extended receiver autonomous integrity monitoring eraim for … · 2019-02-18 · extended receiver...

Extended Receiver Autonomous Integrity Monitoring„eRAIM… for GNSS/INS Integration

Steve Hewitson, Ph.D.1; and Jinling Wang, Ph.D.2

Abstract: The integration of globe navigation satellite system �GNSS� with inertial navigation system �INS� is being heavily investigatedas it can deliver more robust and reliable systems than either of the individual systems. In order to ensure the integrity of navigationsolutions, it is necessary to incorporate an effective quality control scheme which uses redundant information provided by both themeasurement and dynamic models. As the GNSS receiver autonomous integrity monitoring �RAIM� algorithms are well developed, herethey are adapted to integrated GNSS/INS systems referred as extended RAIM �eRAIM�, which are derived from the least-squaresestimators of the state parameters in a Kalman filter, to assess GNSS/INS performance for a tightly coupled scenario. In addition to theRAIM capabilities, eRAIM procedures are able to detect faults in the dynamic model and isolate them from the measurement model. Theanalysis includes outlier detection and identification capabilities, reliability and separability measures of integrated GNSS/INS systems.The performance of the system is also investigated with respect to diminishing satellite visibility conditions.

DOI: 10.1061/�ASCE�0733-9453�2010�136:1�13�

CE Database subject headings: Global positioning; Quality control; Monitoring; Satellites; Surveys.

Introduction

The integration of globe navigation satellite system �GNSS� withinertial navigation system �INS� delivers an inherently more ro-bust and reliable system than either of the individual systems.INS, while autonomous and immune to interference, is prone tounbounded navigation errors that exponentially increase withtime. GNSS navigation on the other hand has exceptional long-term stability but is dependant on, and therefore limited by, signalquality and availability. In addition to improved reliability,GNSS/INS integration provides superior short and long-termaccuracy, improved availability, and higher data rate in compari-son to either standalone GNSS or INS. The next generation ofGNSS including modernized global positioning system �GPS� andGLONASS and the new Galileo systems will significantly en-hance the measurement geometry, redundancy, and correspondingmodel �Hewitson and Wang 2006� while ongoing improvementsin INS development continually allow for better dynamic model-ing at lower costs. Furthermore, it is widely accepted that theKalman filter �KF� provides optimal estimates of the navigationparameters of a dynamic platform, assuming the state and obser-vation models are correct. Unfortunately, such assumptions do notalways hold and inevitably, significant deviations of the assumedmodels are not uncommon for dynamic systems. However, if the

1School of Surveying and Spatial Information Systems, Univ. of NewSouth Wales, Sydney, NSW 2052, Australia. E-mail: [email protected]

2Associate Professor, School of Surveying and Spatial InformationSystems, Univ. of New South Wales, Sydney, NSW 2052, Australia �cor-responding author�. E-mail: [email protected]

Note. This manuscript was submitted on November 21, 2006; ap-proved on September 11, 2007; published online on January 15, 2010.Discussion period open until July 1, 2010; separate discussions must besubmitted for individual papers. This paper is part of the Journal ofSurveying Engineering, Vol. 136, No. 1, February 1, 2010. ©ASCE,
ISSN 0733-9453/2010/1-13–22/$25.00.
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modeling assumptions are correct, the state parameter estimatesare unbiased with minimum variance within the class of linearunbiased estimates. In order to take full advantage of the superiorperformance of integrated GNSS/INS and ensure the integrity ofthe navigation solution it is necessary to incorporate an effectiveand complementary quality control scheme which makes full useof the redundancy information provided by both the measurementand dynamic models.

The most effective quality control procedures currently em-ployed in integrated navigation systems are generally based onthe predicted residuals �innovations� of the KF or a derivative ofthe maximum solution separation method. Sturza �1989� pre-sented a fault detection algorithm based on hypothesis testing inparity space. Quality control for integrated navigation systemsusing innovations and recursive filtering is described in Teunissen�1990�. A fault detection algorithm based on the GPS solutionseparation method is adapted to an integrated GPS/INS system inBrenner �1995�. In Diesel and King �1995�, an innovation basedautonomous integrity monitoring extrapolation for integratednavigation systems is presented and analyzed. Gillesen and Elema�1996� presented the results of an innovations based detection,identification, and adaptation �DIA� procedure with reliabilityanalysis in an integrated navigation system. Two integrity proce-dures, the extrapolation and solution separation methods, aretested in Lee and O’Laughlin �2000� with respect to the detectionof the presence of a slowly growing error �SGE� for a tightlycoupled GPS/INS system. Nikiforov �2002� presented fault, de-tection, and exclusion algorithms for multisensor integrated navi-gation systems based on the KF innovations. More recently,Farrell �2005� describes a Q, R matrix decomposition based de-tection and exclusion technique for GPS/INS with performancecomparable to the parity space approach. Hwang �2005� adaptedthe novel integrity-optimized receiver autonomous integritymonitoring �RAIM� concept to the multiple solution separationmethod.

In this paper, the RAIM algorithms and quality measures de-
scribed in Hewitson et al. �2004� and Hewitson and Wang �2006,
AL OF SURVEYING ENGINEERING © ASCE / FEBRUARY 2010 / 13

ASCE license or copyright; see http://pubs.asce.org/copyright

2007� are adapted to an integrated GNSS/INS system. Thisadapted RAIM procedure is referred to as extended RAIM�eRAIM�. In addition to RAIM capabilities, eRAIM proceduresshould also be able to detect faults in the dynamic model andisolate them from the measurement model and vice versa. TheeRAIM algorithms are derived from the least-squares estimatorsof the state parameters in a Gauss-Markov KF �Wang 2000; Wanget al. 1997� and are used to assess GNSS/INS RAIM performancefor a tightly coupled simulation scenario. Herein, the measure-ment model incorporates pseudorange and accumulated deltarange measurements. The dynamic model is driven by the INS toprovide a reference trajectory for the measurement model. Analy-ses compare the outlier detection and identification capabilitiesand reliability and separability measures of a combined GPS/GLONASS/Galileo/INS system, GPS/GLONASS/INS system,and a GPS/INS system. The performance of the GPS/INS systemis also investigated with respect to diminishing satellite visibilityconditions.

GNSS/INS Integration

Herein, the GNSS/INS integration is performed using a tightlycoupled KF scheme. The tight coupling approach, used herein,processes the raw pseudorange and delta-range GPS measure-ments together with the corresponding INS predicted measure-ments in a single filter. In this way the INS is essentiallyproviding the reference trajectory via the dynamic model basedon the strapdown INS error equations for the filter measurementupdate, which is based on the difference between the INS pre-dicted measurements and the GPS measurements. The major ad-vantage of this approach is that the measurement update can stillbe executed when a standalone GPS solution is unavailable.

The model used in an extended KF �EKF� to describe thesystem dynamics depend on the selected error states and the errormodel describing these error states. Herein, the psi-angle errormodel is adopted to describe the nine INS navigation errors relat-ing to position, velocity, and attitude. The three gyroscope andthree accelerometer bias states are modeled by first order Gauss-Markov processes and the receiver clock error is modeled by atwo-state �bias and drift� random process model �Huddle 1983;Pue 2003�. The KF state vector has 17 elements, including posi-tion, velocity, attitude errors, accelerometer and gyroscope biases,and receiver clock bias and drift, plus 12 or more GNSS rangebias states �Hewitson 2006; Hewitson and Wang 2007�.

Regardless of the states and error model employed, the stateevolution model of the discrete EKF is described by

x̂k− = �k,k−1x̂k−1 + wk �1�

and the linearized measurement model relating the measurementsto the state of the system is expressed as

zk = Hkxk + �k �2�

where x̂k−1=mk dimension updated state parameter vector atepoch k−1; x̂k

−=mk dimension predicted state vector for epoch kmade at epoch k−1; �k,k−1=mk�mk−1 state transition matrixfrom epoch k−1 to k; wk=mk dimension random error vectorrepresenting the dynamic process noise at epoch k; zk=nk dimen-sion measurement vector at epoch k; Hk=nk�mk geometrymatrix relating the measurements to the state parameters; and�k=nk dimension error vector of the measurement noise at epoch
k.
14 / JOURNAL OF SURVEYING ENGINEERING © ASCE / FEBRUARY 2010


Furthermore, a closed loop update procedure is employedwhere the navigation errors are used to correct the INS navigationsolution. This updating scheme controls the error growth of theINS navigation solution provided the GNSS measurement updateis available. The extent of control is dependant on the number ofGNSS measurements available.

eRAIM Algorithms

Through adopting least-squares principles for the state estima-tions in a KF, the same quality control algorithms, as for thesingle epoch snapshot approach, can be used. In such a case, thepredicted state parameters can be included as measurements in theadjustment. The algorithms used herein are based on the adoptedDIA procedure. For a detailed background to the DIA procedureused herein, see Wang and Chen �1994�, Hewitson et al. �2004�,and Hewitson and Wang �2006, 2007�. The inclusion of dynamicinformation, in the form of the state parameter predictions of theKF, increases the redundancy of the adjustment. The improve-ment in redundancy has significant effects on the quality control.

It has been shown that by integrating the measurements zk withthe predicted values of the state parameters x̂k

−, optimal estimatesfor the state parameters xk can be obtained using least-squaresprinciples. The corresponding measurement model is �e.g., Wanget al. 1997�

lk = Ak + vk

and lk = �zk; x̂k−�;vk = �vzk;vx̂k

−�;Ak = �Hk;E� �3�

where lk=least-squares measurement vector containing zk and x̂k−;

Ak= �nk+mk��nk design matrix; vzk=nk dimension residual vec-tor of the measurements zk; vx̂k

− =mk dimension residual vector ofpredicted state parameters x̂k

−; and E=mk�nk identity matrix.The corresponding stochastic model is described with the sto-

chastic variance covariance Clk of the measurement vector lk,including measurement covariance matrix Rk and the predictederror covariance matrix Pk

−

Clk= �Rk

0

0

Pk− � �4�

The optimal estimates for the state parameters x̂k and the errorcovariance matrix Qx̂k

are

x̂k = �AxTClk

−1Ak�−1AkTClk

−1lk �5�

Qx̂k= �Ax

TClk−1Ak�−1 �6�

The filtering residuals vk, consisting of vzk and vx̂k, can thenbe calculated from

vk = �vzk

vx̂k−� = Akx̂k − lk �7�

From the least-squares principles the cofactor matrix of thefiltering residuals Qvk

is

Qv̂ = Clk− AQx̂k

AT �8�

The most import components of the eRAIM are outlier iden-tification, reliability, and separability. They are briefly explainedin the following three subsections. More detailed information can
be found in Hewitson �2006�.

Outlier Identification

Once a fault has been detected with a global detection algorithmsuch as the variance factor test, the w-test can then be used toidentify the corresponding measurement, where the test statistic is�e.g., Baarda 1968; Cross et al. 1994; Teunissen 1998�

wi = � eiTClk

v̂

�eiTClk

Qv̂Clkei� �9�

where ei=unit vector in which the ith component has a valueequal to one and dictates the measurement to be tested.

Under the null hypothesis, wi has a standard normal distribu-tion for a outlier �Si, wi has the following noncentrality:

�i = �Si�eiTClk

Qv̂Clkei �10�

The critical value for the test is depended on the significancelevel �.

Reliability

The internal reliability is expressed as a minimal detectable bias�MDB� that specifies the lower bound for detectable outliers witha certain probability and confidence level. The MDB is deter-mined, for correlated measurements with single error considered�e.g., Baarda �1968� and Cross et al. �1994�� by

�0Si =�0

�eiTClk

Qv̂Clkei

�11�

where �0=noncentrality parameter, which depends on the detect-ability � and false alarm rate �significance level ��. The externalreliability is then evaluated as

�0x̂ = QxATClkei�0Si �12�

Separability

For situations arising where an outlier is sufficiently large tocause many w-test failures, resulting in many alternatives, it isessential to ensure any two alternatives are separable so that agood measurement is not incorrectly flagged as an outlier. Theprobability of incorrectly flagging a good measurement asthe detected outlier is dependant on the correlation coefficient ofthe test statistics wi and wj �e.g., Förstner 1983; Wang and Chen1994�

�ij =ei

TClkQv̂Clk

ej

�eiTClk

Qv̂Clkei · �ej

TClkQv̂Clk

ej

�13�

The correlation coefficient has the property �ij�1, where 1and 0 correspond to full and zero correlation between two teststatistics, respectively. The greater the correlation between twotest statistics, the more difficult they are to separate. The degreeof correlation of measurements is dependent on the measurementredundancy and geometric strength. If the measurement redun-dancy is equal to 1 an outlier can be detected but cannot beidentified as all the identification test statistics are fully corre-lated. When determining the separability, it suffices to only con-sider the maximum correlation coefficient �MCC� �ij max�∀j� i�
for each statistic.
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Simulation Studies

Single frequency pseudorange and accumulated delta-rangeGNSS measurements and delta-velocity and delta-theta INSmeasurements were generated using a modified version of theGPSoft satellite navigation, INS, and navigation system integra-tion and KF toolboxes �Braasch 2007�. The 3D reference trajec-tory in Fig. 1, along with a simple straight and constant velocity,was used to simulate the GNSS and INS measurements of anairplane. The measurement update rate was 1 Hz.

The pseudorange and accumulated delta range measurementsare generated with standard deviations of 1 m and 0.1 m, respec-tively, considering measurement noise and modeling error, etc.Accumulated delta-range measurements are taken 50 ms prior tothe filter update time as well as at the filter update time to derivethe delta-range observables. The delta-range measurements werethen used to estimate the receiver’s velocity and provide thedynamic information in KF for the state predictions. The satel-lite coordinates were calculated from the Keplerian elements ofthe nominal GPS, GLONASS, and Galileo constellations �seeHewitson and Wang 2006� and all simulations were conductedwith a 5° masking angle. The INS was simulated with an outputrate of 200 Hz. The simulated errors included initial alignmentand velocity errors �0.1 millirad and 0.02 m/s horizontally andzero vertically�, and accelerometer and gyroscope biases �50 �gand 0.01°/h�. The error growth characteristics of the simulatedINS can be seen in Fig. 2.

In order to assess the performance of tightly coupled GNSS/INS systems with respect to outlier detection and identificationseveral scenarios were considered. First, the low dynamic three-dimensional trajectory �Fig. 1� was used to investigate the eRAIMperformance of GPS/INS, GPS/GLONASS/INS and GPS/GLONASS/Galileo/INS systems. The eRAIM performance wasthen also assessed with respect to SGE and instantaneous biasesunder simulated low visibility conditions using a simple straightand constant velocity trajectory.

All the integrity solutions used in the following analyses werederived from the least-squares principles and the critical valueused for the w-test was 3.290 5 for a false alarm rate �� of 0.1%.The internal reliabilities �MDBs� were determined with a detect-

Fig. 1. 3D simulation reference trajectory

ability �� of 80%, as recommended by Cross et al. �1994�.



Three-Dimensional Trajectory Analysis

The simulated GNSS and INS measurements for the 3D trajectoryin Fig. 1 were used to determine the horizontal position errors,w-statistics, internal reliabilities, and MCCs associated with GPS/INS, GPS/GLONASS/INS, and GPS/GLONASS/Galileo/INSsystems. The measurements were simulated for a helicopter witha speed of approximately 4.7 m/s after accelerating from rest atapproximately 0.12 m /s2. The centripetal acceleration was ap-proximately 0.34 m /s2 for all turns. Line plots of the horizontalposition errors and statistics and histograms of the internal reli-abilities and MCC were then generated to analyze the perfor-mances and distribution of values over the whole trajectory. Thehistograms were separated with respect to the pseudorange anddelta range measurements and the predicted states for each esti-mation scenario. It should be noted that the correlation coefficientresults, however, were not isolated to type of measurement beinganalyzed, i.e., the results for the pseudorange measurements in-

Fig. 2. Horizontal position error of simulated INS

Fig. 3. GPS/INS EKF horizontal position error for 3D trajectory



clude the correlations with the delta range and predicted statestatistics as well as the statistics corresponding to the other pseu-doranges.

Integrated Globe Navigation Satellite System/InertialNavigation SystemFig. 3 shows the horizontal position errors for the GPS/INS sce-nario where seven to eight satellites were visible for the entiretrajectory. Fig. 4 shows the w-statistics for the measurements,predicted states, and the variance factor of the measurement up-dates. It is clear that no false alarms have occurred. Though thereare some small failures for the w-test it is usual practice to ignorethese if the variance factor test has passed. No biases have beeninduced and these w-test failures are due to the simulated mea-surement noise.

Fig. 5 gives the distribution of the MDBs for the pseudorangeand delta-range measurements and the predicted states. TheMDBs corresponding to the pseudorange measurements rangefrom about 4.39 m to approximately 4.66 m with the majority ofthe values between 4.4 and 4.5 m. The delta-range MDBs spreadover values from 1.26 m/s to about 1.306 m/s with most of thevalues between 1.26 and 12.603 m/s. The MDB values for thepredicted states fall between 0.5 and 4.6. It should be noted thatthe predicted states include the receiver clock bias and drift errorsas well as the position and velocity error states and that the INSdoes not provide any additional observable for the clock states.

The MCC distributions associated with the pseudorange anddelta-range measurements and predicted states are given in Fig. 6.Here, the correlation coefficients corresponding to the pseudor-ange statistics approximately range between 0.3 and 0.62. Thedelta-range statistics range from about 0.35 to 0.65. The correla-tion coefficients corresponding to the predicted states lie between

Fig. 4. EKF w-test statistics for GPS/INS measurements �top�, pre-dicted states �middle�, and unit variance statistics �bottom� for 3Dtrajectory

the values 0.5 and 0.9. There are a large proportion of the pre-


dicted states with corresponding correlation coefficients between0.8 and 0.9. This is due to the weighting of the dynamic modelwith respect to the clock drift.

Integrated GPS/GLONASS/Inertial Navigation SystemThe horizontal position error for the GPS/GLONASS/INS systemis given in Fig. 7. We can see that the estimation accuracy is

Fig. 5. Histogram of internal reliabilities along the 3D trajectory forpseudorange �top�, delta-range �middle� measurements, and predictedstates �bottom� for GPS/INS

Fig. 6. Histogram of MCCs along the 3D trajectory corresponding topseudorange �top�, delta-range �middle� measurements, and predictedstates �bottom� for GPS/INS

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noticeably greater than for the GPS/INS system �see Fig. 3�.In this case there were 15 to 16 satellites visible for the entiretrajectory.

In Fig. 8 we can see an outlier has occurred at 7 min with afailure of the variance factor test due to measurement noise. The

Fig. 7. GPS/GLONASS/INS EKF horizontal position error for 3Dtrajectory

Fig. 8. EKF w-test statistics for GPS/GLONASS/INS measurements�top� and predicted states �middle� and unit variance statistics �bot-tom� for 3D trajectory



MDBs of the GPS/GLONASS/INS system �see Fig. 9� are sig-nificantly lower and more stable overall with respect to the pseu-doranges, delta-ranges, and predicted states than the GPS/INSsystem �Fig. 3�. The lower limits of the delta-range and predictedstate MDBs however, appear to have been reached at the valuesof approximately 1.26 m and 0.5 m, respectively.

Notable improvements are also achieved over the GPS/INScase with respect to the pseudoranges, delta-ranges, and predictedmeasurement statistic correlations. Fig. 10 reveals that the pseu-

Fig. 9. Histogram of internal reliabilities along the 3D trajectory forGPS/GLONASS/INS

Fig. 10. Histogram of MCCs along the 3D trajectory correspondingto pseudorange �top�, delta-range �middle� measurements, and pre-dicted states �bottom� for GPS/GLONASS/INS



dorange correlations are reduced by approximately 0.1 for boththe lower and higher limits, the delta-range lower limit is reducedby about 0.05 with upper limit reduced by over 0.1 and the lowerlimit for the predicted states is also lowered by over 0.1 with ahuge reduction of greater than 0.25 of the upper limit.

Integrated GPS/GLONASS/Galileo/InertialNavigation SystemThere were 23 to 24 visible satellites for the GPS/GLONASS/Galileo/INS scenario and the corresponding horizontal positionerror is given in Fig. 11. A slight improvement in the accuracyover the GPS/GLONASS/INS system has been achieved. No falsealarms were raised in this scenario �see Fig. 12�. Again the lowerlimits of the delta-range and predicted state MDBs �see Fig. 13�seem to have been reached. The lower limit for the pseudorange isapproximately 1.26 m with the delta-range MDB lower limit nowslightly lower at 0.4 for the GPS/GLONASS/Galileo/INS case.There is also some overall improvement with respect to the pre-dicted state MDBs with the weight of the distribution centeredslightly more toward the lower limit.

Obvious improvements in the correlation coefficients corre-sponding to the pseudoranges, delta-ranges, and predicted statesof the GPS/GLONASS/Galileo/INS system are shown in Fig. 14.Both the lower and upper limits of the correlations correspondingto the pseudoranges have been lowered by approximately 0.05and 0.1, respectively. The delta-range test statistic correlationcoefficients have greatly stabilized and appear to have reacheda lower bound limit of just over 0.3. The lower limit of thepredicted state correlation coefficients have also improved byabout 0.5

Outlier Detection and Identification during LowSatellite Visibility

A simple straight trajectory was used to assess the performance of

Fig. 11. GPS/GLONASS/Galileo/INS EKF horizontal position errorsfor 3D trajectory

GNSS/INS integration under low satellite visibility conditions


with respect to outlier detection and identification. The measure-ments were simulated for an airplane moving along the trajectorywith a constant speed of 200 m/s. Initially, a 6-m instantaneousbias was induced in the same satellite at exactly 4.5, 5.5, 6.5, and7.5 min corresponding to satellite visibilities of 4, 3, 2, and 1,respectively. The variance factors, w-statistics, internal reliabili-

Fig. 12. EKF w-test statistics for GPS/GLONASS/Galileo/INS mea-surements �top�; predicted states �middle�; and unit variance statistics�bottom� for 3D trajectory

Fig. 13. Histogram of internal reliabilities along the 3D trajectory forpseudorange �top�; delta-range �middle� measurements; and predictedstates �bottom� for GPS/GLONASS/Galileo/INS

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ties, and correlation coefficients were then examined. Further-more, outlier identification analyses were then made with respectto the presence of a SGE.

Instantaneous Bias Detection and IdentificationFig. 15 shows the degrading satellite visibility and the corre-sponding horizontal position error. The results of the statisticaltests, namely the variance factor and w-tests, used for detectionand identification of the induced biases are given in Fig. 16. Fromthe variance factor results it is clear that the outliers correspond-

Fig. 14. Histogram of MCCs along the 3D trajectory correspondingto pseudorange �top�, delta-range �middle� measurements, and pre-dicted states �bottom� for GPS/GLONASS/Galileo/INS

Fig. 15. GPS/INS EKF horizontal position error under low satellitevisibility conditions with instantaneous biases induced



ing to four, two, and one visible satellites were correctly detected.Though it is not obvious, the bias induced corresponding to threevisible satellites was also detected with a test statistic of 3.274 8and threshold of 3.091 2. The satellite corresponding to the in-duced bias was correctly identified in the four, three, and twovisible satellites scenarios, however the pseudorange in the onevisible satellite case was fully correlated �see Fig. 17� with, and

Fig. 16. EKF w-test statistics for GPS/INS measurements �top� andpredicted states �middle� and unit variance statistics �bottom� underlow satellite visibility conditions with instantaneous biases induced

Fig. 17. �Color� EKF w-test statistic correlation coefficients of biasinduced pseudorange with respect to other pseudoranges, predictedstates and clock bias �top�, and pseudorange MDBs for GPS/INSunder low satellite visibility conditions with instantaneous biases in-duced �bottom�



inseparable from, the predicted position and clock bias states. Forthis reason the predicted position and clock bias states were alsoidentified. Furthermore, Fig. 17 also shows that the 6-m biaseswere above the MDB threshold for the duration of the simulation.

Slow Growth Error Detection and IdentificationSlow growth errors, or slowly increasing ramp errors, are lesscommon that instantaneous biases but far more difficult to detect.The difficulty in detecting SGE arises from the fact that effect ofthe error is similar in magnitude to the dynamics of a movingsystem, whereas instantaneous biases are inconsistent and implyunrealistic vehicle dynamics. In order to show a major integrityissue regarding the detection and identification of SGE for inte-grated GNSS/INS systems under low satellite visibility condi-tions, a 0.2-m/s error was induced in the only satellite visible forthe duration of the simulation. The SGE was induced after 250 swhen one satellite was visible. The satellite visibility and horizon-tal position error for this simulation is shown in Fig. 18.

In Fig. 19, it can be seen that the error is not detected until 160s after it is induced and when four satellites are visible. At thistime the SGE is equivalent to a 32-m bias. The MDBs for thepseudoranges in this simulation are comparable to those given inFig. 17 for the same visibilities. This suggests that a minimum offour range measurements are required to detect an SGE in anintegrated GNSS/INS system. With less than for satellites visiblean SGE is indistinguishable from normal system dynamics.

Conclusions

Investigations into the performance of RAIM as adapted to inte-grated GNSS/INS systems, named as eRAIM, have been carriedout considering different GNSS constellations in this paper. Faultscenarios include the detection and identification capabilities ofthe integrated systems with respect to instantaneous biases and

Fig. 18. GPS/INS EKF horizontal position error in east �middle� andnorth �bottom� components under low satellite visibility �top� condi-tions with SGE induced

SGE.


It been shown that for integrated GNSS/INS systems, instan-taneous biases can be detected and identified when there aretwo or more visible satellites. The detected instantaneous biasesmay not be isolated when there is only one satellite visible. It isalso shown that the additional redundancy provided by an inte-grated GPS/Galileo/GLONASS/INS significantly enhancesRAIM performance with respect to GPS/INS or GPS/GLONASS/INS systems, even for full sky visibility conditions above a 5°mask angle.

In addition, a major integrity issue regarding the detection ofSGE of an integrated GNSS/INS system has been identified. It isshown that the SGE cannot be distinguished from the normalsystem dynamics and is therefore an undetectable error for anintegrated GNSS/INS system when less than four satellites areavailable.

Acknowledgments

This work has been supported by the Australian Research CouncilDiscovery research grant on “Robust positioning based on ultra-integration of GPS, pseudolite and inertial sensors,” and the Uni-versity of New South Wales Goldstar research grant on GNSSintegrity monitoring. The writers thank Dr. Jianguo Jack Wang forthe valuable discussions and his assistance in preparing the re-

Fig. 19. �Color� EKF w-test statistics for GPS/INS measurements �tosatellite visibility condition with SGE induced

vised version for this paper.

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