Tightly Coupled Integration Of GPS-PPP And MEMS-Based .

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Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System UsingEKF and UKFMahmoud Abd Rabbou and Ahmed El-Rabbany, CanadaKey words: GPS, Precise Point Positioning, GPS/INS integration, tightly coupledintegrationSummaryIn this paper, an improved Precise Point Positioning GPS/MEMS-based integratedsystem is introduced for precise positioning applications. Un-differenced ionosphere-freelinear combinations of carrier phase and code measurements are processed. Troposphericdelay, satellite clock, ocean loading, Earth tide, carrier-phase windup, relativity, andsatellite and receiver antenna phase-center variations are accounted for using rigorousmodeling. Tightly coupled mechanism is adopted, which is carried out in the rawmeasurements domain. Both Extended Kalman filter (EKF) and Unscented Kalman filter(UKF) are developed to merge the GPS and inertial measurements. The performance ofintegrated system is analyzed using a real test scenario in downtown Kingston.It is shown that both Extended Kalman and Unscented Kalman filters have comparableperformance. The positioning results of the integrated system show that decimeter-levelaccuracy is achievable. During the GPS outages, the integrated system showed meterlevel accuracy when a 60-second outage was introduced. However, the positioningaccuracy was improved to sub-decimeter and centimeter level when 30- and 10-secondGPS outages were introduced, respectively.Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20141/11

Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System UsingEKF and UKFMahmoud Abd Rabbou and Ahmed El-Rabbany, Canada1. IntroductionCurrently, the highest accuracy GPS positioning solution is obtained through carrierphase observables in differential mode, involving two or more receivers. However, therequirement of a base station is usually problematic for some applications as it limits theoperational range of the system and increases the system cost and complexity. Recentresearch shows that comparable positioning accuracy can be achieved through precisepoint positioning (PPP) technique. PPP use un-differenced or between-satellite singledifferenced carrier phase and pseudorange observations (Elsobeiey and El-Rabbany2013).Unfortunately, accurate GPS positioning solution may not always be available due toGPS outages. To overcome these limitations, GPS can be integrated with a relativelyenvironment-independent system, the inertial navigation system (INS). Currently, mostintegrated GPS/INS systems are based on differential GPS (DGPS) due to the highaccuracy of differential mode (Petovello, 2003 and Nassar, 2003). More recently, GPSPPP was integrated with a tactical grade IMU to achieve comparable accuracy with thatof differential mode (Zhang and Gao, 2007). However, the use of high-end INS isgenerally limited due to their high cost and size. Recently, micro-electro-mechanicalsensors (MEMS) inertial sensors have been developed, which are characterized by theirsmall size and low cost compared with high-end inertial sensors. Generally, however,MEMS inertial sensors have poorer performance and stability compared with high-endINS due to the high noise level and severe biases and drifts affecting them.This research is aimed to develop a new integrated system based on integrating GPSbased PPP with MEMS accelerometers and fiber optic gyros for precise positioningapplications. The proposed integrated system requires rigorous modeling of all errors andbiases affecting inertial sensors and GPS observations. We use un-differencedobservations for GPS PPP. Inertial sensors biases are accounted for through calibration,while Gaussian-Markov stochastic process model is used to account for the sensor’srandom errors.Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20142/11

2. Un-differenced ionosphere-free model PPP modelThe most common PPP model is the un-differenced ionosphere-free combination of codeand carrier phase observations (Hofmann-Wellenhof et. al. 2008). This model eliminatesthe first order ionosphere delay by combining the observations of Lଵ andLଶ . Themathematical model for ionosphere-free PPP can be written as:P3 φ3 f12 P1 f 2 2 P2f12 f 2 2f12φ1 f 2 2φ2f12 f 2 2 ρ c [ d t r - d t s ] T c [ 2 . 5 4 6 d r 1 - 1 . 5 4 6 d r 2 ] c [ 2 . 5 4 6 d s1 - 1 . 5 4 6 d s 2 ] e P 3(1) ρ c [ d tr - d t s ] T c [ 2 . 5 4 6 δ r 1 - 1 . 5 4 6 δ r 2 ] c [ 2 . 5 4 6 δ s1 - 1 . 5 4 6 δ s 2 ] λ N eφ 3(2)where Pଵ and Pଶ are code measurements on Lଵ and Lଶ , respectively; Φଵ and Φଶ are thecarrier phase measurements on Lଵ and Lଶ , respectively; dt and dt ୱ are the clock errorsfor receiver and satellite, respectively; d and dୱ are frequency-dependent code hardwaredelay for receiver and satellite, respectively; δ and δୱ are frequency-dependent carrierphase hardware delay for receiver and satellite, respectively; e୮ଷ , e ଷ are relevant systemnoise and un-modeled residual errors for the un-differenced ionosphere-free combinationof the code and carrier-phase measurements, respectively; and λ are the wavelengths for is un-differenced ionosphere-freeun-differenced ionosphere-free carrier frequencies; Nambiguity bias; c is the speed of light in vacuum; and ρ is the true geometric range fromthe antenna phase centre of the receiver at reception time to the antenna phase centre ofthe satellite at transmission time.3. GPS/MEMS-based IMU integrated system mechanismIn this paper, the tightly coupled (TC) architecture is implemented adopting a centralfilter to process GPS raw pseudorange, carrier phase and Doppler measurements and theINS-derived observations to produce estimates of the state vector including position,velocity and attitude. The basic state vector consists of the nine navigation parametererrors, namely three position errors, three velocity errors and three attitude errors.Additional states are added to the INS error model in order to account for the effects ofthe inertial sensor and GPS errors. The complete state vector consists of 24 statesdescribing the basic state vector (the nine navigation parameter errors) and the inertialsensors errors (bias drift and scale factor).Knowing the precise GPS satellites ephemeris, the outputs of position and velocity fromthe INS mechanization are used to predict the pseudorange, phase and Dopplermeasurements. The corrected GPS pseudorange, carrier phase and Doppler measurementsare differenced with the INS-predicted measurements. Then, the estimated filterprocesses those residuals to estimate the integrated system state vector. Finally, theobtained state estimates are feed backed to the INS mechanization using the closed loopTightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20143/11

approach. Both Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) aredeveloped to merge the GPS and inertial measurements.3.1.Extended Kalman Filter (EKF)EKF transforms the nonlinear system for both the motion and observation models tolinear through linearization process by applying Taylor series expansion and neglectingthe second and higher order terms assuming Gaussian distribution density which isapplied in Kalman filter (KF) estimation. Generally, EKF gives optimal estimationsolution for linear models. In other words, for the integrated GPS/INS system, EKF givesoptimal solution for the approximate system (linearized system) rather than the originalsystem (nonlinear system). Using first order Taylor linearization may cause divergenceof motion models especially during GPS outages due to the impact of neglecting higherorder terms especially when low cost MEMS-based IMU is used.The prediction step is given by (Jekeli, 2001):δ x k ,k 1 Φ k ,k 1δ x k 1(3)Pk ,k 1 Φ k ,k 1 Pk 1 Φ Tk ,k 1(4)))The update step is given by (Jekeli, 2001):K k Pk ,k 1 H kT ( H k Pk ,k 1 H kT Rk ) 1(5)Pk ( I K k H k )Pk ,k 1(6)δ xk δ xk,k 1 Kk ( δ Zk Hk δ xk,k 1 ))))(7)where , ିଵ is the updated error state vector, , ିଵ is the state-transition matrix, , ିଵ is the variance-covariance matrix for the prediction state , is variance covariancematrix for the measurement state, is the Kalman gain, k is the epoch number, is thedesign matrix related the measurement vector by the error state vector and is themeasurement vector.3.2.Unscented Kalman Filter (UKF)In UKF, a set of scaled sigma points with appropriate weights is deterministically chosenso as to capture the mean and covariance of this random vector up to a third orderaccuracy. Consider a random vector x with mean x and covariance matrixP୶ . The scaledsigma points and the corresponding weights can be defined according to Bergman, (2001)as follows:Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20144/11

1. Initialize with (k 0);x0 E[ x0 ](8)P0 E[(x0 x0 )(x0 x0 )T ](9)2. Define sigma points;12( n λ )xki 1 x ( n λ )Px , Wi xki n1 x ( n λ )Px , Wi n ( 10 )12( n λ )( 11 )Where i 1:n, are the sigma points and n is the dimension of the state vector. Theparameter λ is a scaling parameter.3. Time update step;x ki ,k 1 f ( x ki 1 , u i ) w k( 12 )4. Measurement update;2nZki ,k 1 h(xki ,k 1 ), Zk ,k 1 2n W Zii k,k 1 , xk ,k 1i 0 W xii k ,k 1( 13 )i 02nPzk W (Zik .k 1 Z ki ,k 1 )(Z k ,k 1 Z ki ,k 1 )T( 14 )i 02nPxk ,k 1 W (xik ,k 1 xki ,k 1 )(xk ,k 1 xki ,k 1 )T( 15 )i 0K k Pxk ,k 1 Pyk T( 16 )xk xk ,k 1 K k Z k ,k 1( 17 )Pxk Pxk ,k 1 K k Pzk K k T( 18 )where ̅ and are the initial state vector and variance-covariance matrix respectively. and are the state and observation vectors for the corresponding sigma points, f andTightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20145/11

h are the non-linear motion and observation models respectively. , , , and , are the time prediction state vector, observation vector and variance-covariancematrix respectively. , and are the time update state vector variance-covariancematrix respectively.Vehicular test is conducted to evaluate the performance of the developed integrated GPSPPP/MEMS-based IMU system. The vehicular test was carried out in downtownKingston, Ontario (Figure 1). The test location represents difficult scenarios for satellitenavigation, with frequent partial GPS outages of several seconds. Novatel SPAN-CPTsystem is used for obtaining the inertial data records and Trimble R10 receiver isemployed for obtaining GPS observations. The SPAN-CPT system consists of a NovatelOEM4 receiver and MEMS IMU consisting of three MEMS-based accelerometers andthree fiber optic gyros. Only the performance of the positioning accuracy is considered inthis paper. The positioning results of the integrated system show that decimeter-levelaccuracy is achievable for both EKF and UKF. To simulate the challenging conditions ofthe trajectory trip including high and slow speeds, twelve simulated GPS outages of 60s,30s and 10s are introduced. Both EKF and UKF have similar accuracy-level during theoutages.Figures 2, 3 and 4 show the positioning errors referenced to carrier-phase-based DGPSsolution for latitude, longitude and altitude. The results show decimeter-level positioningaccuracy for both EKF and UKF. Figure 5 shows the root-mean-square error (RMSE) andthe maximum errors of the positioning results. Figure 6 shows the accuracy of theintegrated system during various complete GPS outages. As can be seen, the integratedsystem showes meter-level accuracy when a 60-second outage is introduced. However,the positioning accuracy is improved to sub-decimeter during 30- and 10-second GPSoutages, respectively.Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20146/11

Figure 1. Trajectory test areaFigure 2. Latitude accuracy using EKF and UKFFigure 3. Longitude accuracy using EKF and UKFTightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20147/11

Figure 4. Altitude accuracy using EKF and UKFFigure 5. Maximum and RMSE errors for EKF and UKFTightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20148/11

Figure 6. The average of max positioning errors during GPS 60 sec, 30 sec and 10 secoutages using EKF and UKF4. ConclusionThis research developed new algorithms for the integration of GPS PPP and MEMS-based IMU.Tightly coupled mechanization was implemented using both EKF and UKF. The performance ofintegrated system was analyzed using a real test scenario in downtown Kingston, Ontario. Undifferenced ionosphere-free linear combinations of code and carrier-phase measurements wereconsidered. The positioning results of the integrated system showed that decimeter-levelaccuracy is achievable for both EKF and UKF. During the GPS outages, the integrated systemshowed meter-level accuracy when a 60-second outage was introduced. However, thepositioning accuracy was improved to sub-decimeter and centimeter level when 30- and 10second GPS outages were introduced, respectively. These results are very encouraging as theyare comparable to high-end differential-based GPS/INS systems.5. ReferencesBergman, N. (2001). Posterior Cramer-Rao Bounds for Sequential Estimation, inSequential Monte Carlo methods in practice (A. Doucet, N. de Freitas, and N.Gordon, eds.). pp. 321–338, New York: Springer Verlag,.Elsobeiey, M. and El-Rabbany, A. (2013). Efficient Between-Satellite Single-DifferencePrecise Point Positioning Model. Journal of Surveying Engineering.,10.1061/(ASCE)SU.1943-5428.0000125 , 04014007.Hofmann-Wellenhof, B., H. Lichtenegger, and E. Wasle. (2008). GNSS GlobalNavigation Satellite Systems; GPS, GLONASS, GALILEO & more. Springer WienNew York.Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 20149/11

Jekeli, C. (2001). Inertial navigation systems with geodetic applications, Berlin, NewYork, de Gruyter. ISBN 3-11-015903-1.Nassar, S. (2003). Improving the Inertial Navigation System (INS) Error Model for INSand INS/DGPS Applications. PhD Thesis, Department of Geomatics Engineering,University of Calgary, Canada,Petovello, M. (2003). Real-time Integration of a Tactical-Grade IMU and GPS for HighAccuracy Positioning and Navigation. PhD Thesis, Department of GeomaticsEngineering, University of Calgary, Canada, UCGE Report No. 20173.Zhang, Y., and Gao, Y. (2007). Integration of INS and Undifferenced GPS Measurementsfor Precise Position and Attitude Determination. The Journal of Navigation, 61, TheRoyal Institute of Navigation, pp.1-11.Biography – Mahmoud Abd El-RahmanMahmoud obtained his B.Sc. and M.Sc. degrees from the Department of CivilEngineering at Cairo University in 2007 and 2010, respectively. He worked as anassistant lecturer of civil engineering at Cairo University since graduation. In 2011, hejoined the Geomatics research group in the Department of Civil Engineering, RyersonUniversity, as a Ph.D. student. His research focuses on navigation system technology,global navigation satellite systems (GNSS), and GNSS/INS integration.Biography - Ahmed El-RabbanyDr. Ahmed El-Rabbany obtained his PhD degree in GPS Satellite Navigation from theDepartment of Geodesy and Geomatics Engineering, University of New Brunswick,Canada. He is currently a full professor and Graduate Program Director at RyersonUniversity, Toronto, Canada. He also holds an Honorary Research Associate position atthe University of New Brunswick. Dr. El-Rabbany’s areas of expertise include SatelliteNavigation, Geodesy and Hydrographic Surveying. He is an Associate Editor ofGeomatica and Editorial Board member for the Journal of Navigation and the AINJournal. He also holds the position of President-Elect with the Canadian Institute ofGeomatics. Dr. El-Rabbany received numerous awards in recognition of his academicachievements, including three merit awards and distinguished service award fromRyerson University and best papers and posters at various conferences and professionalevents. He was also honoured by a number of academic and professional institutionsworldwide.Tightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 201410/11

CONTACTSMahmoud Abd RabbouRyerson University350 Victoria StreetToronto, OntarioCANADATel. 1 (647)774-6799Email: Mahmoud.abdelrahman@ryerson.caDr. Ahmed El-Rabbany, P.Eng.Ryerson University350 Victoria StreetToronto, OntarioCANADATel. 1 (416) 979-5000 ext. 6472Fax 1 (416) 979-5122Email: rabbany@ryerson.caWeb site: http://www.civil.ryerson.caTightly Coupled Integration of GPS-PPP and MEMS-Based Inertial System Using EKFand UKF ( 7269)Mahmoud Abd Rabbou and Ahmed El-Rabbany (Canada)FIG Congress 2014Engaging the Challenges, Enhancing the RelevanceKuala Lumpur, Malaysia, 16 – 21 June 201411/11

GPS outages. To overcome these limitations, GPS can be integrated with a relatively environment-independent system, the inertial navigation system (INS). Currently, most integrated GPS/INS systems are based on differential GPS (DGPS) due to the high accuracy of differential mode (Petovello, 2003 and Nassar, 2003). More recently, GPS-

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