GPS/GLONASS/Galileo/QZSS Receiver Autonomous Integrity Monitoring (RAIM)


Introduction

Phenomenal advances in the achievable accuracies of GPS positioning have been demanded and realised by the navigation and surveying communities. Despite this remarkable technology, industry demands are far from satisfied. The availability of GPS signals is a major limitation for many existing and for even more potential applications. Fortunately, with the development of Galileo by the European Commission (EC) and European Space Agency (ESA) and the restoration of the Russian GLONASS underway, the future for satellite based positioning and navigation applications is extremely promising. Additional augmentation systems such as the Japanese Quasi-Zenith Satellite System (QZSS) will also contribute to the enhancement of satellite navigation. With the simultaneous inter-operation of all these Global Navigation Satellite Systems (GNSS) and augmentations significant advances in integrity levels are certain.

A Receiver Autonomous Integrity Monitoring (RAIM) scheme is described below along with the performace measures of Reliability and Separability. These performance measures are used to assess integrity performance levels of standalone GPS and integrated GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo systems.


Fault Detection

Essentially, the detection phase of the RAIM procedure tests the overall adjustment of the solution for using the so called Variance Factor (VF) test. The VF is a ratio of the 'a priori' and 'a posteriori' spread of errors and is expected to be equal to one. The two-tailed test limits are derived from the Chi-squared distribution for a given significance level. If the VF test fails it is assumed that there is a gross error in at least one of the measurements.




Fault Isolation

In order to isolate the fault or faults the w-test is performed on all of the measuremnts within the positioning adjustment. For situations where the test statistic exceeds the critical value for the desired significance level, the corresponding measurement is flagged as a possible outlier. The critical value for the test is derived from the normal distribution for a specic level of significance. Standard procedures involve removing the measurements from the adjustment one at a time based upon which has the greatest test statistic. If more than one outlier is identified previously removed measurements should be tested again with the clean data set. This is necessary due to false alarms and masking. False alarms relate to outliers causing inliers to be flagged as erroneous while masking occurs when an outlier is undetected. The w-test statistic is defined as (Baarda, 1968; Cross et al., 1994; Teunissen, 1998):




Reliability

Reliability comprises the ability of the system to detect outliers and the measure of effect undetectable outliers have upon the parameter estimations of an adjusted solution. The systems ability to detect outlying observations is expressed in terms of Minimal Detectable Biases (MDB) and the measure of their effect is external reliability (Baarda, 1968).


Internal Reliability

The MDB is the magnitude of the smallest bias that can be detected for a specific level of confidence and is determined, for correlated measurements (Baarda, 1968; Cross, 1994) by:




External Reliability

The external reliability of the system is characterised by the extent to which an MDB affects the adjustment and is expressed in terms of the estimated parameters as (Baarda, 1968; Cross, 1994):




Separability

If there is a strong correlation between two statistics and the measurement corresponding to one is a real detectable outlier, then the other statistic is likely to exceed the critical value as well becoming difficult to distinguish from the real outlier. In some cases the non-outlying correlated measurement can have a larger test statistic. The ability to accurately identify an outlier is therefore dependent upon the outlier magnitude and the correlation of the test statistics. This ability is referred to as the separability. The multiple outlier scenario can unpredictably exacerbate this difficulty. The degree of correlation of two test statistics is determined through derivation of the correlation coefficient (Forstner, 1983; Tiberius, 1998):




Simulted Results


GPS/GLONASS/Galileo RAIM Perfomance Studies

A series of simulations were carried out in order to analyse the performance of the GNSS RAIM algorithm with particular attention to the correlation, and thus separability, of the measurements. Studies were conducted for GPS only, combined GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo scenarios. UNSW GNSS (GPS and Pseudolite) measurement simulation and analysis software (Lee et al, 2002), originally designed for GPS and Pseudolite simulation, has been adapted to include the GLONASS and Galileo systems and generate the results below. The analyses are based on the GPS, GLONASS and Galileo satellite coordinates and given receiver coordinates.

The GPS satellite coordinates were determined by actual ephemeris (converted from the almanac files). The implemented GLONASS constellation was essentially 24 satellites in three orbital planes whose ascending nodes are 120 ° apart. 8 satellites are equally spaced in each plane with argument of latitude displacement 45 °. The orbital planes have 15 ° argument of latitude displacement relative to each other. The satellites operate in circular 19100 km orbits at an inclination 64.8. The Galileo constellation comprises 27 operational satellites in a Walker constellation with three orbital planes, equally spaced with a 56° nominal inclination and an altitude of 23222km. Each orbital plane contains nine satellites nominally 40° apart and one spare.

Visibility for GPS, GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo (Top to Bottom)	Maximum correlation coefficients for GPS, GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo (Top to Bottom).
Maximum internal reliability values for GPS, GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo (Top to Bottom)	Horizontal external reliability values for GPS, GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo (Top to Bottom)

Quasi-Zenith Satellite System (QZSS)

Another system which is expected to provide additional resources for satellite based positioning in Japan, Australian and Eastern Indonesia is the Japanese Quasi-Zenith Satellite System (QZSS). QZSS is being designed as a GPS augmentation system by the Japanese private and government sector with U.S. support and will most likely consist of 3 satellites in 3 different orbital planes inclined at 45 degrees to the Geostationary Orbit (GEO). This system is designed to maintain at least one satellite with a high elevation, at least 80 degrees for 8 hours over Japan. Full operation is expected to commence in 2011 (Kogenei, 2004). QZSS will be maintained to provide users with GPS-equivalent time with an offset of less than 3 nanoseconds RMS via the time coefficients in the satellite ephemeris broadcasts (Kogenei, 2004). Such an alignment will mean that no additional parameters need to be estimated for GPS/QZSS augmentation.

QZSS Satellite Elevations for Tokyo over 24 hours.

QZSS Satellite Elevations for Tokyo over 24 hours.