Satellite selection methods for multi-constellation advanced RAIM

Available online at www.sciencedirect.com

ScienceDirect Advances in Space Research xxx (2020) xxx–xxx www.elsevier.com/locate/asr

Satellite selection methods for multi-constellation advanced RAIM Silong Luo a,b,c, Li Wang a,b,d, Rui Tu a,c,e,⇑, Weiqi Zhang a,b, Jiancheng Wei a,b Cunting Chen a,b a State Key Laboratory of Geographic Information Engineering, Xi’an 710054, PR China School of Geological Engineering and Geomatics, Chang’an University, Xi’an 710054, PR China c National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, PR China d National Administration of Surveying, Mapping and Geo-information Engineering Research Center of Geographic National Conditions Monitoring, Xi’an 710054, PR China e University of Chinese Academy of Sciences, Beijing 100049, PR China b

Received 19 March 2019; received in revised form 11 December 2019; accepted 15 December 2019

Abstract The increased number of potential threat modes under multi-constellation advanced receiver autonomy integrity monitoring (ARAIM) requires an increase in the number of subsets and a correspondingly high computational load. A new satellite selection method based on integrity support message (ISM) parameters is proposed and compared with GDOP-based selection. The performance was tested on five days of data measurements from 21 multi-global navigation satellite system experiment (MGEX) stations distributed around the world, as well as simulation using the broadcast ephemeris. The results show that the proposed ISM-based satellite selection method is highly compatible with the baseline ARAIM. This method could reduce the computational times by about 60–70% quickly, with minimising vertical protection level (VPL) loss, which was consistently within 1 m, even a reduced VPL value in some epochs, and resulting in an improved availability. The simulation results were similar to the MGEX data. It appears that the application of ISMbased satellite selection can effectively reduce computational burden with a minimal impact on availability. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Advanced RAIM; Satellite selection; Multi-GNSS; ISM; LPV-200

1. Introduction Integrity, a significant criterion in civil aviation safety-oflife applications, must be assured in the application of the Global Navigation Satellite System (GNSS) to aviation (ICAO, 2009). With the dual-frequency and multiconstellation (DFMC) GNSS environment development, the concept of advanced RAIM, or ARAIM is proposed for providing global precision approach vertical guidance services such as the Localizer Performance with Vertical guidance down to 200/250 feet service (LPV-200/250) ⇑ Corresponding author at: National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, PR China. E-mail address: [email protected] (R. Tu).

(GEAS, 2010; Blanch et al., 2015; EU-U.S., 2016). To meet the stringent availability criteria, such as accuracy, integrity, availability and continuity of LPV-200/250, ARAIM must consider a more complex set of threat modes. The Multiple Hypothesis Solutions Separation (MHSS) ARAIM is one of the widely applied baseline ARAIM algorithms, which has been evaluated through a number of GNSS observation data and simulations (Rippl et al., 2011; Blanch et al., 2010; Wu et al., 2013; Wang et al., 2018; Choi et al., 2011, 2012; ElMowafy et al., 2016; El-Mowafy 2017). In these studies, it has been found that a large number of satellites inevitably increases the computational load, particularly for MultiGNSS users, making it necessary to reduce ARAIM complexity (Rippl et al., 2011). Walter et al. (2014) and Blanch et al. (2018) proposed a subset optimisation concept

https://doi.org/10.1016/j.asr.2019.12.015 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

2

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

involving consolidation of the fault modes by grouping faults, so that one subset solution can monitor multiple faults. Ge et al. (2017) proposed a method based on the use of different orbital planes to reduce the monitoring subset, which is essentially an improvement on the constellationout method proposed by Walter et al. (2014). Satellite selection quickly reduces the number of satellites processed by the receiver. Gerbeth et al. (2016) proposed a heuristic optimization that significantly reduces the number of satellites but requires additional computational effort. Walter et al. (2016) proposed a ‘‘downdate” satellite selection for multi-constellation satellite-based augmentation systems (SBAS). Inspired by the above ideas, an improved ISM-based method for selecting satellites were tested and evaluated, in which the weight of each satellite is calculated based on its ISM parameters and the downdate method is applied in place of heuristic or greedy optimisation to reduce the complexity. To verify the proposed method, the performance of several standard satellite selection methods were analysed and compared, where the test data were collected from 21 MGEX stations of 5 days, and a large range of availability simulation using corresponding broadcast ephemeris. The results show that geometry-based selection using elevation and azimuth and signal-quality-based selection using elevation and signal-tonoise ratio (SNR) can both effectively reduce the number of satellites processed by the receiver, and reduce computational load by an average of more than 60%. However, the solution availability and stability drop significantly. ISM-based selection method reduces computational time to a similar degree, but the vertical protection level (VPL) loss under the former is less than 1 m, even reduced VPL in some epochs. The simulation results were similar to the MGEX station results. The availability after ISMbased satellite selection is significantly better than those obtained using fast satellite selection, and it is expected to be further improved as the enhancement of currently GNSS. These results suggest that the ISM-based method is more effective and feasible for reducing MHSS ARAIM subsets and improving computational efficiency, and can be a helpful extension of multi-GNSS ARAIM in the future. The rest of this paper is organized as follows. Section 1 briefly describes the basic principles of the MHSS ARAIM algorithm. And introduces several satellite selection methods, including fast satellite selection based on geometry or signal quality, and the ISM-based method we proposed. In Section 2, the performance results of the respective satellite selection methods are compared through an analysis of measured data and simulation results and, finally, Section 3 presents conclusions and an outlook for future work. 2. Principle and method 2.1. MHSS ARAIM algorithm The core of the ARAIM algorithm can be implemented in range domain and position domain, respectively. The

latter, such as MHSS ARAIM, is widely applied because of a concise relationship between the upper limit of positioning error and the given integrity risk. In the MHSS method, a position error bound is created for each fault mode by computing a position solution unaffected by the fault, then an error bound around this solution was calculated for the difference between the all-in-view position solution and the fault tolerant position (Blanch et al., 2013). The MHSS ARAIM baseline algorithm we used refer to EU U.S. (2016), and more details will not be described. As the performance requirements in the vertical direction are more stringent than in the horizontal direction, thus only the VPL is calculated as: ! ! ð0Þ ðk Þ N Faultmodes X VPL
b3 VPL
T k;3
b3 2Q pfault;k Q þ ð0Þ ðk Þ r3 r3 k¼1 ¼ PHMI VERT ð1


P sat;notmonitored þ P const;notmonitored Þ PHMI VERT þ PHMI HOR

ð1Þ

In Eq. (1), each term of the left hand side is an upper bound of the contribution of each fault to the integrity risk, where the allocation of the integrity budget into the N fault mode hypotheses. The VPL can be obtained using an iterative process, and specifically, a half interval search is adopted by EU U.S. (2016). It begins with the lower and upper bounds which relate to full and even allocation of the integrity risk, respectively, and stop when   VPLup
VPLlow   TOLpl ð2Þ or when the number of iterations exceeds N iter;max , where TOLpl ¼ 5e
2; N iter;max ¼ 100 in this study. 2.2. Availability criterion The following LPV-200 performance requirements in the ICAO GNSS standards and recommended practices (SARPs) can be used for the evaluation of ARAIM availability:    

4 m: 95% accuracy; 10 m: 99.99999% fault-free accuracy; 15 m: 99.999% effective monitor threshold (EMT); 35 m: 99.99999% limit on the position error, (i.e., the VPL must be below a vertical alert limit (VAL) of 35 m).

The last requirement is in the hazardous category, while the others are usually met when this requirement is encountered. For other criterions, refers to EU U.S. (2016).   EMT ¼ max T ðiÞ ði ¼ 1;    ; nÞ ð3Þ Accuð95%Þ ¼ K Acc  racc   VPE0 10
7 ¼ K FF  racc

ð4Þ ð5Þ

In these equations, K Acc ¼ 1:96, K FF ¼ 5:33, racc is the standard deviation of the vertical position solution. It is not difficult to have racc  10 m=K Acc < 4 m=K FF in the Eqs. (4) and (5), thus accuracy requirements of the LPV-

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

200 can also be equivalent to racc  10 m=K Acc ¼ 1:87 m,   where VPE0 10
7 is the more stringent requirement. However, under the premise that the coordinates of the station are known, VPE can also be computed as the difference between the computed position from the observations and the known position. 2.3. Subset complexity with multi-GNSS

Number of Subsets

Baseline ARAIM with solution separation testing allows for the handling of more potential threat modes than the conventional slope-based RAIM algorithm. As the number of potential threat modes increases, however, makes it necessary to detect and identify more fault subsets, which in turn inevitably efforts the computational load. The fault subset complexity is determined by the number of visible satellites, the prior fault probability of the satellites and the prior fault probability of the constellation. Fig. 1 shows the number of monitored subsets as a function of P Sat for a geometry with four constellations and P const fixed at 10
4 . When P Sat and NVS increase to a specific value, it will causes the probability of simultaneous fault by multiple independent satellites to exceed the threshold of integrity risk from unmonitored faults, which complicates the fault mode and increases the number of subsets that must be monitored. Fixing P Sat at 10
5 and monitoring 32 satellites from 4 GNSS constellations requires the calculation of C 132 þ C 14 þ C 24 ¼ 42 subsets, where C mN indicates the total number of possible combinations of N elements taken from m different elements, which is given by N! . However, this assumption is relatively optimistic m!ðN
mÞ! because to date only the Global Positioning System (GPS) has produced a sufficiently long history of constellation performance monitoring. Standard Positioning Service - Performance Standard (SPS PS) of GPS has provided assurances that there would not be more than three major service failures per year for the GPS as a whole, thus the GPS satellite prior fault probability is about 10
5 =ðhour  satÞð 3=½365d  24h  31satÞ (Blanch et al., 2010). For other constellations, especially those under con10

6

10

5

10 10 10 10 10

4

3

struction such as BDS and Galileo, the more conservative, rather than accurate P Sat ¼ 10
4 should be applied. At this time, the number of subsets required for monitoring by 1 2 the baseline MHSS method is ðC 32 þ C 14 Þ þ ðC 32 þ C 24 þ C 132 C 13 Þ ¼ 637. Although subset-filtering measures are contained in the baseline MHSS method, the number of subsets is still greater than 500. It should be pointed out that if P Sat at or above 10
3 , it is likely it will be rejected by certified aviation receivers. 2.4. Satellite selection method 1) GDOP-based Satellite Selection To carry out a performance comparison, we selected three fast satellite selection methods: S1, which is based on the signal quality (i.e. elevation angle and SNR); S2, a GDOP-based fast selection improvement method developed by Gerbeth et al. (2016) and S3, which adds a GDOP threshold constraint to S2 and selects an unspecified number of satellites. The basic processes applied by these selection methods are shown as flow diagrams in Fig. 2. In S1, all satellites are divided into regions based on satellite elevation angle. The regions fall into the respective ranges [<30, <60, <9 0] and are called the high, medium and low regions, respectively. The number of satellites to be selected in each region are 3: 3: 4, or ‘high’: ‘medium’: ‘low’, respectively. The satellite selection conducted in a given region is given with the following weight in terms of elevation angle and SNR:

Psat=1e-5 Psat=5e-5 Psat=1e-4 Psat=5e-4 Psat=1e-3

3

2

1

0

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Number of satellites Fig 1. Number of subsets as a function of NVS, P Sat .

Fig. 2. Flow charts of fast satellite selection methods.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

4

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

weight ¼ ( S ¼

1 ða0 þ a1  expð
El =10ÞÞ  S9

9; floor

SNR 5

SNR 45 ;

else

ð6aÞ ð6bÞ

The constant terms a0 and a1 are 0.13, 0.56 respectively. When the total number of satellites in a certain region is less than the number of satellites to be selected, additional satellites are selected in an adjacent region. The selection process of S2 proceeds as follows. First, two high-elevation angle satellites are selected to avoid a weak geometry for the remaining satellites, because a subsequent solution separation test needs to remove some high-elevation angle satellites. The optimal azimuth distribution of the remaining satellites is then calculated based on the azimuth of the lowest elevation angle satellites and, finally, the difference between the satellite azimuth and its optimal azimuth value is calculated for weight selection: Azopt;i ¼ Az0 þ i  Elopt;i ¼ 0

360 ðmod360Þ; k
2

i ¼ 1;    ; k
3;

weighti ¼ a  DAzi þ ð1
aÞ 

ð7aÞ ð7bÞ

DElbi ;

ð7cÞ

where the weighting factors a and b are 0.95 and 2, respectively. S3 just appends a DOP constraint procedure compare to S2. If the DOP value of the satellite subset selected under S2 does not meet the threshold requirement (such as GDOP < 2), in which the one of the remaining satellites with the largest GDOP improvement will be added. The procedure repeated until the requirement is met. Undoubtedly, for the performance of the satellite selection method, a fixed upper bound on the number of satellites provides a fair comparison of their performance. However, one of the things we want to study is: are more satellites better for the ARAIM user performance? In other words, is there always a positive correlation between VPL and GDOP? Accordingly, S3 was added for this secondary objective, which was to evaluate the correlation between GDOP and PL etc. Here, however, it is mainly used for further comparison of GDOP-based satellite selection methods, more detailed results are beyond the scope of this study. 2) ISM-based Satellite Selection An updatable ISM helps users adapt to a changing GNSS environment. ISM content generally includes the notional parameters listed in Table 1 (EU-U.S. 2016). The underlying concept of ISM-based satellite selection methods is that users can reduce the weights for some satellites with a high priori fault probability:

  S vert;i ¼ g P sat;i ; P Const;j ; URAi ; UREi ; bnom;i ; G

 1 1 ¼ jS 3;i j þ a  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ blog10 P sat;i URA2i þ b2nom;i  1 þ clog10 ; P Const;j

ð8Þ

where jS 3;i j is the vertical component of the ith satellite on the U  N dimensional projection matrix S, and
1

S ¼ ðGT WGÞ GT W ; a, b and c are weight factors for different ISM parameters, they were calculated following a large number of tests and numerical simulations. The overall flow chart of ISM-based satellite selection is shown in Fig. 3. 2.5. Determine the value of weight factors After the Eq. (8) is determined, determine the magnitude of these ISM parameters, or their assumption of prior weights is very essential at first. In design and valuation process for these parameters, a priori empirical hypothesis assumption that the satellite prior probability P sat is the most important parameter

for ARAIM, thus the value of its related term blog10

1 P sat;i

should be given a larger

weight, and the URA, P Const and vertical error parts jS 3;i j are the second, that is, the above weight ratio is about 2:1:1:1. Then, a large number of observation data and simulation were tested to obtain a satisfactory result, with the adjustment of these parameter values. Hypothetical function: hH ðXÞ ¼ S vert;H ðXÞ ¼ HT X

ð9Þ

H ¼ ½ h0 h1 h2 h3  ¼ ½ h0 a b c 

T X ¼ xi0 xi1 xi2 xi3 



 T 1 1 1 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi S log log j j 3;i ¼ 10 P sat;i 10 P Const;i URA2 þb2 T

i

T

nom;i

Cost function: Minimize

J ðH Þ ¼

m 1 X 2 ðVPLjh X i
VPLj0 Þ ; Hð Þ 2m j¼1

j is the jth epoch of training samples m

ð10Þ

Subject to hj > 0; j ¼ 0; 1; 2; 3 Under ideal conditions, the goal is to minimize the cost function J ðHÞ, which can be determined by various optimization methods, such as gradient descent. However, due to the fact that optimal parameter values change with the GNSS ISM parameters, and that VPL is not a direct function result of the hypothesis function hH ðXÞ, it is difficult to compute the differential of the cost function directly. As a preliminary study and engineering applications, a suboptimal result is enough to terminate the iterative search.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx Table 1 GNSS ISM parameters and descriptions. Parameter

Description

P Sat;i P Const;j rURA;j rURE;j

Probability of fault in satellite i at a given time Probability of fault in constellation j at a given time User range accuracy/signal in space accuracy for integrity User range error/signal in space error for continuity & accuracy Nominal bias term in metres

bnom;j

For example, by observing the trend of the cost function curve to find the optimal interval, and then using binary search method to continuously narrow the range of the optimal interval to search for parameter values, as shown in Fig. 4. This process simplifies the complex parameter optimization process and speeds up search efficiency. Taking a as an example, fixed the value of parameter b and c as 1 in the first search, it is preferred to give it different gradient values for testing, such as a from 0 to 10.0,

5

with a gradient 0.5, and then calculating the cost of each epoch at different parameter values. Where, in order to the comparison and analysis of each parameter, the cost calculated by each epoch will be processed with the MinMax normalization. The optimal interval of parameters b and c follows the same way in the first search. Noteworthy is that the optimal interval of a parameter depends on the trend of its cost function curve. For example, the optimal interval of parameter b is the range in which it begins to converge, while in other cases, it is the range of the lowest cost (around the local optimum) as the result. Then, narrow the search window and gradient step size to conduct the second parameter training search. However, different from the first search, in the subsequent parameter search, the fixed values of other parameters are the median of the range of their optimal interval and are updated with next parameter. In this search, a, b and c were conducted through three global searches, then a set of parameters was initially selected and verified through the test dataset.

Cost of normalization point

Fig. 3. Overall selection flow chart of ISM-based satellite selection method.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

cost of samples median cost of samples

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

value of parameter

α

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

cost of samples median cost of samples

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

value of parameter β

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

cost of samples median cost of samples

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

value of parameter

γ

Fig. 4. The optimal interval obtained by the first overall interactive search (window length = 2).

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

6

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

Finally, a satisfactory results, with the value a ¼ 2, b ¼ 3:5 and c ¼ 0:5 are obtained and used in Eq. (8) This is only an engineering rather than a theoretical optimization method, we can’t prove that these parameters are theoretically optimal, which requires further research and verification. However, it is enough to meet the needs of this study. 2.6. ‘‘Downdate” selection In calculating the weights of satellites using ISM-based selection, those satellites with higher prior fault probabilities and lower precisions are given lower weights. The ISM-based satellite selection process is as follows:  the projection matrix S and the vertical component of each satellite are calculated;  the ISM-based weight value S vert;i is then calculated for each satellite using Eq. (8);  the satellites corresponding to the k-highest weight values are retained. Instead of applying a heuristic or greedy optimisation algorithm, the value S vert;i of each satellite in Eq. (8) are obtained using the ranking selection method at one time. This method differs from conventional GDOP-based fast satellite selection in that its weighting is based on prior ISM parameters rather than satellite geometry. Unlike heuristic or greedy optimisation, it is not necessary to calculate other cost functions and perform iterations as the weights of the satellites can be calculated simultaneously. 2.7. Experiment and result In order to evaluate the effect of different satellite selection methods applied to MHSS ARAIM, both multiGNSS measurement data and simulation used to compare and analyze the availability and computational efficiency. As well as, due to the differences in the performance of different GNSS constellations, it is necessary to make corresponding numerical assumptions on ISM parameters.

various national agencies, universities and other institutions, the MGEX network comprised nearly 170 active stations as of October 2016. (Montenbruck et al., 2017). The simulations using the corresponding broadcast ephemeris for 001–005, 2018 provided by IGS, and the global coverage region [70S–70N,
180W–180E] was divided into 5°  5° grids, at 5 min intervals, with the cut-off elevation angle set to 10° to allow for the small banking of aircraft. The following schemes were subjected to performance analysis using measured data and simulation:    

No satellite selection ARAIM (S0); Signal-quality-based satellite selection method 1 (S1); Geometry-based satellite selection method 2 (S2); GDOP threshold constraint satellite selection method 3 (S3);  ISM-based satellite selection method 4 (S4). As a reminder, because no observations were used for the simulations, the signal-quality-based S1 approach were not assessed through simulation. 2.9. Assumed error model parameters Based on the current GNSS prior constellation performance and related researches, the assumed ISM parameters for each GNSS constellation are listed in Table 2. The URA/SISA values were set to 2.4 m for GPS, Galileo and BDS’s medium altitude Earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites (DoD U. S, 2001; EU-U.S. 2016; El-Mowafy and Yang. 2016; ElMowafy 2017; Montenbruck et al., 2017), while the GLONASS URA was set to 4 m following Walter et al. (2013). In particular, because BDS is a heterogeneous constellation, its geostationary Earth orbit (GEO) satellites are assessed to have larger orbit errors and require frequent orbital manoeuvring (CSNO, 2013; Li et al., 2015; Montenbruck et al., 2017); accordingly, its SISA was conservatively assumed to be 4 m (Wang et al., 2018). The updated URE/SISE parameters were assumed to be twothirds of the URA/SISA (EU-U.S. 2016). These values will hopefully be reduced following the launch of the next generation of modernized GNSS satellites.

2.8. Data and scheme Applying different satellite selection methods, ARAIM performance was tested and evaluated to five days (denoted here as ‘001–005, 2018’) of measurement data from 21 MGEX stations (shown in Fig. 5), the sampling interval of 30 s and an elevation angle of 10° (ftp://igs.ign.fr/pub/ igs/data/campaign/mgex/daily/rinex3/2018/). MGEX is an IGS initiative for the collection and analysis of data from GPS, GLONASS, BDS and Galileo. As a backbone of the MGEX project, a new network of Multi-GNSS monitoring stations has been deployed around the world in parallel to the legacy IGS network for GPS and GLONASS tracking. Building on volunteer contributions from

Fig. 5. MGEX stations location.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

7

Table 2 ISM parameters assumptions for Multi-GNSS. GNSS GPS Galileo GLONASS BDS

GEO MEO/IGSO

URA/SISA

URE/SISE

2.4 2.4 4.0 4.0 2.4

2 3 URA

The GPS was assumed to have aP sat of 10
5 =approach. As the other GNSS constellations lack a long-term history of performance monitoring, most the otherP sat values were conservatively assumed to be 10
4 =approach (Choi et al., 2011, 2012), except the P sat of GEOs was assumed to be 2  10
4 /approach. For vertical ARAIM, a P Const set at 10
4 =approach for all GNSS constellations was recommended (EU-U.S. 2016; El-Mowafy 2017). For all GNSS constellation, bnom was assumed to be 0.75 m. A more stringent and accurate definition for these parameters is beyond the scope of this research, they are however sufficient for the purpose of this study. 2.10. Performance of satellite selection Below, only the results for HKSL and KAT1 are presented, as those for the other stations were similar. It should be noted that fault detection and identification is beyond the scope of this paper, it needs future efforts to improve this function module. 2.11. ARAIM availability The NVS values for the five-day period 001–005, 2018 for stations HKSL and KAT1 are plotted in Fig. 6. There were sufficient numbers of available satellites at the two stations over the five-day period, which are both located in the Asia-Pacific region, with an average

Number of Satellites

40

NVS(HKSL)

P Sat
5

10 10
4 10
4 2  10
4 10
4

P const 10


4

bnom 0.75

availability of approximately 28 per station. Using the respective satellite selection methods, we alternately fixed the number of satellites at the stations to 10, 12, 14, 16, 18 and 20 to analyse how the number of satellites affected the performance of ARAIM. Fig. 7(a, b, top) shows the ARAIM results for various satellite selection methods at HKSL and KAT1, respectively, when the number of satellites is fixed at 18. Among them, we highlight the VPL sequence results obtained by all schemes, and specifically added EMT and VPE results for no-selection (S0) and ISM-based satellite selection (S4). The latter, VPE, is obtained by calculating the difference between the known position and the solution position of the MGEX station. A set of negative values of the VPL value symmetry was added to facilitate the display of the integrity overbounding capability of the ARAIM algorithm. It is seen that the VPL sequences obtained using the fast satellite selection methods (VPL (S1), VPL (S2), VPL (S3)) are all unstable relative to VPL (S0), which obtains VPL without satellite selection. Furthermore, for the fast satellite selection methods S1 and S2, their instability unfortunately cause the VPL of some epochs are greater than VAL, thereby reducing availability. The reasons for these results are not exactly the same, however, they are fundamentally similar. For selection method S2, it depends only on the strength of the user-satellite geometry without considering inherent satellite performance. Conversely, relying on satellite signal quality alone and regardless of the geometry, it also leads to unimproved availability, even

NVS(KAT1)

36 32 28 24 20 16 12 0

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000

Epoch/(30s) Fig. 6. Number of satellites available at HKSL and KAT1 from 01/01/2018–05/01/2018.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

8

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

Performance Criterions(/m) Performance Criterions(/m)

when the number of satellites is increased. For example, this effect is typically reflected in VLP (S1) at KAT1 station, which has a very poor satellite-user geometry during testing. When satellite selection performance is poor, a threshold constraint can generally be applied under GDOP to appropriately increase the number of satellite subsets, thereby improving the VPL and compensating the loss of user availability. However, such as VPL (S3) shown in Fig. 7(a, b, top), this is accompanied by further weakening of VPL in some epochs because the GDOP threshold constraint can only meet user needs in terms of geometric strength. In this case, when some satellites with poor prior integrity performance but significant geometric contribution are added, such as the GEO satellites of BDS constellation, it reduces the overall ARAIM availability as a side effect unexpectedly. 60

VPL(S0) VAL

40

VPL(S1) EMT(S0)

VPL(S2) EMT(S4)

VPL(S3) VPE(S0)

VPL(S4) VPE(S4)

20 0 -20 -40 -60 0

3000

40 30 20 10 0 -10 -20 -30 -40

VPL

0

3000

6000 9000 Epoch(/30s) VAL

EMT

12000

Accu(95%)

15000

VPE

6000 9000 Epoch(/30s)

12000

15000

Performance Criterions(/m)

Performance Criterions(/m)

a) HKSL: VPL results(top) and the extraction result of S4(bottom) 60

VPL(S0) VAL

40

VPL(S1) EMT(S0)

VPL(S2) EMT(S4)

VPL(S3) VPE(S0)

VPL(S4) VPE(S4)

20 0 -20 -40 -60 0 40 30 20 10 0 -10 -20 -30 -40

3000 VPL

0

3000

6000 9000 Epoch(/30s) VAL

EMT

12000

Accu(95%)

6000 9000 Epoch(/30s)

15000

VPE

12000

15000

b) KAT1: VPL results(top) and the extraction result of S4(bottom) Fig. 7. ARAIM availability criterions at HKSL and KAT1 station with the fixed N = 18.

The performance of ARAIM under ISM-based satellite selection is significantly better than that of the fast satellite selection approaches. The ISM approach produces a very small VPL loss, that is nearly equivalent to that of the VPL sequence produced under no satellite selection. Thus, the magenta line corresponding to ISM-based satellite selection VPL (S4) sequence is inevitably partially obscured by curve line of VPL (S0), and a similar situation exists for VPE (S0) and VPE (S4). For further analysis, we extract the results of S4 as Fig. 7(a, b, bottom). It is seen that it indicates the high compatibility of ISM-based satellite selection, which relies on not only the a priori performance of satellites, but also takes into account the geometry or signal quality, to the characteristics of ARAIM. In conclusion, from a given set of available satellites, the ISM approach can more effectively select a group satellites, its VPL is always bounded within VAL, and VPE is bounded by VPL. At the same time, other indicators of ARAIM availability, such as EMT and Accu (95%), can both satisfy the performance requirements of the LPV-200. Thus, the result shows that ISM-based approach has optimal ARAIM performance and assures user availability and integrity. However, accuracy, similar to availability, continuity and integrity, that is also an important and fundamental criterion, and even the basis of the latter. Thus, taking a fixed 18 satellites as an example, the following figure shows the change of the number of satellites and vertical positioning accuracy of each satellite selection method. Since S1, S2 and S4 both applied the same strategy (i.e. a fixed number of satellites), only the number of satellites for the ISM-based method S4 is depicted. As shown from Fig. 8(a), S4 can effectively reduce the number of satellites to 18. However, the number of satellites in S3 is partially uncertain, as it requires a different number of satellites to guarantee GDOP. As shown from Fig. 8(b), the overall accuracy of the VPE(S0) without the satellite selection method is optimal, and the mean value is 0.44 m and
0.34 m at HKSL and KAT1 stations, and the standard deviation is 1.89 m and 1.47 m, respectively. It also can be seen that, the ISM-based satellite selection reduced the number of receiver satellites to 18 quickly, and the loss of vertical positioning accuracy is the smallest after selection. The GDOP-based satellite selection method unexpectedly increases the vertical positioning residual value. The VPE obtained by the methods S1 and S2 fluctuates greatly from the Table 3. The maximum value of VPE are around 10 m and 12 m at HKSL and KAT1, respectively. For the selection method S3, which is constrained by GDOP, reduces this instability to some extent. However, it does not significantly improve the user accuracy, and additional satellites are required at HKSL. As a result of this instability, although the mean of VPE obtained by various methods is similar, both within 1 m, but the standard deviation (Std) is quite different. In particular, after the ISM-based selection fixed 18 satellites, the standard deviation of S4 is closest to the original result VPE(S0). It is 1.95 m and

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

Num. of Sats

40 36 32 28 24 20 16 12

Num. of Sats

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

40 36 32 28 24 20 16 12

HKSL

0

2000

NVS(S0)

4000

6000 8000 Epoch(/30s)

KAT1

0

2000

NVS(S3)

10000 NVS(S0)

4000

6000 8000 Epoch(/30s)

12000 NVS(S3)

10000

12000

DVPL ¼ VPLfixed
VPLall
in
view and RatioVPL ¼ VPLfixed = VPLall
in
view , respectively. It is seen from Fig. 9 that the loss of VPL diminishes as the number of fixed satellites increases. At NVS = 10, the loss of VPL is within the range 10–25 m, averaging around 12 m. As the number of satellites increases to 16 and then 18, the VPL loss by ISMbased satellite selection converges to 3 and then 1 m. This suggests that the marginal improvement in Multi-GNSS ARAIM VPL per added satellite flattens out above NVS = 18. However, a statistical analysis of RatioVPL at 18 satellites reveals a more significant result. In Fig. 10, RatioVPL > 1 indicates an increase in VPL value after fixed the number of satellites (ie, VPLfixed > VPLall
in
view ), which means a decrease in user availability performance and vice versa. It is seen that 40–50% of the epochs have VPL values that decrease (corresponding to improvements in availability) at NVS = 18. This indicates that VPL is not strictly positively correlated with the number of satellites or the geometry. VPL differs from GDOP in that, it is affected by both geometry and ISM. The latter measure always decreases with the number of satellites increase, however, availability does not necessarily increase/decrease as the number of satellites increases/decreases, which reflects the fact that availability can actually be improved after removing some satellites with poor prior ISM performance.

NVS(S4)

14000 NVS(S4)

14000

a) change of the number of satellites 9

VPE(S0)

VPE(S1)

VPE(S2)

VPE(S3)

VPE(S4)

VPE(/m)

6 3 0

-3 -6 -9 0

3000

9

6000 VPE(S0)

VPE(S1)

9000 Epoch(/30s) VPE(S2)

VPE(S3)

12000

15000

VPE(S4)

VPE(/m)

6 3 0

-3 -6 -9 0

3000

6000

9000 Epoch(/30s)

12000

9

15000

2.12. VPL stability with fixed satellite number

b) vertical position error obtained by various selection schemes Fig. 8. Change in the number of satellites (a), VPE at HKSL (top) and KAT1 (bottom) with NVS = 18 (b).

1.54 m at HKSL and KAT1, respectively, which means a more robust accuracy performance. Therefore, according to the above analysis, when there are a sufficient number of available satellites, the loss of positional accuracy is completely acceptable due to the reduction in the number of satellites. VPL shows an unexpected but interesting result. With the number of selected satellites fixed at 18, the VPLs before and after ISM-based satellite selection were used to calculate the differential and ratio statistics, that is the

As the number of satellites increases, both fast satellite and ISM-based selection can gradually improve the VPL and decrease the loss of ARAIM availability, but they do so with different results. Taking the HKSL and KAT1 station as examples, the VPLs obtained by satellite selection methods S1, S2 and S4 as a function of number of fixed satellites are shown in Fig. 11. It is seen from Fig. 11(a, b) that for a small number of selected satellites, e.g., NVS = 10 and 12, the conventional fast satellite selection methods can ensure a relatively optimal user-satellite geometry (such as GDOP) but produce poor availability. This is because under the threat mode triggered by the simultaneous fault of two independent satellites, when the number of satellites decreases due to

Table 3 Vertical position error statistic results for different satellite selections. Station

Statistics

S0

S1

S2

S3

S4

HKSL

Mean Std Minimum Median Maximum

0.4449 1.8925
6.6503 0.4288 9.7979

0.4731 3.1478
9.7888 0.3829 14.1986

0.6452 2.8979
9.8471 0.6719 7.3773

0.4296 2.3353
11.3023 0.4102 12.2679

0.5822 1.9504
7.4666 0.3618 11.4864

KAT1

Mean Std Minimum Median Maximum


0.3388 1.4663
5.3776
0.3535 5.4659


0.2625 2.1040
11.2863
0.2996 13.598


0.4275 2.3983
12.4773
0.2370 12.2634


0.3376 2.5609
7.1179
0.3250 7.9371


0.3396 1.5437
4.8626
0.3451 5.3324

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

10

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

Fig. 9. DVPL under different numbers of selected satellites produced by ISM-based satellite selection method at (a) HKSL and (b) KAT1.

solution separation, the satellites with the largest contribution of the geometric strength is likely to be excluded, resulting in a significant decrease in the geometric intensity. This indicates that, for an ARAIM user, a subset’s geometrical stability is more significant than its number of satellites. There are also some cases of very poor VPL selection when a relatively small number of satellites are fixed under the ISM approach. However, the convergence and stability of ISM-based satellite selection are significantly higher than under conventional fast satellite selection. As shown in Fig. 11 (c), the ARAIM availability improves rapidly as the number of satellites increases, reaching a sufficient stability at NVS = 14 with an average loss of about 5 m. 2.13. Simulation performance The simulated availability coverage performance of LPV-200 under GDOP-based and ISM-based satellite

Fig. 10. Values of RatioVPL at NVS = 18 produced by ISM-based satellite selection method at HKSL and KAT1.

selection methods S2 and S4, respectively, are shown in Fig. 12. The simulated grid point ‘Cov (>m%) = n%’ availability, indicates the ratio of the time for which VPL < VAL to the total time is greater than m %, and its coverage ratio of n % to the worldwide. It is a significant criterion used to describe the availability coverage of grid points. Under LPV-200, the (>99.5%) availability is generally required to be above 95% (EU-U.S. 2016). Fig. 12(a, b) shows the Multi-GNSS ARAIM availability coverage performance of fast satellite and ISM-based selection (NVS = 16), respectively. It should be noted that in the simulation, Accu (95%) is more optimistic to the real data because of no observations and noise. Thus, it is sufficient and more common to judge availability through VPL. From the figures it is seen that, when the number of selected satellites is fixed, the ARAIM availability following ISM-based selection is significantly better than that following fast GDOP-based selection. The worldwide availability of ground grid points following ISM-based selection is mostly above 70%, although it is relatively weak in low latitude areas. The (>90%) availability performance coverage is 24.75%, while the (>99.5%) coverage performance is only 0.28%. The grid point availability under GDOP selection is mostly below 10%, with a maximum availability of less than 25%, resulting in a surprisingly low (>90%) availability coverage of 0%. Fig. 12(c) shows the ARAIM availability performance distribution of the ISM-based selection method at NVS = 18, from which it is seen that increasing the number of satellites to 18 results in worldwide grid point availabilities that are mostly over 80%, with (>90%, >99.5%) availability coverages increased to 45.23 and 7.40%, respectively. Although these availabilities are still reduced by 14.27 and 19.34%, respectively, compare to the availabilities of Multi-GNSS ARAIM with no satellite selection (Fig. 12(d)). Because the current GNSS constellation is still in development and not fully operational, the worldwide performance of Multi-GNSS ARAIM is to a certain extent

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx 14 16 all-in-view

10 18

350

12 20

14 16 all-in-view

350

300

300

250

250

200 150 100

200 150 100 50

50

0 10 12 14 16 18 20 all-in-view

Fi

Fi

xe d

xe d

NV S

NV S

0 10 12 14 16 18 20 all-in-view 3000

6000

9000 12000

Epoch(/30s)

3000

15000

VPL(/m)

12 20

VPL(/m)

10 18

11

6000

9000

12000

15000

12 20

14 16 all-in-view

Epoch(/30s)

a) S1 at HKSL (left) and KAT1 (right) 12 20

10 18

14 16 all-in-view

350

350

300

300 200 150 100

250

VPL(/m)

250

200 150 100 50

0 10 12 14 16 18 20 all-in-view

0 10 12 14 16 18 20 all-in-view

3000

6000

Fi

Fi

xe d

xe d

NV S

NV S

50

VPL(/m)

10 18

3000

9000 12000 15000

Epoch(/30s)

6000

9000

12000

Epoch(/30s)

15000

b) S2 at HKSL (left) and KAT1 (right) 12 20

10 18

14 16 all-in-view

12 20

14 16 all-in-view

350

350

300

300 200 150 100

250

VPL(/m)

250

200 150 100 50

0 10 12 14 16 18 20 all-in-view

0 10 12 14 16 18 20 all-in-view

Fi

xe d

Fi xe d

NV S

NV S

50

3000

6000

9000 12000 15000

Epoch(/30s)

VPL(/m)

10 18

3000

6000

9000

12000

Epoch(/30s)

15000

c) S4 at HKSL (left) and KAT1 (right) Fig. 11. VPLs at HKSL (left) and KAT1 (right) for different numbers of satellites under different satellite selection methods: (a) S1, (b) S2, (c) S4.

limited. As shown in Fig. 12(d), the regional distribution characteristics of the BDS makes the availability performance of Multi-GNSS ARAIM in the Asia-Pacific region significantly superior to that in other regions. As a result, there is a significantly greater loss of availability outside of the Asia-Pacific under any ISM-based satellite selection method, and the simulated current ARAIM availability coverage accordingly failed to meet the 95% performance criterion. The simulated Multi-GNSS ARAIM (>90%, >99.5%) availability coverages were 59.46 and 26.74%,

respectively. However, these figures are expected to improve as the constellation is completed. 2.14. Efficiency of satellite selection The computational loads of all the satellite selection approaches are compared finally. Given the divergence of computer hardware performance, rather than the absolute time spent in computing we compared the rate of relative reduction in the average satellite selection time spent per

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

12

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

Fig. 12. Multi-GNSS ARAIM simulated global availability under different satellite selection methods.

epoch, which is given by tselection =tnoselection ð100%Þ. Obviously, the smaller the reduction rate, the better the improvement in computational efficiency. If the reduction rate is nearly 100%, it means that the calculation time before and after the application of the satellite selection is almost no reduction. Once again, we used the efficiency results for HKSL and KAT1 as proxies for all of the stations, and assessed the results for NVS = 9–20 satellites under the various selection approaches. The results, shown in Fig. 13, are not unexpected. The conventional fast satellite selection methods (S1, S2) show the lowest relative reduction rates, with the ISM-based selection method (S4) performing a little worse than S1 and S2, while S3, which applies a GDOP threshold, performed the worst. With NVS = 9, the satellite selection methods without GDOP threshold constraints significantly reduce the computational time and improve efficiency by about 90% at both stations. As the number of satellites for selection increase, the selection times spent by all methods increase as well. At NVS = 20 the computational efficiency decreases to a minimum of about 60–70%. These results indicate that the appropriate satellite selection method can reduce the computational time required by baseline Multi-GNSS ARAIM by more than half.

Although S3 requires a relatively longer computational time for satellite selection at each station, it still experiences a reduction rate of about 40%. Fig. 14 shows the computational time reduction rates of all 21 MGEX stations under the respective satellite selection methods (NVS = 18). It is seen from the figure that, although the reduction rate of ISM-based satellite selection is larger than that of the fast selection methods (S1, S2) at most of the MGEX stations, the loss of average VPL under the ISM approach is minimal and generally fluctuates around 0 m. Some of the MGEX stations are limited by geographic location and receiver channel, such as AJAC and GAMB, this resulting in fewer observations and weaker geometries, with about 20 available satellites. In these cases, there is a negligible improvement in computational time following satellite selection; for stations with sufficient observational resources, however, such as CUT0, DARW, HKSL, KAT1, etc., combining satellite selection with MultiGNSS ARAIM can improve the computational efficiency by more than 60%. It is also seen that the ISM-based satellite selection performance has higher stability, which indicates that this method is less affected by solution separation testing and therefore not as prone to reduced overall

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

13

Station:HKSL

S1-T S2-T S3-T S4-T

40 30 20 10 0 50

Station:KAT1

Time reduction rate in computation (%)

50

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

S1-T S2-T S3-T S4-T

40 30 20 10 0 8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

Number of fixed satellites

4 2 0 -2 -4 -6 -8 -10 -12 -14

S1-Time

S2-Time

S3-Time

S4-Time

AJ A CH C PG CU T DA 0 RW DJ I G G AM B HK SL HO FN KA T KO 1 UR LA UT M IZ U NK LG PO HN RO I2 ST FU ST J SU 3 TM TO N UR G UM XM IS

Time reduction rate in computational (%)

100 90 80 70 60 50 40 30 20 10 0

ΔVPL(/m)

Fig. 13. Reduction rates in computational time under various fixed satellite numbers and selection methods at HKSL and KAT1.

S1-vpl

S2-vpl

S3-vpl

S4-vpl

Fixed number of satellites = 18

Fig. 14. Average VPL loss and reduction rates in computational time under different fixed satellite numbers and satellite selection methods at MGEX stations.

satellite availability following the removal of satellites with important geometric strength contributions. 3. Summary and discussion The DFMC GNSS environment poses opportunities and challenges for the development of ARAIM. A greater number and more complex threat modes must be consid-

ered during precision approach phases, such as LPV-200, to ensure security for ARAIM users. In this study, conventional fast satellite selection methods were evaluated compared with a proposed ISM-based approach, that is optimised for ARAIM features. Based on the use of MGEX station data and simulation results to evaluate the effectiveness of the respective satellite selection methods, the following conclusions could be drawn:

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

14

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx

(1) In terms of satellite selection performance, ISMbased satellite selection is significantly better than geometry-based or signal-quality-based fast satellite selection methods. Results obtained using MGEX station data show that ISM-based satellite selection has the least loss of availability, the fastest convergence rate and the smoothest performance. At NVS = 14, the ISM-based VPL sequence already has sufficient stability, with an average VPL loss of approximately 5 m. At NVS = 18, the VPL loss is within 1 m and availability is actually improved in 40–50% of the epochs. (2) In terms of computational efficiency, the reduction in computational time under ISM-based optimisation is slightly lower than under the fast satellite selection methods. As the number of selected satellites increases, the trends in increase in computational time are fairly consistent across all methods, except for the DOP threshold method. At NVS = 20, satellite selection increases the computational efficiency by 60–70%. At NVS = 18, the VPLs produced by the ISM-based satellite selection method at various MGEX stations fluctuates around 0 m, with minimal VPL loss and even improvement in some cases, while the other selection methods result in more variable PLs. (3) In simulation using broadcast ephemerides and limited by the operational state of some GNSS constellations (such as BDS), the results for Multi-GNSS ARAIM do not meet the criterion of availability greater than 99.5% with coverage of more than 95%. At NVS = 16, the (>90%) availability of GDOP-based coverage is 0%, while the (>90%, >99.5%) availabilities of ISM-based coverage are 24.75 and 0.28%, respectively. At NVS = 18, these figures increase to 45.23 and 7.4%, respectively. However, they are still respectively 14.27 and 19.34% below those of baseline ARAIM without satellite selection. These results should improve once several GNSS systems reach their fully operational states.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We are very grateful to IGS and MGEX for providing Multi-GNSS data. We are also very grateful to the reviewers for their kind comments, especially the corrections in English expression. This research is partly supported by the National Natural Science Foundation of China (41877289, 41731066, 41604001, 41674034, 41974032), the Chinese Academy of Sciences (CAS) programs of ‘‘Pioneer

Hundred Talents” and the State Key Laboratory of Geoinformation Engineering, NO. SKLGIE2017-Z-2-1; National Key R&D Program of China (No. 2018YFC1504805). References Blanch, J., Walter, T., Enge, P., 2010. RAIM with optimal integrity and continuity allocations under multiple failures. IEEE Trans. Aerosp. Electron. Syst. 46 (3), 1235–1247. https://doi.org/10.1109/ TAES.2010.5545186. Blanch, J., Walter, T., Enge, P., 2013. Optimal positioning for advanced RAIM. Navigation: J. Instit. Navigation 60 (4), 279–289. https://doi. org/10.1002/navi.49. Blanch, J., Walker, T., Enge, P., et al., 2015. Baseline advanced RAIM user algorithm and possible improvements. IEEE Trans. Aerosp. Electron. Syst. 51 (1), 713–732. https://doi.org/10.1109/TAES.2014. 130739. Blanch, J., Walter, T., Enge, P., 2018. Fixed Subset Selection to Reduce Advanced RAIM Complexity. In: Proceedings of the 2018 International Technical Meeting of The Institute of Navigation, Reston, Virginia, January 2018, pp. 88–98. China Satellite Navigation Office (CSNO), 2013. BeiDou Navigation Satellite System Open Service Performance Standard (BDS-OS-PS1.0). http://www.beidou.gov.cn/xt/gfxz/201710/P02017120269322860 3215.pdf (2018/12 available). Choi, M., Blanch, J., Akos, D., et al., 2011. Demonstrations of multiconstellation advanced RAIM for vertical guidance using GPS and GLONASS signals. In: Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, pp. 3227–3234. Choi, M., et al., 2012. Evaluation of multi-constellation advanced RAIM for vertical guidance using GPS and GLONASS signals with multiple faults. In: Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), Nashville, TN, September 17–21, pp. 884–892. DoD U S, 2001. Global positioning system standard positioning service performance standard. Assistant secretary of defense for command, control, communications, and intelligence. https://www.gps.gov/technical/ps/2008-SPS-performance-standard.pdf (2018.12 available). EU-U.S, 2016. Cooperation on Satellite Navigation Working Group. CARAIM Technical Subgroup Milestone 3 Report. https://www. gps.gov/policy/cooperation/europe/2016/working-group-c/ARAIMmilestone-3-report.pdf (2018/12 available). El-Mowafy, A., Yang, C., 2016. Limited sensitivity analysis of ARAIM availability for LPV-200 over Australia using real data. Adv. Space Res. 57 (2), 659–670. https://doi.org/10.1016/j.asr.2015.10.046. El-Mowafy, A., 2017. Advanced receiver autonomous integrity monitoring using triple frequency data with a focus on treatment of biases. Adv. Space Res. 59 (8), 2148–2157. https://doi.org/10.1016/j. asr.2017.01.037. GNSS Evolutionary Architecture Study Phase II Report (GEAS), 2010. https://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/library/documents/media/GEASPhaseII_Final.pdf (2018/12 available). Ge, Y., Wang, Z., Zhu, Y., 2017. Reduced ARAIM monitoring subset method based on satellites in different orbital planes. GPS Solutions 21 (4), 1443–1456. https://doi.org/10.1007/s10291-017-0658-x. Gerbeth, D., Martini, I., Rippl, M., et al., 2016. Satellite selection methodology for horizontal avigation and integrity algorithms. In: Proceedings of the GNSS+ of the ION, Portland, OR, USA, pp. 12–16. ICAO, Annex 10, 2009. GNSS standards and recommended practices (SARPs). Section 3.7, Appendix B, and Attachment D, Aeronautical Telecommunications, Vol. 1 (Radio Navigation Aids), Amendment 84. Li, X., Ge, M., Ai, X., et al., 2015. Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J. Geod. 89 (6), 607–635. https://doi.org/10.1007/s00190-015-0802-8.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015

S. Luo et al. / Advances in Space Research xxx (2020) xxx–xxx Montenbruck, O., Steigenberger, P., Prange, L., et al., 2017. The MultiGNSS Experiment (MGEX) of the International GNSS Service (IGS)– achievements, prospects and challenges. Adv. Space Res. 59 (7), 1671– 1697. https://doi.org/10.1016/j.asr.2017.01.011. Rippl, M., Spletter, A., Gu¨nther, C., 2011. Parametric performance study of advanced receiver autonomous integrity monitoring (ARAIM) for combined GNSS constellations. In: Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, pp. 285–295. Wang, L., Luo, S., Tu, R., et al., 2018. ARAIM with BDS in the AsiaPacific Region. Adv. Space Res. 62 (3), 707–720. https://doi.org/ 10.1016/j.asr.2018.05.015. Walter, T., Blanch, J., Choi, M.J., et al., 2013. Incorporating GLONASS into aviation RAIM receivers. In: Proceedings of the

15

2013 International Technical Meeting of The Institute of Navigation, pp. 239–249. Walter, T., Blanch, J., Enge, P., 2014. Reduced subset analysis for multiconstellation ARAIM. In: Proceedings of the 2014 International Technical Meeting of the Institute of Navigation, San Diego, California, Jan 2014, pp 89–98. Walter, T., Blanch, J., Kropp, V., 2016. Satellite selection for multiconstellation SBAS. In: Proceedings of the ION GNSS+, Portland, OR, USA, 2016, pp. 12–16. Wu, Y., Wang, J., Jiang, Y., 2013. Advanced receiver autonomous integrity monitoring (ARAIM) schemes with GNSS time offsets. Adv. Space Res. 52 (1), 52–61. https://doi.org/10.1016/j.asr.2013.03.002.

Please cite this article as: S. Luo, L. Wang, R. Tu et al., Satellite selection methods for multi-constellation advanced RAIM, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.12.015