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GAGAN performance assessment for aircraft precision approach
The study provides an assessment of GAGAN services for APV-I and APVII over the Indian territory. Satellite error bounds and ionospheric error bounds are analyzed as the main contributing integrity parameters. |
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Abstract
This article provides an assessment of GAGAN performances for precision aircraft approach and landing. The singlefrequency GPS-based SBAS requirements set by ICAO are used to assess the GAGAN satellite integrity messages and compared against other existing global SBAS systems. It is evident from the analysis that GAGAN is capable to support RNP 0.1 aircraft procedures and for most of the period also the APV-I procedures. But the 99.99% availability is not met for APV-I and APV-II is a bit far-fetched. The impact of the ionospheric events is larger for the GAGAN system than the established WAAS and EGNOS. For the characterization of the observed performances, three critical points are focused on throughout the article: a. zero-mean Gaussian assumption of the integrity system b. correction confidence bound for satellite clock and orbit, and c. ionospheric model and threat space. An insight into the potential evolutions of the integrity systems and the performances are given considering two aspects: a. Dual-Frequency Multi-Constellation b. consideration of individual bias to accommodate non-zero mean and nonGuassian measurement errors rather than conservative inflation of the variances. The findings from the article attempt to bridge the gap in the literature regarding the GAGAN system integrity performances.
Introduction
GPS Aided Augmentation System (GAGAN) is one of the latest SBAS systems certified for en-route aircraft operation since 2013 (PBI, 2015). As the first system in the equatorial region, GAGAN System was certified by DGCA in 2015 for Approach with Vertical Guidance (APV 1) and enroute (RNP 0.1) operations. In recent years, there have been successful trials and implementation of GAGAN-based aircraft procedures in Indian airports). There is also a mandate by DGCA for all new aircraft after 2021 to be GAGAN equipped (PBI, 2022). On top of that the recent public information regarding the order of a large number of aircraft fleets from Airbus and Beoing is a testament to a flourishing downstream market for the GAGAN system (Indiantimes, 2023). The technical description of the system and application is provided in the GAGAN information portal and its literature section (AAI, 2023). From a technical perspective, the integrity system is similar to the existing EGNOS and WAAS and adheres to the ICAO MOPS (AAI, 2023). However, the literature on the performance evaluation of the GAGAN system is very limited (Insidegnss, 2016). There is couple of analysis from Thailand and Srilanka (Sophan, 2022) but only focused on the user positioning accuracy.
Regarding the necessity of the integrity performance assessment, it has been well known that it is not possible to compute the actual error introduced by satellites in real-time flight operations. At the same time, the errors introduced by the user aircraft, mostly the noise and multipath, are not known to the SBAS integrity monitoring system. The only way possible for integrity provision is to bound in real-time the potential user error in the worst-case scenario and protect the user from hazardously misleading information. This has to be validated by the data analysis based on the established model. It has been a common concept since the early days of the SBAS integrity system to consider the zero-mean Gaussian nature of measurement errors that are observed in the system monitoring side. The total variance of error terms can be computed by a simple summation of each error term as all errors are independent and uncorrelated. These simple assumptions allow the propagation of covariance from psuedorange domain to the position domain and obtain the protection level (Walter et. al, 1999, NAVIPEDIA, 2006, Ober et .al, 2023).
Figure 1 represents the Gaussian distribution of the actual errors fully defined by the variance term and the mean value and the overbounding Gaussian distribution defined by only the variance term. It is the overbounding gaussian distribution that is broadcast to the user as the integrity parameter. The inflation of the Gaussian distribution is activated when the threshold is reached by the bias in the measurement error. The bias caused by the faulty situation could still be well below the threshold and covered by the tail of the zero-mean nominal gaussian distribution. The K- factor makes sure that only the allowed probability of missed detection of bias and faults occurs. When the bias is just above the threshold, the Gaussian distribution is inflated but the zero-mean property is still conserved. In this way, the overbound distribution covers the tail error probability as well as the peak error probability. The K
The zero-mean Gaussian assumption is key because it overbounds the nominal (fault-free) errors in the measurements. The individual error (residual variance) is independent and uncorrelated and hence the total variance per satellite is also Gaussian in nature. This also has an implication in the system monitoring where statistical analysis such as the Chi-square test can be used to detect and remove bad data as the summation of multiple Gaussian distributions follows the Chi-Square distribution. In such a distribution, the K factor inflates the variance to consider the probabilities of error occurrence in the tail of the Gaussian distribution. This same approach and assumption in the system side of the SBAS and the user aircraft allow to compute the integrity. There is no reliable way to know the actual errors in real-time at any location and there could be a bias coming from the user location which is violating the Gaussian distribution, in that case, it would be a hazardous situation if position error is indeed above the protection level and the alert limit. Though, it needs to be recalled that even in the nominal situation the error distribution does not follow the perfect Gaussian distribution (as explained in Figure 1). The only way to provide integrity is to overbound it using the Gaussian distribution with inflated variance. When propagated in the position domain, the PL is increased to protect the user. It is also difficult to inflate the PL for all scenarios in real-time and the incorporation of biases originating in fault scenarios is not straightforward. (Insidegnss, 2020) shows in an intuitive statistical simulation why and how Gaussian distribution is assumed and how inflated distribution protects the user. The bias coming from Satellites is well observed by the RIMS. The correction confidence bound (covariance matrix) helps to lower the variance based on the location of users. Only the ionospheric events are tricky to handle where the specific bias could arise to some users which are not captured by the observations in the RIMS Iono model. But to some extent, this factor is also considered in the GIVE computation. The only drawback with these is that the variance is inflated for all users to protect from any threat and hence the availability is impacted. Such conservative assumptions have multiple limitations: a. the actual correlations appear to be negative b. they combine to reduce the overall positioning error rather than increase it (Walter et. al, 1999).
Is there a way to consider the integrity on the user side where the biases are also considered without having to inflate the variance? Some insights into it will be provided later in this paper.
In terms of mathematical formulation, the following equations (Equations 3-8) capture the essence of individual errors characterized by independent, zero-mean normal distributions, and the global residual pseudo-range error for each satellite (i-th ranging source) that may also be characterized by the zero mean normal distribution whose variance is simply expressed as the summation (Equation 4).
here P gives the full covariance matrix which is available in the position solution computation.
The right side of equation 3 is in fact the third diagonal element from this covariance matrix. The S term is the partial derivative of the error in vertical direction w.r.t the pseudorange error for the ith satellite. The weight matrix W is the inverse of the variance for each satellite broadcast in the integrity message.
Impacts of satellite orbits and clocks on GAGAN
Each existing SBAS has its threat model for satellite orbits and clocks to generate corrections and confidence-bound information meeting integrity requirements. Each threat model should fit its service area. The range error due to the fault on board the satellite clocks can be observed from all ground stations simultaneously and thus detected easily. For the satellite orbit error, a non-nominal condition is not likely as the GNSS satellites follow the orbit dynamics. The exceptional case of orbit delta V maneuver and attitude maneuver is also predicted and detected by the network of the ground station. The pseudodynamic orbit prediction which uses both the deterministic approach based on the physics and the measurement data provides better confidence in the orbit position. To some extent, the satellite clock estimation is stochastic as the clock offset is characterized by a random walk process. Regardless of it, the anomaly in the satellite clock can be detected by all ground stations. In the nominal scenario, the most important consideration for satellite ephemeris is needed regarding the service coverage zone. The Message Type 28 Covariance Matrix provides the confidence weight for each satellite based on the user location. Equation 5 shows the relationship between the modified variance of the satellite corrections using the information from MT 28. It allows the lower inflation of the variance for the satellite which has been well-monitored (through good geometry) in the system. The confidence bound for GPS satellite orbit and clock correction is location dependent, where I is the line of sight from satellite to user aircraft, P is the covariance matrix derived from the same estimation procedures that compute the range error of the satellite clock and orbit (often called User Differential Range Error (UDRE)).
To experimentally test this, the covariance matrix from MT28 is used to compute the delta User Differential Range Error (UDRE), which is dependent on the location of the airspace from where the aircraft will receive the satellite signals. The confidence interval of each satellite orbit and clock error on the line of sight is multiplied with the broadcast UDRE to get the final variance in the protection level calculation. The better the location of the aircraft w.r.t the observability of GPS satellites monitored by the GAGAN network, the better the protection level. An example analysis using the Kazakstan airspace (within the GAGAN Geo footprint) is shown in the results and interpretation chapter.
Impacts of Ionospheric events on GAGAN
Non-nominal ionospheric events make the largest threat to aircraft procedures. Each existing SBAS has its ionosphere threat model to generate ionospheric correction information meeting integrity requirements. Each threat model should fit its service area. As ionospheric activity is a dynamic and natural phenomenon, none of the threat models assure overbound anomalous events forever (ICAO, 2016). Regular ionospheric monitoring is therefore essential to confirm that the threat space is overbounding the anomalies. For the GAGAN system, the distribution of the monitoring network is not robust enough to capture anomalies in the coverage edge (Sophan, et. al, 2020). On top of that the coverage zone consists of a highly active equatorial ionospheric zone. Scintillation effects are also prominent and impact the received power and phase of GNSS signals and as such can cause loss of lock on the GNSS signals and render the unavailability and discontinuity of the system. The ionosphere threat model is the actual function representing the associated threat space which has to cover the existence of the largest ionospheric irregularities that might not have been sampled in the system ground station (Sparks, et. al, 2021, ICAO, 2016). This is depicted in Figure 2. In the next section, a detailed analysis is performed to examine the GAGAN performances during the nominal ionospheric situation and active geomagnetic storm days.
Analysis data set and methods
The selected timeframe for the analysis is summarized in Table 1. The GAGAN messages are retrived from CNES ftp server. For the user observation of GPS satellites, the RINEX files from UNAVCO and CDDIS ftp servers are used. The user observation of GPS data are collected from different GNSS stations as indicated in Table 1. The site name “KTM” refers to the station data from Kathmandu, Nepalese airspace. Similarly “KZT” referes to Kazakhstan.
As the current solar cycle 25 is approaching its maximum, there are frequent opportunities to analyze the impact on the performance of the GAGAN system. The recent large geomagnetic storm characterized by a Kp index higher than 7 is selected for the analysis. It is observed in past studies that the GIVE index for SBAS systems is highly inflated to protect the users against high uncertainty during the storm period.
The analysis method is based on the parameters obtained in the position domain using the gLAB software. For supplementary analysis and interpretation, ESA’s SBAS MENTOR tool is used. Information regarding ionospheric events and geomagnetic storms is derived from the public information portal (Spaceweatherlive, 2023).
Equations 3-8 are used to compute the protection levels for each data set with a sampling rate of 15 minutes. The protection levels are checked against the ICAO SARPs (RTCA, 2020) requirement for various aircraft procedures (RNP 0.1, LPV, LPV-200, APV-I, APV-II, and CAT-I).
For the simulation where the impact of reduced ionospheric activities is assessed, the assumptions of independent, uncorrelated, and zero-mean distribution for individual errors are kept. The errors from the satellite ephemeris and the aircraft local errors are unchanged and only the variance parameter of ionospheric distribution is changed and reflected in the integrity parameter GIVE index. Higher confidence in the ionospheric estimation for IGP surrounding the 85° E 25° N Airspace is simulated. The impact on the protection level and GAGAN availability are discussed in the next chapter.
Results and Interpretation
The vertical protection level (which is the important performance parameter that enables higher precision landing down to autolanding in GBAS CAT) is not promising to support APV-I (threshold: 50 m) or APV-II (threshold: 20 m) for Nepalese airspace. From the horizontal and vertical protection level analysis and Stanford analysis (Figure 3 – Figure 6), it is evident that the GAGAN system is currently not suitable to support a precision approach and landing in this region. This is also in line with the recommendation from the Airport Authority of India, that during the nominal ionospheric activities, the GAGAN performances show APV I availability of 99 % of the time over only 76% of the Indian landmass (AIM, 2023). The main reasons for the unavailability of APV-I and APV-II are:
a. The higher ionospheric delays and the associated variance for the GAGAN coverage. This has been verified by an experimental test where the satellite broadcast message is modified to have a lower variance for ionospheric grid points (surrounding the 85° E 25° N) in Nepalese airspace. A tool from ESA (SBAS mentor) is used to generate the modified GAGAN messages, and then the horizontal and vertical protection levels are computed. The protection levels are improved with better ionospheric correction confidence. It is an important point to be considered by the aviation authority and related entities that in the next few years the SBAS systems, including GAGAN, will drive towards dual frequency (using L1 and L5) which allows to cancel the ionospheric errors at the user level. Also, the number of monitoring reference stations will increase to have denser coverage (ICAO, 2022). Therefore, this simulation to lower the ionospheric errors and variances (close to the situation when there is dual frequency SBAS or better ionospheric coverage and model) gives performance indications mostly triggered by the quality of satellite orbit and clock corrections. Figure 4 (right plot) shows protection levels computed with the simulated data and the improved protection levels are visible mostly around 06:00 to 09:00 UTC (compare against nominal days protection levels in the left plot). The vertical protection levels are reduced below 50 m which supports the APV-I approach.
The stanford plots are the established plots to visualize the GNSS system integrity. Figure 5 and Figure 6 show the statistical results for horizontal and vertical navigation using the GAGAN APV-I approach in Nepalese airspace. As discussed earlier the requirement set by ICAO is not met, mostly due to the degraded performance in vertical domain. The availability of horizontal navigation with 99.4 % shows a great promise for further enhancement of the system. The 8 epochs identified as Hazardously Misleading Information (HMI) are not investigated in detail, as the focus is on the system availability. The vertical availability of 77.3% is a long way off from the required specification. It is well understood that the impact of the ionospheric errors is larger in the vertical position domain. In this regard, the simulation performed earlier (Figure 4) where the ionospheric variance was lowered provided a better vertical protection level. It is also a testament that the GAGAN system holds great potential going forward. The analysis so far focused on the Nepalese airspace which lies towards the northern edge of the GAGAN coverage. To also analyze the performance which is towards the inner coverage, the data from Delhi is analyzed. Both nominal ionospheric days and high ionospheric activity days are used to characterize the performances. Figure 7 and Figure 8 show the variability of horizontal and vertical protection levels. As with the case in Nepalese airspace, the APV-I requirements are not met in nominal days. The performance is degraded to a larger extent during non-nominal ionospheric activities. The overall performance observed in the period used in this study corroborates the public information provided by the Airport Authority of India (GAGAN, 2023).
To better understand the large difference in protection level during nominal and non-nominal ionospheric activities, the ionospheric confidence bound is computed for the given location. Figure 9 shows the degraded (two columns plots on the right) user vertical ionospheric error on the high storm day in comparison to the nominal day (two columns plots on the left). All satellites have higher error terms associated to enhanced ionospheric disturbances.
b. The regional network of GAGAN station is not dense as of now (ICAO, 2022). There is a plan to increase the network in the surroundings of the Indian subcontinent. This has a direct implication in the performance improvement not only for ionospheric monitoring (better confidence bound in terms of variance) but also well for better confidence bound in terms of satellite orbit and satellite clock error corrections (broadcast through Message Type 28 Covariance Matrix). To experimentally test this, the covariance matrix from MT28 is used to compute the delta User Differential Range Error (UDRE), which is dependent on the location of the airspace from where the aircraft receives the satellite signals. The confidence interval of each satellite orbit and clock error on the line of sight is multiplied with the broadcast UDRE to get the final variance in the protection level calculation (Walter et. al, 2021). The better the location of the user w.r.t the observability of GPS satellites monitored by the GAGAN network, the better the protection level. The UDRE of each satellite from the GAGAN broadcast is the same value for all airspace locations in the GAGAN service volume. However, the delta UDRE is different from one location to the other. Figure 10 shows the delta UDRE for airspace in Kazakhstan and Nepal. The difference is evident, i.e. the observability of satellites from Nepal has more confidence in terms of error as the GAGAN network provides better confidence. Whereas in Kazakhstan, the GAGAN network has lesser observabilities of satellites and hence, weaker confidence.
Comparison with existing systems
As the global SBAS system promotes seamless integration of navigation procedures from one region to another, it is vindicative to compare the performance of the existing global SBAS system during high solar activities. WAAS and EGNOS are the forerunner providing better services up to CAT-I like approach and landing. Regular performance monitoring and reporting of these systems are publically available. About the MSAS system, the potential has not been fully exploited as it can only support RNP 0.1 procedures. The sparse regional monitoring network and the severe ionospheric conditions are the root causes of it. In this study, the performance of all these SBAS systems experienced service degradation to different levels. EGNOS appears as the quintessential system which has the better availability for both APV-I and AVP-II even during the Kp > 7 events. The slight degradation in the edge of EGNOS coverage, however, is a testament to the necessity of a robust system monitoring that can cover ionospheric irregularities without conservative inflating of the IGPs.
The following plots Figure 11-Figure 15 characterize the performance of protection levels in the position domain computed using the respective SBAS integrity messages for EGNOS, WAAS, and MSAS. The description in each figure caption briefly interprets the results.
Future evolution and potentials
The safety analysis for SBAS has always encountered the presence of small biases and non-Gaussian behavior observed in data used to validate the system. The analysis performed in this study focused on the integrity equations based on zero-mean Gaussian behavior. And only considered the variance term broadcast from the satellite. Several kinds of literature have corroborated the inclusion of nominal bias terms into the protection level equation to account for non-zero means and non-Gaussian behavior (Walter et.al, 2009, Walter et.al, 2010, Ober, 2023, Speidel et al, 2013). A relevant example is the GBAS system which considers the faulted integrity model where bias arising from the ground receivers is also broadcast to the aircraft. As per this literature, the equation 3 formulated earlier in the chapter can be redefined:
here the element of S is taken from the projection matrix, is the nominal variance, and is the nominal bias term. The last term takes the largest bias during the fault event. In the case of the fault-free scenario, this term vanishes. The scalar factor represented can be optimized to get it well below 5.33 and consequently minimize the protection level values (Walter et. al, 2010). The bias term can also be isolated per differentiated parameters such as the ground receivers’ errors and satellite errors. And the maximum value of the protection level from the possible scenarios is used to protect the user aircraft.
When the DF system is considered, the ionospheric variance term, except for the higher-order ionospheric terms, is eliminated in equation 4 (Ober, et. Al, 2023). It has to be noted that the uncertainty in the ionospheric computation is the major source of the degradation of the GAGAN availability for APV-I and APV-II The opportunity of the DF system (ICAO, 2023) will certainly provide better performances. Add to it the robust approach to consider the individual bias term rather than the conservation inflation of the variance as shown in equation 9, and the prospect of GAGAN-based aircraft approach procedures is very promising.
The ICAO has recently adopted the Galileo constellation for the provision of GNSS-based air navigation services (EUSPA, 2023). This allows to use of dual constellation in the augmentation system such as SBAS. The implication in the protection level is that more satellites and signals are available which improves the satellite user geometry and as per equation (3-8) the protection level values are lowered rendering better availability of APV-I and APV-II.
The potential of more precise carrier-phase signals has been studied in the past and could be the subject of investigation in the coming years as well. The inherent challenges of the carrier phase, such that cycle slips and phase ambiguities, however, hinder the implementation in safety-critical systems with high requirements of integrity (Du, 2021). A-RAIM with DFMC is also a promising approach and its success could also benefit the evolution of the SBAS algorithm. The A-RAIM concept is based on the local integrity computation where the pseudo-range from all satellites is statistically checked to detect and isolate the faulty satellite. It has also been demonstrated in literature the possibility of using a particle filter that can provide better results for the nonzero-mean non-Guassian error model.
Conclusion
The study provided an assessment of GAGAN services for APV-I and APVII over the Indian territory. Satellite error bounds and ionospheric error bounds are analyzed as the main contributing integrity parameters. It is observed that during nominal periods the protection level performance requirements of APV-I are mostly met but still not enough to meet the 99.99% availability requirement. It is still a far-fetched goal to meet the APVII requirement. During the enhanced ionospheric activities triggered by geomagnetic storms with a Kp index > 7, the protection levels are highly inflated to protect the users at the expense of service availability. With simulated data, it is verified that lowered ionospheric variance improves the performance and regularly meets the APV-I requirement. The wellestablished EGNOS and WAAS provide better services including LPV, LPV-200, APV-I, and APV-II. At the edge of EGNOS coverage, the performance is not as robust, and inflation of ionospheric variance is frequently triggered. The WAAS system also experienced a short interruption in service availability on the 24th of March, 2023 during the high Kp index period. MSAS is currently only serving RNP 0.1 approach and hence, it is expected to have very large protection levels during the ionospheric events. Some insights were provided into the potential development of DFMC and a less conservative integrity approach that includes an individual bias term.
Acknowledgment
The analysis performed for this study is based on the gLAB software publicly available from the UPC website. The simulation and SBAS message interpretation is done using both gLAB and ESA’s SBAS mentor.
Disclaimer
The work done in this study has no commercial interest. It is the author’s voluntary support to facilitate the GNSS capacity-building activities in the framework of ICG, UNOOSA agenda. There was no funding received and no support was used from any organizations. The analysis, interpretation, and discussion are solely based on the author’s expertise in GNSS and air navigation.
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