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Performance of rate detector algorithms for an integrated GPS/INS system in the presence of slowly growing error

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Performance of rate detector algorithms for an integrated GPS/INS system in the presence of slowly growing error
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  ORIGINAL ARTICLE Performance of rate detector algorithms for an integratedGPS/INS system in the presence of slowly growing error Umar I. Bhatti  • Washington Y. Ochieng  • Shaojun Feng Received: 30 August 2010/Accepted: 8 June 2011/Published online: 9 July 2011   Springer-Verlag 2011 Abstract  In the Global Positioning System, there is noprovision for real-time integrity information within theStandard Positioning Service, by design. However, insafety critical sectors like aviation, stringent integrity per-formance requirements must be met. This can be achievedusing the special augmentation systems or RAIM (ReceiverAutonomous Integrity Monitoring) or both. RAIM, themost cost-effective method relies on data consistency, andtherefore requires redundant measurements for its opera-tion. An external aid to provide this redundancy can be inthe form of an Inertial Navigation system. This shouldenable continued performance even when no redundantsatellite measurements are available. An algorithm pre-sented in previous papers by the authors detects the rate of slowly growing errors. The algorithm was shown to beeffective for early detection of slowly growing errors thatbelong to the class of most difficult to detect errors. Firstly,rate detector is tested for varying faults. Secondly, real dataare used to validate the rate detector algorithm. The dataare extensively analyzed to ascertain whether it is suitablefor integrity and fault diagnostics. A modification to thesrcinal rate detector algorithm is suggested by addition of a bias state to the dynamic model. The performance is thencompared with the existing techniques and substantialimprovement is shown. Keywords  GPS    INS    Integrity    Integration   Rate detector Introduction The Global Positioning System (GPS) is a widely usedsatellite navigation system. Due to the recent shift in focusof worldwide aviation from ground-based to space-basednavigation systems, the safety of use of GPS for suchpurposes has currentlybecome the subject ofglobalresearch.After the discontinuation of Selective Availability (SA) in2000, GPS performance available to the civilian communityis specified in the GPS Standard Positioning Service (SPS)Performance Standard (US Department of Defence 2001)providing information on service accuracy, availability, andreliability with respect to the signal-in-space (SIS).To use GPS for aviation, stringent standards, establishedby the International Civil Aviation Organization (ICAO),have to be met (ICAO SARPS 2004). One of the require-ments is integrity, a measure of the degree of trust that canbe placed in the correctness of the navigation information.However, the GPS SPS does not provide real-time integrityinformation. Hence, for safety critical applications likeaviation, GPS signals must be monitored. The vulnerabilityof GPS signals has been investigated for example byOchieng et al. (2003) and Volpe report (US Department of Transport 2001). Furthermore, recent research activities arefocussed on the quantification of the failure modes of GPS(Bhatti and Ochieng 2007a; Ochieng et al. 2003; Van Dyke et al. 2003, 2004; Walsh et al. 2004). These approaches are based on the exhaustive search for potential failure modesthat can affect GPS navigation performance. In this regard,work on FMEA (Failure mode and Effect Analysis) for thecomplex and multi-segmented GPS is still ongoing.GPS augmentations like GBAS (ground-based aug-mentation systems) and SBAS (satellite-based augmenta-tion systems) monitor GPS signals in real time. They relayintegrity information by signals that are vulnerable to U. I. Bhatti ( & )    W. Y. Ochieng    S. FengCentre for Transport Studies, Department of Civiland Environmental Engineering, Imperial College London,London SW7 2AZ, UK e-mail: uiqbal3@hotmail.com  1 3 GPS Solut (2012) 16:293–301DOI 10.1007/s10291-011-0231-y   jamming and interference, a principal failure mode of GPS.A potentially effective method to address these risks is tointegrate GPS with other navigation systems such anInertial Navigation System (INS).The INS is a self-contained system with high short-termstability, immune to jamming as well as interference.However, high grade systems are very expensive. Theemergence of INS sensors exploiting MEMS (micro-elec-tromechanical systems) technology is creating the potentialfor affordable integrated GPS/INS architectures if theproblems associated with performance could be overcome.This has the potential to offer a cost-effective alternative toother forms of augmentations depending on the user(operational) requirements.INS can be integrated synergistically with GPS so thatshort-term and long-term stabilities of INS and GPS,respectively, can be exploited. The traditional integrationmethod is the usage of a Kalman filter. In order to realizean optimal integrated system, a number of issues need to beconsidered. These include the type of INS and the inte-gration architecture. These have implications on systemintegrity. Various types of integration methods are avail-able and broadly classified as loosely coupled, tightlycoupled, and ultra-tight/deep (Gautier and Parkinson 2003).Loosely coupled systems combine processed measure-ments of the two systems, while tightly coupled systemsgenerally carry out the integration at the raw measurementlevel. Ultra-tight systems generally have feedback loopsbetween the two systems.It was shown in a set of companion papers (Bhatti et al.2007b, c) that tightly coupled systems provides most benefit in terms of access to measurements and simplicity of theintegration structure. Hence, this is the preferred architec-ture for dealing with the integrity of the integrated system.Furthermore, a rate detector algorithm is presented therein.It was shown that it can achieve 40% reduction in the timeto alert (TTA) achievable by the existing techniques. Thisrate detector algorithm is analyzed further in this paper.First of all sensitivity analysis is performed in order toascertain the validity of the detector for different errors.Secondly, this algorithm is subjected to real data. The dataare extensively analyzed to check the suitability of the datafor integrity analysis. As a result of the analysis, a modifi-cation is suggested to the srcinal rate detector algorithm.Section ‘‘Implementation of the rate detector algorithm’’summarizes the rate detector algorithm. Section ‘‘Sensi-tivity analysis’’ presents the results of sensitivity analysisof the rate detector algorithm. Section ‘‘Profile of realdata’’ provides analysis of the real data used. Section‘‘Detection of a single SGE in real data’’ shows results fordetection of a slowly growing error (SGE) by usingexisting techniques and the proposed technique. Section‘‘Conclusion’’ concludes the paper. Implementation of the rate detector algorithm The rate detector algorithm needs the test statistics of theAIME (Autonomous Integrity Monitoring by Extrapolationmethod) configuration (Diesel and Dunn 1996). The  Autonomous Integrity monitoring by Extrapolation Method (AIME)  is a sequential algorithm in which the measure-ments used are not limited to a single epoch. The teststatistic is a weighted average of Kalman filter innovationover the past measurements. The weight matrix used in thetest statistic is the inverse of the innovation covariancematrix of the Kalman filter. The test statistic exhibit centraland non-central Chi-square distributions for the no faultand fault cases, respectively. Three test statistics areformed  s 1 ,  s 2 , and  s 3 ; averaged over 150 s, 10 and 30 min.The decision threshold is also based on chi-square distri-bution. This is selected on the basis of a false alert rate of 10 - 5 per h in a fault free environment. In practice, the ratedetector algorithm can be implemented alongside theAIME algorithm to detect the slowly growing errors early.The flowchart for practical implementation of the ratedetector algorithm is shown in Fig. 1.Itcanbeseen thatthe AIME teststatistic isobtainedfromthemainnavigationKalmanfilterandfedtotheratedetectoralgorithm. The rate detector algorithm estimates the rate of the test statistic and compares it with the threshold values(computed offline). An integrity flag is set if velocity isgreater than the corresponding threshold. Otherwise newmeasurements from GPS and INS are accepted and theprocess continues (Bhatti 2007). Preliminary analysis of therate detector algorithm is presented in Bhatti et al. (2007c).This will be treated in detail in this paper. The sensitivityanalysis of the rate detector is presented next. Sensitivity analysis The rate detector algorithm has been simulated using asimulation platform that has the capability of simulatingGPS, INS, and various error sources (Bhatti et al. 2007b, c). The main navigation Kalman filter is allowed to settle to itssteady state for1 h. ItwasshowninBhatti etal.(2007c)thata40%reductionindetectiontimeisachievedwithrespecttothe AIME and MSS algorithms. The multiple solution sep-aration (MSS) method is based on forming the solutionusing different sub-filters by removing one measurement ata time and comparing it with the full solution (Brenner1995). In effect it is a snapshot method that uses the mea-surements only at the current time. The test statistics isformed using the horizontal measurements of the full andthe sub-solution. This is assumed to follow zero meannormal distribution in the no fault case and non-zero meannormal distribution in the faulty case. The decision 294 GPS Solut (2012) 16:293–301  1 3  threshold (to compare the test statistic with) is chosen basedupon the maximum probability of false alert. Anotherthreshold is computed for which it is assumed that if thereoccurs a fault it should not cross the threshold except withthe specified missed detection probability. In contrast to theAIME method, this is a position domain method. The effi-ciency of the rate detector algorithm is possible due to thedetection of the rate of the test statistic in contrast to onlymonitoring its magnitude. A sensitivity analysis has beenperformedforthe proposedratedetectoralgorithm. Itcanbeseen from Fig. 2 that the proposed algorithm is successful indetectingerrorswithdifferentrates.Theseinclude steperrorof100 m andgrowingerrors of 1,2, and 3 m/sintroducedina satellite pseudorange. It can also be noted that the fasterthe growth of the error, the earlier the detection. This isbecause this algorithm detects the rate of the signal.The proposed rate detector configuration is efficient indetecting a single slowly growing error. The results can beaffected if the modeling of measurement signal is notaccurate in the rate detector Kalman Filter (Fig. 1). Theperformance can be improved by varying the measurementnoise matrices and covariance matrices or in other wordstuning of the Kalman filter for the rate detector algorithm(Brown 1992). This will minimize the effect of measure-ment noise on the estimation of the rate of the test statistic.Detection of error in real data is performed to validatethe rate detector configuration. The characteristics of realdata are studied in detail so that it can be used to quantifyintegrity performance. Profile of real data The real data consist of IMU and GPS data. The IMU dataconsist of velocity and attitude increments; time tagged Main Navigation Kalman Filter forthe AIME method 1. Initialize Kalman filter2. Perform Time update3. Accept measurements from GPSand INS4. Perform measurement updateTest StatisticsCalculation Initialize Rate Detector Kalman Filter 1. Initialize State Variables2. Initialized State Estimate Covariance Vallues3. Define Measurement Noise Matrix4. Define Dynamic Matrix5. Define Sample Time Kalman Filter Operation 1. Propagate state variables through time2. Propagate state covariance through time3. Calculate Kalman Gain4. Perform update step5. Calculate Innovation and its covariance6. Calculate velocity of the test statisticOffine calculation ofvelocity thresholdIntegrity FlagVelocity of the test statistic >velocity threshold Fig. 1  The flowchart for therate detector algorithm 59.859.96060.160.260.360.460.560.660.760.800.511.522.533.54x 10 -3 Time (min)    V  e   l  o  c   i   t  y   (   1   /  s   ) 1 m/s2 m/s3 m/s100 m step) Fig. 2  Detection of different types of errors using the rate detectoralgorithmGPS Solut (2012) 16:293–301 295  1 3  with GPS time. GPS data are in the form of the ReceiverINdependent EXchange Format (RINEX) file set. GPS datawere captured by the Novatel OEM dual frequency recei-ver. The data were collected in Nottingham on August 13,2005, by staff of the IESSG (Institute of EngineeringSurveying and Space Geodesy), University of Nottingham.RINEX is the most common exchange format for GPS datain the Geodesy community. This RINEX data come in theform of two files, observation and the navigation file. Theobservation file includes GPS observables, code phase, andcarrier phase measurements (L1 and L2) for the observedsatellites temporally referred to the receiver time (UTC)(L1 is used in this analysis because this is the onlyobservable available to a typical aviation user). The navi-gation message file contains the broadcast ephemeris,ionospheric coefficients, and clock correction parameters.The IMU data are available at 200 Hz, while GPS data areavailable at 4 Hz. The IMU used is a Honeywell Com-mercial Inertial Measurement Unit (CIMU). It is a navi-gation grade IMU with the performance specificationsshown in Table 1 (Hide et al. 2005). From Table 1, it can be seen that the Honeywell CIMUis a very good quality IMU. It was mounted on the back of a vehicle. The vehicle and the equipment are shown inFig. 3. As can be seen from Fig. 3, the IMU and GPS antenna are not collocated. Therefore, lever arm correc-tions are required in this case. These are calculated byusing a steel ruler and are tabulated in Table 2. The rulerused has a measurement resolution of millimetres hence theaccuracy of the lever arm is suitable for the purpose of checking integrity since it is much smaller than theinherent accuracy of the GPS code signal which is incentimetres.These parameters were provided by the IESSG. Theseare required because GPS pseudoranges are predicted frompositions derived from INS measurements in a tightlycoupled architecture.GPS data profileFigure 4 shows the position profile (trajectory) of thevehicle obtained from the raw GPS data from the RINEXfiles. The data was captured from multiple runs of thevehicle along the same trajectory. The vehicle positionswere computed using the least squares algorithm to processthe pseudoranges. The start point is marked by A andendpoint is marked by B. The error compensation for thedelays due to the ionosphere and troposphere was carriedout. Multipath compensation has not been attempted in thiswork since this is small in magnitude due to the used of choke ring antenna.Due to the nature of the data capture scheme adopted,repeated trajectories facilitate a level of data validationagainst blunders. Figure 5 shows an enlarged part of therepeated ground track presented in Fig. 4. The number of satellitesinviewofthe vehiclemountedantennaisshowninFig. 6. It can be seen that the minimum and maximumnumber of satellites available during the run are 6 and 9,respectively.TheDilutionOfPrecision(DOP)valuesduringthe trajectory are shown in Fig. 7. It can be seen that theimprovement in the PDOP in the later part of the trajectory(Fig. 7) is principally due to the availability of larger num-ber of satellites (Fig. 6) in a good geometric configuration.The INS data profileFigure 8 shows the ground track of the vehicle using INSbased positions. The typical error growth which is a wellknown characteristic of inertial measurement units is Table 1  CIMU performance specificationsParameters ValuesGyro rate bias 0.0035   /hGyro rate scale factor 5 ppmAngular random walk 0.0025   /h 1/2 Accelerometer range  ± 30 gAccelerometer scale factor 100 ppmAccelerometer bias 0.03 mg Fig. 3  The GPS/INS equipment and the van used to collect real data(INS is packaged in the box while round GPS antenna can be seen) Table 2  Lever arm corrections between IMU and GPS antennaAxis ValuesX-axis 0.015 mY-axis 0.169 mZ-axis 0.240 m296 GPS Solut (2012) 16:293–301  1 3  evident in Fig. 8. This is in contrast to GPS derived posi-tions that have long term error stability. The INS velocitiesin the North and East directions are shown in Figs. 9 and10 respectively.It is very interesting to observe that the magnitude of both the velocities change with the turns of the vehicle. TheEast and North components of the velocity vary during aturn, even if the magnitude of the horizontal velocity doesnot vary much. This cross-validates the multiple about-turnmanoeuvres of the vehicle as seen from the GPS basedtrajectory (Figs. 4 and 5). The divergence in the position estimate by the INS(Fig. 8) can be controlled by GPS/INS integration asshown in Fig. 11. The results shown are for the tightlycoupled integration because it is the representative con-figuration selected for best performance with regard tointegrity (Bhatti et al. 2007b). The validity of the data isdiscussed in the next section.Data validityBefore analysing the data further it is important to ascertainthat the data are valid and do not contain any blunders. Astwo independent navigation systems are installed on thesame vehicle, there is no need to validate it using methodssuch as carrier phase processing or map-matching. Thefollowing points are notable in this regard:1. The vehicle repeatedly traversed a specific path hence,validating the data for the presence of large blunders.Since the purpose of this paper is to compare integrityalgorithms, very precise measurements such as carrierphase are not required.  A B -4.564-4.562-4.56-4.558-4.556-4.554-4.552-4.55-4.548-4.54652.11352.113552.11452.114552.11552.115552.11652.116552.117 Longitude (deg)    L  a   t   i   t  u   d  e   (   d  e  g   ) Fig. 4  The ground track of the vehicle as computed from the GPSdata   -4.5518 -4.5516 -4.5514 -4.5512 -4.551 -4.5508 -4.5506 -4.5504 -4.5502 -4.55 -4.549852.115852.115952.11652.116152.116252.116352.116452.116552.116652.1167 Longitude (deg)    L   a   t   i   t  u   d   e   (   d   e   g   ) Fig. 5  The zoomed in view of the vehicle trajectory to show turns 010203040506066.577.588.59 time (min)     N  u  m   b  e  r  o   f   G   P   S   S  a   t  e   l   l   i   t  e  s Fig. 6  Number of the satellites in view during the course of trajectory 0 10 20 30 40 50 60 70 801.822.22.42.62.83 Time (min)    P   o   s   i   t   i   o   n   D   i   l  u   t   i   o   n   o   f   P   r   e   c   i   s   i   o   n Fig. 7  Position dilution of precision during the trajectoryGPS Solut (2012) 16:293–301 297  1 3
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