Multiconstellation satellite navigation is critical in signaldegraded environments where signals are strongly corrupted. In this case, the use of a single GNSS system does not guarantee an accurate and continuous positioning. A possible approach to solve this problem is the use of multiconstellation receivers that provide additional measurements and allows robust reliability testing; in this work, a GPS/GLONASS combination is considered. In urban scenario, a modification of the classical RAIM technique is necessary taking into account frequent multiple blunders. The FDE schemes analysed are the “Observation Subset Testing,” “ForwardBackward Method,” and “Danish Method”; they are obtained by combining different basic statistical tests. The considered FDE methods are modified to optimize their behaviour in urban scenario. Specifically a preliminary check is implemented to screen out bad geometries. Moreover, a large blunder could cause multiple test failures; hence, a separability index is implemented to avoid the incorrect exclusion of blunderfree measurements. Testing the RAIM algorithms of GPS/GLONASS combination to verify the benefits relative to GPS only case is a main target of this work too. The performance of these methods is compared in terms of RMS and maximum error for the horizontal and vertical components of position and velocity.
GNSS (Global Navigation Satellite Systems) are worldwide, allweather navigation systems able to provide threedimensional position, velocity, and time synchronization to UTC (Coordinated Universal Time) scale [
Satellite navigation in difficult scenarios (e.g., urban canyons, and mountainous areas) is more critical, because many GNSS signals are blocked or strongly degraded by natural and artificial obstacles; in these scenarios GPS only cannot guarantee an accurate and continuous positioning due to the lack of measurements and/or the presence of erroneous measurements. A possible way to fill this gap is the use of a GNSS multiconstellation receiver, considering the combined use of GPS with other GNSS such as Galileo, Beidou, and GLONASS.
The performance of the integrated system is increased in terms of
continuity, directly related to satellite availability,
accuracy, enhanced by observation geometry improvement, and
integrity, as the increased availability improves the detection process of gross errors [
Galileo currently has only four satellites in orbit, in the IOV (InOrbit Validation) phase, while Beidou is currently in the development phase. The enhancement of the Russian space program has made GLONASS an ideal candidate to form a multiconstellation with GPS. The combined use of these two systems implies the estimation of a further unknown (in addition to navigation parameters), representing the timescale offset between the considered systems, with the “sacrifice” of one measurement.
Integrity monitoring has a great importance in safetycritical operation, like air navigation, or in signaldegraded scenario, where solution could be unacceptably inaccurate.
Measurements in urban scenario are strongly affected by gross errors, degrading navigation solution; hence a quality check on the measurements, defined as RAIM, is important. The integrity of a navigation system is defined as the ability to provide timely warnings to users when the system should not be used [
In this work GPS and GLONASS are considered because they are the only systems declared fully operational; they are similar for many aspects, such as the operational principle detailed in Section
GPS and GLONASS positioning is based on the oneway ranging technique: the time of travel of a signal, transmitted by a satellite, is measured and scaled by the speed of light to obtain the satelliteuser distance, called pseudorange (PR), whose equation is [
Trilateration uses PR measurements to compute the navigation unknowns that are the tridimensional receiver coordinates and the receiver clock offset relative to the system time scale.
GNSS receivers are also able to obtain Doppler measurements, defined as the time derivative of observable phase [
GPS and GLONASS are based on the same operating principle but they have several differences, which can be classified in terms of constellation, signal, and reference. The differences between the two systems are summarized in Table
GPS/GLONASS differences.
Parameter  GPS  GLONASS  

Constellation  Number of SV  24 (expandable)  24 
Orbital planes  6  3  
Orbital altitude  20200 km  19100 km  
Orbit inclination  55°  64.8°  
Ground track period  1 sidereal day  8 sidereal days  
Layout  Asymmetric  Symmetric  
 
Signal  Carrier frequencies (MHz)  1575.42 
1602 + 
Ranging code frequencies (MHz)  C/A: 1.023 
C/A: 0.511  
Multiple access schemes  CDMA  FDMA  
Broadcast ephemerides  Keplerian  ECEF  
 
Reference  Datum  WGS84  PZ90.02 
Time scale  GPS time  GLONASS time 
A comprehensive description of the aforesaid differences among GPS and GLONASS is provided in Angrisano 2010 [
For our scope the main difference is related to the different time scale adopted by the systems. GPS time is connected with UTC(USNO), the UTC maintained by US Naval Observatory; UTC scale is occasionally adjusted to one second to keep the scale close to the mean solar time. GPS time scale differs from UTC(USNO) of an integer number of seconds (called leap seconds, currently 16 s); a further difference between GPS and UTC(USNO) time scale (typically less than 100 ns), due to the different master clocks used, is broadcast to the users within the GPS navigation message. GLONASS time scale is connected to UTC(RU), the UTC maintained by Russia; it is corrected by leap seconds, according to the UTC adjustments, so the difference between these time scales is less than 1 millisecond and is broadcast in the GLONASS navigation message.
GPS and GLONASS time scales are connected by the following relation [
To perform the transformation (
In this work the adopted estimation technique is the weighted least squares (LS), which uses only a measurement model made up by simultaneous PR and PR rate observables.
Regarding PR, a set of equations like (
The measurement model of PR rate observable is
For the PR measurement, the follow accuracy, dependent on satellite elevation, is assumed:
The PR rate measurement accuracy is assumed inversely proportional to
The optimization criterion of the LS is to minimize the sum of the squared residuals defined as
Reliability refers to the consistency of the results provided by a system; internal and external reliability are, respectively, the ability to detect gross errors and the effect of an undetected blunder on the solution [
The integrity of a navigation system is defined as the ability to provide timely warnings to users when the system should not be used [
Before RAIM application, a check is performed to screen out bad geometries, which could imply erroneous detections; in this work, the WARP (WeightedARP) parameter, a generalization of the classical ARP [
The FDE schemes analysed are obtained by combining different basic statistical tests. Specifically a socalled global test (GT) is adopted to verify the selfconsistency of the measure set; if the measurement set is declared inconsistent, a local test (LT) is performed to identify and reject a blunder, after a separability check. Separability refers to the ability to separate any two measurements from one another [
In the first test the decision variable
If the GT does not pass, a LT is performed analyzing standardized residual
Subset testing is an FDE technique that uses only GT [
Subset algorithm.
The Subset test is applied separately to pseudorange and Doppler measurements and is computationally heavy because several measurement combinations have to be checked [
ForwardBackward is an FDE technique that involves the use of both global and local tests; it consists of two different steps [
If the solution is declared reliable and
A complete scheme of the ForwardBackward technique is shown in Figure
ForwardBackward algorithm.
Least squares estimation is very susceptible to outliers; a possible way to solve this problem is an iterative deweighing of erroneous measurements [
A measurement set is checked for the geometry, as in the previous FDE techniques and then the GT is performed. If observations are declared not consistent by GT, the LT is carried out to identify the blunder, and its related weight is reduced only if allowed by the separability check (i.e., if the measurement is not strictly correlated to the others). The variance of the suspected measurement is exponentially increased (and consequently the weight is decreased) as follows:
If the normalized residual of the
The scheme of the Danish procedure is shown in Figure
Danish algorithm.
A static test of about 6 hours was carried out on February 24, 2012. The antenna was placed on the roof of the PANG (PArthenope Navigation Group) laboratory building, Centro Direzionale of Naples (Italy), a typical example of urban canyon (as shown in Figure
Antenna position.
The used receiver is a NovAtel FlexPakG2, able to provide single frequency (L1) GPS/GLONASS measurements, connected to a NovAtel antenna 702GG.
The reference solution is computed by a postprocessing geodetic method, guaranteeing a position accuracy of
PANG station coordinates and accuracy.
Latitude 
Longitude 
Height 
Standard deviation north 
Standard deviation east 
Standard deviation up 

40°51′23.5163′′  14°17′03.8997′′  90.6257  0.0006  0.0008  0.0011 
Herein eight different GNSS configurations are compared, combining the two systems considered and the different RAIM scheme developed:
GPS only without RAIM application (briefly indicated as GPS no RAIM);
GPS/GLONASS without RAIM application (GG no RAIM);
GPS only with Subset RAIM application (GPS Sub);
GPS/GLONASS with Subset RAIM application (GG Sub);
GPS only with ForwardBackward RAIM application (GPS FB);
GPS/GLONASS with ForwardBackward RAIM application (GG FB);
GPS only with Danish method applied (GPS Dan);
GPS/GLONASS with Danish method applied (GG Dan).
Results are analyzed in terms of RMS and maximum errors for horizontal and vertical components in the position and velocity domains. The percentage of time mission when solution is available is referred to as solution availability; in case of RAIM application, the concept of reliable availability, defined as the time percentage when solution is reliable, is introduced.
The session is characterized by high solution availability (about 98% for GPS and 100% GPS/GLONASS configuration) and by very large errors (more than 1 km without RAIM application); the application of the developed RAIM schemes reduces the availability of the position solution. In GPS standalone configuration, the Subset test guarantees the highest reliable availability (76.2%), while 20% of solutions are flagged as unreliable; for Danish and ForwardBackward schemes, the reliable availability is halved with respect to the solution availability. The inclusion of GLONASS measurements, without RAIM application, improves the solution availability of 2% with respect to the GPS standalone configuration. For the GPS/GLONASS multiconstellation, the Subset testing guarantees an high reliable availability (only 3.5% of solutions are rejected by the quality control) which is increased to 20% with respect to the GPS only configuration. The effect of the GLONASS inclusion is more evident in the Danish and ForwardBackward schemes; in these cases the reliable availability reaches about 75% with an improving of 25–30% with respect to the GPS only configurations. The solution availability and the reliable availability of the position are summarized in Table
Position availability/reliable availability.
No RAIM 
Subset 
Danish 
ForwardBackward  

GPS  98.1  76.2  49.0  43.6 
GG  100  96.5  75.8  74.0 
Similar results are obtained in velocity domain; the GLONASS measurements increase the reliable availability for the three RAIM schemes relative to GPS only configurations; as in the position domain, the Subset testing guarantees higher reliable availability with respect to the other developed schemes. The solution availability and the reliable availability of the velocity are summarized in Table
Velocity availability/reliable availability.
No RAIM 
Subset 
Danish 
Forwardbackward  

GPS  98.1  70.5  56.3  56.3 
GG  100  97.8  73.4  72.9 
The configurations without RAIM are characterized by large errors: in case of GPS only, the maximum horizontal error exceeds 1 km and the inclusion of GLONASS measurements improves the performance reducing the maximum error to 245 meter. RAIM application improves all considered configurations, reducing both maximum and RMS errors, as shown in Figure
Horizontal position.
In Figure
Horizontal position error.
In Figure
Horizontal velocity error.
In Figures
Altitude.
Vertical velocity error.
The qualitative analysis, provided by the previous plots, is confirmed by the results summarized in Tables
Position results.
RMS (m)  MAX (m)  






No RAIM  GPS  54.9  85.6  1264.5  1685.9 
GG  34.8  65.4  245.6  372.2  
Subset  GPS  27.5  56.4  299.0  327.0 
GG  15.1  36.1  321.6  398.5  
Forwardbackward  GPS  17.9  44.5  159.7  285.8 
GG  13.4  31.3  159.7  284.3  
Danish  GPS  23.2  56.1  159.7  343.1 
GG  16.0  38.1  159.7  281.5 
Velocity results.
RMS (m/s)  MAX (m/s)  






No RAIM  GPS  0.968  1.573  68.750  108.240 
GG  0.042  0.060  0.442  0.822  
Subset  GPS  0.053  0.084  0.669  1.251 
GG  0.042  0.067  0.928  1.337  
ForwardBackward  GPS  0.047  0.074  0.649  1.251 
GG  0.036  0.055  0.367  0.653  
Danish  GPS  0.046  0.073  0.649  1.251 
GG  0.035  0.054  0.295  0.642 
In signaldegraded environments such as urban canyons, GNSS navigation suffers the presence of gross errors which strongly worsen the solution; therefore, in these scenarios the use of RAIM algorithms is necessary. In this work three RAIM FDE schemes, well known in literature [
The obtained results show the effectiveness of the adopted algorithms in terms of reliable availability and of RMS and maximum errors. The reliable availability is the percentage of time mission when the solution is declared reliable by the adopted RAIM; the highest value of this parameter is obtained with the Subset method, which provides the largest errors too. The ForwardBackward and the Danish methods are instead characterized by similar performances and by the smallest errors, demonstrating the validity of the separability check module (which cannot be applied to Subset method). The proposed algorithms have been tested on both position and velocity domains, showing comparable robustness.
GPS/GLONASS combination shows evident performance improvements, for all the considered parameters, relative to GPS only configurations.