Advanced Receiver Autonomous Integrity Monitoring (ARAIM) Schemes with GNSS Time Offsets

Transcription

1 Advanced Receiver Autonomous Integrity Monitoring (ARAIM) Schemes with GNSS Time Offsets Abstract Yun Wu 1,2, Jinling Wang 2, Yiping Jiang 2 1 School of Geodesy and Geomatics, Wuhan University, P. R. China 2 School of Surveying & Geospatial Engineering, University of New South Wales, Sydney, Australia (jinling.wang@unsw.edu.au) Within the current Advanced Receiver Integrity Monitoring (ARAIM) scheme, the time offsets between different Global Navigation Satellite System (GNSS) constellations are estimated along with a position solution and the GNSS receiver clock error. This scheme is so-called Time-offsets Estimated ARAIM, i.e., TOE ARAIM. In order to enhance the interoperability and compatibility between different constellations, the time offsets are expected to be broadcast to users in future multi- GNSS positioning and navigation applications. This paper describes two new ARAIM schemes to make use of the Broadcasted Time Offsets (BTOs): Time Offset Observed ARAIM (TOO ARAIM) and Time Offset Synchronized ARAIM (TOE ARAIM). It has been shown that the VPL performances of these two new ARAIM schemes rely strongly on the accuracy of BTOs. By varying the error model of BTOs, the simulation results have also demonstrated that the proposed new TOO ARAIM scheme can outperform the existing TOE ARAIM scheme- even if the accuracy of BTOs for integrity is degraded to 4.5m and the probability of a BTO fault is relaxed to. In addition, the new Time Offset Synchronized ARAIM scheme (TOS ARAIM) can also perform better than the existing TOE ARAIM scheme if the accuracy of BTOs for integrity can reach.75m. As the TOO ARAIM also has a very relaxed requirement on BTOs and better performance, the TOO ARAIM is regarded as a better ARAIM scheme for multi-gnss with BTOs available. Keywords: ARAIM; GNSS; Time offsets 1. Introduction Satellite navigation Receiver Autonomous Integrity Monitoring (RAIM) has been used to support supplemental navigation in the en route and terminal area phases of flight and can also be used to support lateral guidance during the approach phase of flight. In the coming years, there will be at least three GNSS constellation: GPS, Galileo and COMPASS will broadcast signals in the two frequency bands: and which are available for civil aviation users. With access to a large number of pseudo-ranges in two frequencies, users can benefit by acquiring more accurate positions and higher integrity - with higher availability/coverage. This also increases the possibility of multiple failures. Thus, a more rigorous RAIM algorithm, so called Advanced RAIM, is expected to accommodate the complex threats to support stringent integrity requirements for both horizontal and vertical navigation defined for precision approaching phases of flight (e.g., LPV-2), ARAIM has been investigated by several researchers (Blanch, et al., 27, Ene, 26, Lee, 21, Report, 21) over the past five years.. The current ARAIM is based on Multiple Hypothesis Separation Solution (MHSS) concept, which can count any credible integrity threats. Compared with the conventional RAIM, ARAIM supplies a rigorous proof of safety while not being unnecessarily conservative(blanch, Ene&Walter, 27). By varying the satellite constellations and parameters of the threats model (Blanch, Ene&Walter, 27, Ene, Blance&Walter, 26, GEAS Phase II Report, 21), the performance of ARAIM has been analysed for years (Blanch, et al., 27, 21; Milner and Ochieng, 21, GEAS Phase II Report, 21, Rippl, et al, 211, Walter, et al., 28). Compared to a single constellation, Multi-Constellation ARAIM performance is significantly enhanced. (GEAS Phase II Report, 21) shows that under the 1

2 assumed parameters, the ARAIM algorithm with 21 GPS satellites and 24 GNSS-2 satellites can provide worldwide (between and ) LPV-2 capability. In the above mentioned multi-constellation ARAIM studies, ARAIM formulas were used by adding one more unknown parameter into the least-squares solution to take into account the time offset between every pairing of two different navigation positioning systems. In this way, the time offset is treated as an unknown to be estimated along with both the position solution and the receiver clock error. This scheme is referred to here as the Time Offsets Estimated ARAIM (TOE ARAIM). By using the TOE ARAIM, users do not need to be subjected to the threats of time offsets between different constellations. This scheme is adopted by (GEAS Phase II Report, 21). However, this advantage is gained at the cost of the user-satellite geometry strength and ARAIM availability as the time offset unknowns have to be estimated. In order to enhance the interoperability and compatibility between different constellations, the satellite navigation system providers have been planning to observe and broadcast the time offsets to users (Galileo-OS-SIS-ICD, 21, Hahn and Powers, 25, ICD-GLONASS, 28, IS-GPS-2D, 26, Lu, 28). Besides, the stability of the time offsets (Cai and Gao, 29, Hahn and Powers, 25) makes feasible the estimation of time offsets as well. Certain accuracies of the Broadcasted Time Offsets (BTOs) have been expected. For example: the accuracy of the time offset between GPST (GPS Time) and GST (Galileo System Time) is expected to be less than 5ns (1.5m in range) with 2- sigma confidence level over any 24 hour period (Hahn and Powers, 25; IS-QZSS, 212). By making use of the BTOs, an earlier study (Wang et al, 211) showed that reliability is enhanced without costing the fifth satellite. And assuming that the a priori known time offset is available to users, Cai and Gao (29) showed that position solution could be obtained with only four GPS/GLONASS satellites only slight loss of accuracy. However, when the BTOs are being used in safety-of-life applications, the current ARAIM cannot be just simply applied without considering the potential threats caused by the BTOs. How the ARAIM to benefit from the use of BTOs, and how much, if at all, the ARAIM performance gains by making use of the BTOs have not been presented in the literature. This paper therefore aims to present two new ARAIM schemes to make use of BTOs. The first approach treats the BTOs as quasi-observations (Cai and Gao, 29) which is called Time Offsets Observed ARAIM (TOO ARAIM) in this context. By using the TOO ARAIM, the time offset unknowns are estimated along with user position and receiver clock error. The second approach, making use of BTOs, is called Time Offsets Synchronized ARAIM (TOS ARAIM). This synchronizes all range observations into a common time system. In this way the position solution can be solved as single constellation. The remainder of this paper is organized as follows. In Section 2, the current ARAIM algorithm for a multi-constellation solution is reviewed. Following this, the two new ARAIM schemes which make use of the BTOs are presented. The Time Offsets Observed ARAIM (TOO ARAIM) scheme and the Time Offset Synchronized ARAIM (TOS ARAIM) scheme are described by rigorously considering the threats caused by the BTO. Section 3 first discusses the sensitivities of the two new ARAIM schemes with time offsets to the relevant parameters. These are then compared with TOE ARAIM, and VPL performances of the two new ARAIM schemes with time offsets, which are assessed by the use of multiple simulations. Finally, in the last section, some conclusions are drawn. 2. ARAIM Schemes with GNSS Time Offsets In this section, the current multi-constellation ARAIM -TOE ARAIM is presented. Then by reconsidering the various threat causes and modifying the nominal error model, the new TOO ARAIM and TOS ARAIM schemes for multi-constellations are described. 2.1 Time Offsets Estimated ARAIM (TOE ARAIM) The ARAIM algorithm is based upon the Multiple Hypothesis Solution Separation (MHSS) which, in turn, directly computes the integrity risk under the combined consideration of all single hypotheses 2

3 and the fault-free hypothesis. The integrity risk is computed by counting the contribution of each threat of the hypotheses, { } weighted by a priori probability of { } occurring, { } (1) in which is the number of fault hypotheses. For the fault-free hypothesis, the a priori probability of it occurring is approximately equal to one. The ARAIM algorithm in (GEAS Phase II Report, 21) makes no attempt to detect simultaneous multiple satellite faults, thus the integrity risk from multiple satellite faults, is subtracted from the required Probability of Hazardous Misleading Information (PHMI),. The simultaneous multiple faults could be caused by problems with the Earth Orientation Parameters (EOPs) or the Earth Orientation Parameter Predictions (EOPPs) and other, not yet fully characterized possible causes (GEAS Phase II Report, 21). In this case, only fault-free and single-satellite fault hypotheses are left in equation (1), so that is the number of visible satellites. Given a vertical error limit VAL (vertical Alert Limit), if integrity risk calculated by equation (1) can satisfy the integrity requirement is declared to be met. Inversely, given the a priori probability, if and the required continuity risk are distributed to each hypothesis,the vertical error bound: (Vertical Protection Level) corresponding to the each hypothesis can be calculated (GEAS Phase II Report, 21). The user s is determined by where is the vertical error bound for the subset vertical solution by eliminating the range observation. In the ARAIM algorithm, is calculated by using a more conservative nominal error model in which and the maximum bias, are used to meet the integrity requirement. A more realistic nominal error model is one in which no-integrityassured ) and nominal bias, are used to satisfy the continuity/accuracy requirement. If satellite fault detection is applied in the position domain, the test statistics for hypothesis is calculated by the Solution Separation (4) where and are the subset vertical solution and the full-set vertical solution, respectively. When the ARAIM is based on one single constellation, for example GPS constellation, the design matrix is expressed as (3) (2) (5) [ ] where is the direction cosine to the satellite and the last column is used to take into account the user receiver clock error which refers to the GPS time. If additional constellations are combined with the GPS constellation, the range observations are (6) where is the GPS range observation vector. If only one additional constellation is combined with the GPS constellation (7) When two additional constellations are combined 3

4 and are the range observation vectors of the first and second additional GNSS constellations, respectively. Corresponding to equation (6), the weight matrix of range observations, used to evaluate integrity is given by where and are the variance matrixes of GPS and the additional constellation range observations, respectively. and are calculated by using the. The weight matrix used to calculate accuracy/continuity is formed in the same way but by replacing by the. Because the range observations in equation (6) conformed to different satellite navigation time systems, the time offset between any two constellations causes a bias. The usual way to handle the time offset bias is to put an unknown in the estimate vector. Thus, the estimate vector is [ ] (1) (9) (8) Corresponding to equation (7) And the design matrix is (11) [ ] [ ] [ ] If the second additional constellation is combined (13) Similarly, the design matrix equation (12) is extended to take into account the time offset. Due to the time offsets being absorbed by, ARAIM users need not be concerned by any potential threats caused by the time offsets. However, this advantage is gained by lowering the ARAIM performance due to the loss of one satellite - which is used to estimate each unknown time offset. 2.2 Time Offsets Observed ARAIM (TOO ARAIM) The stability of the time offset enables us to predict the time offset. When the time offset between two different constellations, the BTO, is broadcasted, can be regarded as a quasi observation and involved in the observation equation. The observation vector is If only one additional constellation is combined with GPS constellation The corresponding design matrix is formed by (14) (15) (12) [ ] [ ] (16) [ ] 4

5 The estimate vector is expressed in the same way as is equation (1) but is estimated differently from the TOE ARAIM. If one more constellation is combined, the quasi-observations are The design matrix is extended in the same way to conform to its observation vector (14) and (17) and the corresponding estimate vector. Because the BTOs are treated as observations, the position solution can be estimated only if at least four satellites of the multi-constellation are visible. The user-satellite geometry is strengthened by the external information of the BTOs. Besides, the fault detection of quasi-observation can be applied in position domain in the same way as for the hypothesis test for the separation solution of range observations. Since the quasi-observation is involved in the observation vector, the nominal error model should be reconsidered. The nominal error of a BTO is caused by the accuracy limits of the ground clock determination process and, as well, the limits of the time offset prediction model. The nominal error can be bounded by a normal distribution with standard deviation and bias. For a quasi-observation, the conservative standard deviation and the maximum bias are used to determine integrity and a more realistic standard deviation and a nominal bias are used for continuity/accuracy determination. Hence, corresponding to the observation vector (14), the weight matrix is (17) (18) where is the variance matrix of (19) or Similarly, the weight matrix. (2) to determine continuity/accuracy is extended by including For the ARAIM user, the algorithm must take into account all credible threats. When is involved in the observations, its risks are imposed on user as well. Thus the risks caused by should be dealt along with the other threats (Blanch et al., 211). First, a fault is the one of the threats to increase risk and diminish its integrity. A fault could be caused by ground and satellite hardware, software error, design flaws or communications link errors. Suppose and are mutually statistically independent as well as on the range observations, the integrity risk caused by a fault is { }, in which is the a priori probability of the faulty. The a priori probability of a faulty BTO can be converted to the frequency per year see Table 1. Table 1 A Priori Probabilities of a BTO Fault and Frequencies of a BTO Fault Frequency 3times/year 3times/year 3times/1 year 3times/1 year Second, even if the BTO is fault free, the nominal error of the BTO could lead to integrity risk. The integrity risk caused by a fault-free BTO is combined with the integrity risk cause by fault-free fullset range observation: { } in which is fault-free hypothesis of equation (14). Suppose the 5

6 probability of fault-free is approximately one, and probability of fault-free full-set is approximate one as well. Thus the a priori probability of occurring will be approximately one. Therefore, the integrity risk hypotheses (Blanch et al., 21) where can be computed by counting the contributions of each possible { } { } (21) is the number of time offsets, i.e., the number of additional constellations. Then the vertical error bound is calculated by removing the fault observation: the is the vertical error bound corresponding to hypothesis and the is the vertical error bound corresponding to hypothesis. The for the position solution is determined as the maximum of and 2.3 Time offsets synchronized ARAIM (TOS ARAIM) Another way to make use of the BTO is to synchronize one navigation time system to another. For example, when GPS/Galileo are used, the Galileo system time can be synchronized with GPS time by adding BTO onto the Galileo range observations. After all range observations are synchronized into a common time system, users can treat all the range observations as if they were from a single constellation. In this way, only the position and the receiver clock error need to be estimated 6 (22) [ ] (23) The observation matrix is the design matrix for a single constellation, shown by equation (5). However, the error of the BTO also is also propagated into the synchronized range observations. Besides, the synchronized range observations are mutually stochastically dependent due to the time synchronization. In this paper, this dependence caused by the time synchronization is neglected. The weight matrix for integrity is therefore given by is formed in the same way but by using the URE and. With the time synchronized range observations, the user can estimate their position solution with only four satellites of a multi-constellation. However, for safe-of-life applications, ARAIM should rigorously examine the potential integrity risk as thoroughly as possible. Once the BTO is faulty, this results in all observations of additional GNSS constellation to be faulty. The consequence of a faulty BTO is the same as the failure of a whole single constellation. To deal with the constellation failure caused by a faulty BTO, two methods are proposed. Method 1 If we consider that the failure of an additional GNSS constellation is caused by a faulty to be hypothesis, and incorporate it into MHSS, then equation (1) can be extended by adding the hypothesis for the whole of constellation fault (24) { } { } (25) where the a priori probability of a fault BTO, is the probability of occurring. In this way, is contributed by a fault-free hypothesis, all single-satellite fault hypotheses and the constellation fault hypothesis caused by a fault. the vertical protection level corresponding to is calculated by removing the all range observations of the additional constellation. is determined by

7 The fault detection of can also be applied in the position domain by applying the hypothesis test to separation solution of. Method 2 An alternative method is to keep the fault-free and the single-satellite fault hypotheses in equation (1), thus the integrity risk caused by time synchronization should be taken out from the (27) in which is the integrity risk caused by synchronizing the additional GNSS constellation range observations into the GPS observations. The remaining integrity risk is then distributed to the fault-free and single-satellite fault hypotheses. is determined by In this paper, by maintaining fault-free and single-satellite fault hypotheses in the MHSS, Method 2 is adopted to test the performance of TOS ARAIM. 3. Performance of the ARAIM Schemes with Time Offsets A set of simulations were implemented by using the modified MAAST platform with the author selfimbedded ARAIM module. To assess the performances of the three ARAIM schemes with time offsets, the simulations have been run under different assumptions. 3.1 Assumptions of Simulation Three sets of multi-constellations with different number of satellites operating in each constellation were used: Multi-Constellation 1:18 GPS +18 Galileo satellites Multi-Constellation 2: 24 GPS+18 Galileo satellites Multi-Constellation 3: 18 GPS + 18 Galileo +18 COMPASS satellites Multi-Constellations 1 and 3 are made up of reduced multiple constellations. There are two reasons to design the multiple reduced constellations. The first is that a reduced constellation may be available years before the respective constellations are fully populated. A second reason is to see how TOO ARAIM and TOS ARAIM perform with limited satellite visibility. By increasing the GPS satellites in Multi-Constellation 1 by 6, Multi-Constellation 2 is made up of the core GPS constellation of 24 satellites and a reduced Galileo constellation with 18 satellites. Multi-Constellation 2 is used to test if TOO ARAIM and TOE ARAIM can improve ARAIM performance when the user-satellite geometry is enhanced. The required integrity risk and the continuity risk are and per approach, respectively. The Integrity risk of simultaneous multiple satellite faults, takes out of the required integrity risk (GEAS Phase II Report, 21). The value of is dependent on how and continuity risk are allocated for each hypothesis. In order to reduce the maximum value of, a numerical search can be done either by optimally allocating the and simultaneously or by taking two steps to allocate and (Blanch, Walter&Enge, 21). Because the improvement of with an optimal allocation of is not as significant as it is with an optimum allocation of, in this paper, is evenly allocated on each hypothesis and is optimally allocated on each hypothesis to reduce. (28) (26) 7

8 Table2 URA, URE, Maximum Bias and Nominal Bias of the BTO URA(m) Maximum Bias(m) URE(m) Nominal Bias(m) The remaining parameters are assumed as follows. The a priori probability of a single satellite fault is. The GPS, Galileo and COMPASS satellite range observations take the identical nominal error model in which the airborne error is bounded by following the formulas in (Blanch, Ene, Walter, 27) and Model A (AAD-A)( RTCA/ DO-229D, 26). And the Satellite clock/ephemeris errors, antenna biases and nominal signal deformations are bounded by URA and maximum bias for the evaluation of integrity, and URE and nominal bias for the evaluation continuity/accuracy (shown in Table 2) Choices of the Time Offsets Observed ARAIM (TOO ARAIM) related Parameters The Time Offsets Observed ARAIM (TOO ARAIM) is related to another two parameters: the a priori probability of a faulty BTO, and the nominal error of the BTOs. In this section, the a priori probabilities of a faulty BTO designed in Table 1 are used to test if is sensitive to. The nominal error of the BTOs is described by the Error Model (EM) of the BTOs designed in Table 3. The standard deviation for accuracy/continuity starts with an optimistic value of.37m, followed by the expected value by GGTO (GPS to Galileo Time Offset) WGA-Subgroup (Hahn and Powers, 25):.75m, then degrades to 1.5m and 2.25m. The standard deviation for integrity is two times bigger than. The biases of BTO for both the integrity and accuracy/continuity are assumed to be zero. Table 3 Error Models (EMs) of the BTOs Accuracy and Bias EM1 EM2 EM3 EM In order to test how the performance of the TOO ARAIM is related to and to the error model of the BTOs, the over the course of a day was computed for a single user located at Sydney with Multi-Constellation 1. The user-to-satellite geometry was simulated every 5 minutes (giving 288 epochs) and for each time a was computed following the TOO ARAIM. First, with the fixed to be, s over course of a day by varying error model of BTOs from optimistic case EM1 to worst case EM4 are given by Figure 1.When the error model of the BTOs changes from EM1 to EM4, has an obvious tendency to increase. The maximum in a day corresponding to the four error model of BTOs is meters. This example indicates of TOO ARAIM tightly depends on the accuracy of BTOs, thus the performance of TOO ARAIM should be assessed by varying the accuracy of BTOs. Second, by fixing the error model of BTOs on the expected accuracy EM2, varying from to, of the single user is shown by Figure 2. Comparing when using different value of, doesn t show significant change even if the a priori probability increases by three orders 8

9 VPL(m) VPL(m) of magnitude. Thus, the of TOO ARAIM is not sensitive to. Therefore, in the following simulations, the performance of TOO BTO was conservatively accessed by fixing in the worst case: (Later simulations show TOO ARAIM has a better performance than TOE ARAIM, thus the performance of TOO ARAIM was conservatively accessed from the safety point of view) Epoch 1 EM1 EM4 EM3 EM2 Accuracy of BTO Epoch P ft_ tj 1-2 Figure 1 TOO ARAIM: VPL as Function of Accuracy of BTO Figure 2 TOO ARAIM: VPL as Function of P ft tj Choices of the Time Offsets Synchronized ARAIM (TOS ARAIM) Related Parameters Method 2 -Time offsets Synchronized ARAIM (TOS ARAIM) Method 2 maintains a fault-free hypothesis and the single satellite fault hypotheses in MHSS. The performance of the TOS ARAIM depends on not only the error model of the BTOs but also on the. The is the integrity risk allocated on the threat caused by a BTO, and then taken out of the required PMHI. In this section, two budgets of are tested: first is set be which is as the same as the ; then is conservatively set to be which takes half of the required integrity risk,. In order to see if the is sensitive to the two parameters, the over the course of a day at a location in Sydney was computed by varying error model of the BTOs and. First, with being, and by changing the accuracy of BTOs from EM1 to EM4, the over a day corresponding to the four error models of the BTOs was computed and is shown in figure 3. Obviously, significantly increases when the accuracy of BTOs degrades from EM1 to EM4. The maximum over a day corresponding to EM1, EM2, EM3 and EM4 are [ ] meters, respectively. Therefore, the accuracy of the BTOs is the critical parameter influencing the performance of the TOS ARAIM. Figure 4 shows how changes with varying from to. In this example, the EM2 model error of BTOs was used. The maximum over a day increases from 31.7m to 36.7m when increases from to. This indicates that the parameter also influences the performance of TOS ARAIM. In this paper, the more optimistic value,, was used in the following simulations. (Later results show the TOS ARAIM has a worse performance than TOE ARAIM in most simulations, and thus the optimistic integrity risk caused by BTOs was allocated on the threat caused by the BTOs.) 9

10 VPL(m) VPL(m) Epoch 1 M1 Figure 3 TOS ARAIM: VPL as Function of Accuracy of BTOs M3 M4 M2 Accuracy of BTO Epoch P HMI_ tj Figure 4 TOS ARAIM: VPL as Function of P HMI tj Results of Simulation We simulated 288 users worldwide located on a grid every 5 degrees in both longitude and latitude (between ). For each location, the geometries were simulated every 5 minutes. For each time and location a was computed by following the three ARAIM schemes with GNSS time offsets specified above. Then of 99.5% availability over course of day (99.5 percentile ) for each location was thus computed. In the following simulations, the performances of TOO ARAIM and TOS RAIM are assessed by varying the error model of the BTOs from M1 to M4. The a priori probability of a faulty BTO was fixed to be in TOO ARAIM. For TOS ARAIM, is optimistically assumed to be Results with Multi-Constellation 1 First, the Multi-Constellation 1 of 18 GPS and 18 Galileo was used to test the performance of the three ARAIM schemes with time offsets. The results of the simulation are tabulated in Table 4. The average 99.5% is an average of the 99.5 percentile over the world ( ). The coverage of 99.5% availability for a given Vertical Alert Limit (VAL) is the fraction of the world that has 99.5% below the VAL. Figures 5, 6 and 7 give plots of the of 99.5% at the 288 simulated users computed by the TOE ARAIM, TOO ARAIM and TOS ARAIM, respectively. The s in Figures 6 and 7 were computed by using the EM2 error model of the BTOs. Compared to TOE ARAIM, if the accuracy of BTOs can meet the accuracy of EM1, the coverage of TOO ARAIM can increase by 26%. However, EM1 defines a more optimistic accuracy value of the BTOs than is achieved to date. If the accuracy of the BTOs can reach the expected accuracy EM2, the coverage of the TOO ARAIM can increase by 2%. The TOO ARAIM gives the better performance than the TOE ARAIM - even if the worst error model of BTO, EM4, was used. The performance of the TOS ARAIM is better than the TOE ARAIM only if the accuracy of BTOs can reach EM2 or better. The results also show when the accuracy of BTO worse than EM2, the performance of TOS ARAIM dramatically degrades. 1

11 Latitude (deg) Latitude (deg) Latitude (deg) VPL as a function of user location Longitude (deg) < 12 < 15 < 2 < 25 < 3 < 35 < 4 < 5 > 5 VPL (m) -99.5%, average 99.5% VPL=32.6m Figure 5 TOE ARAIM with Multi-Constellation 1: 99.5% VPL 6 VPL as a function of user location Longitude (deg) < 12 < 15 < 2 < 25 < 3 < 35 < 4 < 5 > 5 VPL (m) -99.5%, average 99.5% VPL=27.73m Figure 6 TOO ARAIM with Multi-Constellation 1: 99.5% VPL 6 VPL as a function of user location Longitude (deg) < 12 < 15 < 2 < 25 < 3 < 35 < 4 < 5 > 5 VPL (m) -99.5%, average 99.5% VPL=31.94m Figure 7 TOS ARAIM with Multi-Constellation 1: 99.5% VPL 11

12 Table 4 Performance of TOE/TOO/TOS ARAIM with Multi-Constellaiton 1( ARAIM, for TOS ARAIM) for TOO Average 99.5% Coverage of 99.5% Availability (VAL=35) EM of TOE TOO TOS VAL TOE TOO TOS BTOs EM % 91.72% 91.61% EM % 87.92% 77.3% EM % 82.36% 24.28% EM % 78.52% Results with Multi-Constellation 2 Multi-Constelaton 2 with a full GPS constellation of 24 satellites combined with a reduced Galileo constellation of 18 satellites was used to test how TOO ARAIM and TOS ARAIM perform with more satellites in view. The average of and coverage of 99.5% availability are given by Table 5. In this simulation, which has 6 more GPS satellites involved, the performances of all three ARAIM schemes with time offsets all are significantly improved (Compared with Table 4). With the Multi-Constellation 2,when comparing the performance of TOE ARAIM,, the benefit coming from the TOO ARAIM is not as significant as it is for Multi-Constellation 1. However, when the VAL is 35m, the TOO ARAIM can improve the coverage to 1%.As we see in Table 5, with all the error models of the BTO, the TOO ARAIM performs better than the TOE ARAIM. However, the coverage of TOS ARAIM dramaticallydecreases to.14% when accuracy of the BTO degrades to EM4. Table 5 Performance of TOE/TOO/TOS ARAIM with Multi-Constellaiton 2 ( TOO ARAIM, for TOS ARAIM) for Average 99.5% VPL Coverage of 99.5% Availability EM of TOE TOO TOS VAL TOE TOO TOS BTOs EM EM EM EM Results with Multi-Constellation 3 The performances of the three ARAIM schemes with time offsets were tested using the same relevant parameters as used in Section and Section but with Multi-Constellation 3. Average global and coverages of 99.5% availability under different VAL are shown by Table 5. 12

13 With the Multi-Constellation 3, because more satellites are in view, the TOO ARAIM performs better, but does not significently improve the performance of ARAIM even though two BTOs are being used by TOO ARAIM. As seen in Sections and 3.2.2, the performance of TOS ARAIM significantly worsens when the accuracy of the BTO is poorer than M2 especially when VAL is 2m or 12m. Table 6 Performance of TOE/TOO/TOS ARAIM with Multi-Constellaiton 3( ARAIM, for TOS ARAIM) for TOO EM of BTOs Average 99.5% VPL Coverage of 99.5% Availability TOE TOO TOS VAL TOE TOO TOS EM EM EM EM Conclusions The ARAIM has been proposed to enable aviation safety-of-life operations, particularly in vertical guidance of aircraft for precision approaches to airports. In the current ARAIM algrithm, the time offsets between different GNSS constellations are estimated as unknowns (TOE ARAIM), but with the loss of one satellite for each additional combined GNSS costellation. In order to enhance the interoperability and compatibility of GNSS, it is expected that the time offsets between GNSS constellations will be available to users. The issue that needs to be investigated, therefore, is how to make use of the BTOs in ARAIM. This paper presents another two ARAIM schemes to make use of the BTOs: the Time Offsets Observed (TOO) ARAIM and the Time Offsets Sychronized (TOS) ARAIM. By varying relevant parameters, the examples of a single user s show that the accuracy of BTOs is the critical parameter influencing the performances of TOO ARAIM and TOS ARAIM. In this paper, the simulation results were computed by relaxing the a priori probability of a faulty BTO, to be for the TOO ARAIM and optimistically setting the integrity risk caused by a faulty BTO to be. The results of simulation show that with Multi-Constellation 1, by making use of the BTOs, the TOO ARAIM can significantly improve the performance if the BTOs can reach the expected accuracy. With all the simulated Multi-Constellations, by varying the error model of the BTOs from EM1 to EM4, the TOO ARAIM can perform better than TOE ARAIM. When the Multi-Constellation strength becomes stronger, the improvement of the TOO ARAIM becomes less significant. 13

14 The TOS ARAIM is very vulnerable to the accuracy of the BTOs compared with the TOO ARAIM. The results show that the TOS ARAIM only performs better than the TOE ARAIM if the accuracy of the BTOs can reach M1 or M2. When the accuracy of the BTO deteriorates to ME3, the performance of the TOS ARAIM degrades dramatically. TOO ARAIM is robust to the accuracy of the BTOs and maintains a better performance than the TOE ARAIM, even if the accuracy of the BTOs is relaxed to EM4. In all simulations of the TOO ARAIM, the a priori probability of a fault BTOs is conservatively set to be. This indicates the TOO ARAIM does not need a tight requirement for the probability of a faulty BTO. Besides, from proof point of view, With fault detection for the BTOs in position domain, the TOO ARAIM is a more rigorous algorithm than the TOS ARAIM, thus the TOO ARAIM is recommended to make use of the BTOs in future. Acknlowdgement The first author is sponsored by the Chinese Scholarship Council for her research as a visiting academic at the University of New South Wales, Sydney, Australia. References Blanch, J., Ene, A., Walter, T. and Enge, P., An Optimized Multiple Hypothesis RAIM Algorithm for Vertical Guidance, ION GNSS 2th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, TX, , 27. Blanch, J., Walter, T. and Enge, P., RAIM with Optimal Integrity and Continuity Allocations Under Multiple Failures, IEEE Transactions on Aerospace and Electronic Systems, 46, , 21. Blanch, J., Walter, T. andenge, P., A Proposal for Multi-Constellation Advanced RAIM for Vertical Guidance, ION GNSS 24th International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland OR, , 211. Cai, C. and Gao, Y., A Combined GPS/GLONASS Navigation Algorithm for use with Limited Satellite Visibility, Journal of Navigation, 62, , 29. RTCA/ DO-229D, Minimum Operational Performance Standards for Global Positioning System/Wide Area Augmentation System Airborne Equipment, RTCA Special Committee (SC) 159, 26. Ene, A., Blance, J.and Walter, T., Galileo-GPS RAIM for Vertical Guidance, ION NTM 26, Monterey, CA, 1-9, 18-2 January 26. Galileo-OS-SIS-ICD, Galileo Open Service/Signal-In-Space Interface Control Document, European Union, 1.1, 21. Hahn, J.H. and Powers, E.D., Implementation of The GPS To Galileo Time Offset (GGTO), Frequency Control Symposium and Exposition, Vancouver, Canada, 33-37, 25. ICD-GLONASS, Global Navigation Satellite System GLONASS/Interface Control Document, Russian Institute of Space Device Engineering, 5.1, 28. IS-GPS-2D, Navstar GPS Space Segment/Navigation User Interfaces, Navstar GPS Joint Program Office, El Segundo, CA. U.S.A.,

15 IS-QZSS, Interface Specification for QZSS, Japan Aerospace Exploration Agency, Lee, Y.C., Advance RAIM Based on Inter-Constellation Comparisions to Detect Consistent Faults for LPV-2, ION GNSS 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, OR, , 21. Lu, J., Compass/Beidou Navigation Satellite System Development, 3rd Meeting of the International Committee on GNSS, Pasadena USA, 28. Milner, C. and Ochieng, W., ARAIM for LPV-2: The Ideal Protection Level, 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, OR, , September 21-24, 21. GEAS Phase II Report, Phase II of the GNSS Evolutionary Architecture Study, library/documents/media/geasphaseii_final.pdf. Rippl, M., Spletter, A. and Guenther, C., Parametric Performance Study of Advanced Receiver Autonomous Integrity Monitoring (ARAIM) for Combined GNSS Constellations, Proceedings of the 211 International Technical Meeting of The Institute of Navigation, San Diego, CA , 211. Walter, T., Enge, P., Blanch, J. and Pervan, B., WorldwideVertical Guidance of Aircraft Based onmodernized GPS and New Integrity Augmentations, Proceeeding of the IEEE, , 28. Wang, J., Knight, N.L. and Lu X. Impact of the GNSS Time Offsets on Positioning Reliability, Journal of Global Positioning Systems, 1, ,