Families

Two main families can be considered:

- Measurement Rejection Approach (MRA)

MRA use Fault Detection and Exclusion (FDE) techniques to ensure that only valid measurements are used in the navigation solution and the respective protection levels computation. These techniques are suited for the civil aviation community but lead to very low solution availability in urban environments, since a large number of measurements is rejected - e.g. due to Non Line Of Sight (NLOS) multipath.

- Error Characterization Approach (ECA)

It consists on computing protection levels based on the characterization of the measurement errors; these techniques do not necessarily require FDE techniques. This approach considers the errors in Non Line Of Sight (NLOS) measurements and therefore usually leads to higher protection levels, not fulfilling the stringent civil aviation requirements. Nevertheless, solution availability is considerably higher, making these approaches strong candidates for Liability Critical Applications (LCA) especially in urban environments.

## Conventional RAIM

Key Features of traditional RAIM Algorithms:

- Basic hypothesis: only one satellite is “faulty”, probability of multiple satellite failures at the same time is considered negligible,
- Number of satellites in view determines the possibility of providing integrity,
- Protection levels size depend on satellite geometry (DOP),
- RAIM algorithms use code measurements ,
- Receivers implementing RAIM algorithms are used nowadays for aircraft Lateral Navigation (LNAV) en-route.

A few comments on the navigation integrity performance of typical RAIM algorithms:

- Integrity Risk (IR): can be adjusted to the target application by configuration,
- Protection Levels (PL): if the integrity risk is configured to 10-7 (e.g. for civil aviation), the values of Horizontal and Vertical PL - HPL and VPL respectively - are higher than the ones provided by a SBAS,
- Time To Alert (TTA): the concept of TTA is meaningless for RAIM algorithms. If the fault detection mechanism (step 1 mentioned above) detects any failure, that measurement is not considered in the solution computation, i.e. the TTA is null since the detection is immediate.

## Relative RAIM (RRAIM)

RRAIM uses precise carrier phase measurements to propagate older pseudorange based position solutions forward in time. RAIM is performed on the carrier trajectory to ensure its integrity and then new protection levels are calculated based upon the original values and the accumulated uncertainty over time.

The accumulated uncertainty can be defined as the sum of three sources^{[1]}:

- the change of carrier phase receiver noise and multipath over the propagation time,
- the change in tropospheric error over the time interval,
- the satellite clock drift over the time interval.

Each source can be defined by a Gaussian distribution with a sigma characteristic value, which can be provided a-priori by the GNSS system. RRAIM concept shares the integrity burden between the aircraft, the GNSS constellation and the external monitors which provide the a-priori set of validated measurements.
As defined in ^{[1]}, RRAIM propagates both the position and the protection levels and it is based on ionosphere-free and carrier-smoothed pseudoranges.

Algorithms that use past measurements are also called “sequential algorithms” in the literature, as opposed to “snapshot algorithms” that use measurements from a single epoch.

## Solution Separation RAIM

The maximum solution separation method ^{[2]} is based on the observed separation between the position estimate generated by a full-set filter (using all the satellite measurements) and that generated by each one of the subset filters (each using all but one of the satellite measurements).

These techniques can be further extended to include multiple hypotheses. Multiple Hypothesis Solution Separation (MHSS)^{[3]} is a RAIM technique that comprises a protection level computation procedure that admits K simultaneous faulty measurements. MHSS may or may not be accompanied by a fault detection/exclusion (FDE) mechanism. If a FDE mechanism is present, it should be triggered right before the navigation solution and its associated MHSS protection level are computed, and the said computation should use only those measurements that have passed the FDE test successfully.

If the assumption that no more than K measurements can be faulty at the same time is correct, then all faulty measurements (if any) must have been excluded from some of the solutions previously computed, and hence the associated fault-free protection level contains the actual position with its prescribed probability. Thus the region covered by all computed solutions and their protection levels contains the actual position with the prescribed (actually higher) probability. In order to provide a unique navigation solution and an associated protection level, the all-in-view solution (the one using all N measurements) is provided, and the protection level is defined as the minimum circle around it (defined by its radius) such that all other positions together with their associated protection levels are contained within.

## Absolute RAIM

Absolute RAIM is an extension of the conventional RAIM algorithms, based on Multiple Hypotheses Solution Separation, MHSS (see previous section) ^{[1]}.

The proposed Absolute RAIM technique focuses on receiver autonomy, putting the less stringent requirements on the ground segment. In fact, Absolute RAIM needs very limited external information, such as User Range Accuracies (URA) for each satellite, at low latencies (e.g. 1 hour). Another advantage of Absolute RAIM is the possibility to relax the integrity requirement for the ground segment by assigning the remaining component to the on-board algorithm. In addition, absolute RAIM greatly benefits from multiple GNSS systems since its main limitation relies on the geometry and satellite availability (linked to the high level of autonomy). Finally, accuracy requirements are covered by using dual frequency measurements to remove the ionospheric errors, leading to smaller position errors as compared to the GPS-L1 solution.

ARAIM introduces the concept of an Effective Monitor Threshold (EMT), which limits all solution separation terms, i.e. if one of the terms is above EMT then an alarm is raised.

## Isotropy Based Protection Level (IBPL)

The IBPL algorithm ^{[4]} is presented as an example of ECA RAIM family developed for Liability Critical Applications (LCA).
The IBPL autonomous technique computes Protection Levels (PL) based on error isotropy, adapting in real-time to ranging error size and considering multiple fault conditions^{[5]}.
The main challenge in designing an algorithm for LCA relies in the fact that these applications mostly operate in urban environments, which often have low satellite visibility and large measurement errors caused by Non Line Of Sight (NLOS) signal multipath components.
IBPL computes PL based on the all-in-view least squares solution, using the vector of Least Squares estimation residuals as a characterization of the position error: the larger the residual vector, the larger the state estimation error vector (from a statistical perspective).
The protection level is computed as:

[math]xPL=k.|r|.xDOP[/math]

Where

- x stands for H or V, horizontal and vertical respectively,
- k is the Isotropic Confidence Ratio (ICR), a constant that relates the residual size with the state estimation error, and depends on the target confidence level and the number of measurements used for the estimation,
- r is the least squares residual vector.

When compared to RAIM algorithms (usually designed for civil aviation applications), the IBPL yields higher integrity availability at the cost of larger PL in urban environments, but also showed great availability in open sky conditions. The advantage of IBPL techniques is that they are completely autonomous.

## Related articles

## References

- ^
^{a}^{b}^{c}GNSS Evolutionary Architecture Study (GEAS), Phase I - Panel Report, February, 2008. - ^ Brown R. G., P. McBurney, “Self-Contained GPS Integrity Check Using Maximum Solution Separation”, Navigation: Journal of the Institute of navigation, Vol. 35, No. 1, Spring 1988
- ^ An Optimized Multiple Hypothesis RAIM Algorithm for Vertical Guidance, Juan Blanch, Alex Ene, Todd Walter, Per Enge, Stanford University, 2007
- ^ Cosmen-Schortmann, J.; Azaola-Saenz, M.; Martinez-Olague, M.A.; Toledo-Lopez, M.; “Integrity in urban and road environments and its use in liability critical applications”, GMV, Position, Location and Navigation Symposium, 2008 IEEE/ION, 5-8 May 2008, page(s): 972 – 983, Monterey, CA.
- ^ ”Autonomous Integrity – An Error Isotropy-Based Approach for Multiple Fault Conditions”, M. Azaola, J. Cosmen, InsideGNSS 2009, http://www.insidegnss.com/auto/janfeb09-azaoli.pdf