TERRAIN REFERENCED UAV NAVIGATION WITH LIDAR A COMPARISON OF SEQUENTAIL PROCESSING AND BATCH PROCESSING ALGORITHMS

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1 8 H INERNAIONAL CONGRESS OF HE AERONAUICAL SCIENCES ERRAIN REFERENCED UAV NAVIGAION WIH LIDAR A COPARISON OF SEQUENAIL PROCESSING AND BACH PROCESSING ALGORIHS Yeoha Hwag, i-jea ah KAIS (Korea Advaced Istitute of Sciece ad echology) yhhwag@fdcl.aist.ac.r; mjtah@fdcl.aist.ac.r Keywords: SIAN, ERCO, DSAC, Exteded Kalma filter, Cross-Correlatio atchig Abstract his paper discusses terrai refereced avigatio (RN) system usig light detectio ad ragig (LiDAR) ad pressure altimeter i order to compesate for a Iertial Navigatio system () errors. he paper addresses sequetial processig such as Sadia Iertial errai Aided Navigatio (SIAN) ad batch processig algorithms such as Digital Scee atchig Area Correlator (DSAC) ad carries out simulatios with scearios i order to compare the performace of these two processig algorithms ad verify which oe is more useful i each specific eviromet. 1 Itroductio A Iertial Navigatio System () has bee used for estimatig positios, velocities, ad attitude agles of UAVs but it has disadvatages i that errors are accumulated as time goes by because of itegratig measuremets of acceleratio ad agular velocity obtaied from a iertial measuremet uit (IU). For this reaso, the geerally employs Global Positioig System (GPS) i order to correct ad calibrate itself through a Kalma filterig algorithm. However, GPS is easily affected by outside disturbace sigals. As a result, RN (errai Refereced Navigatio), which is a techique that corrects the usig the positio measuremet obtaied through comparig the measured altitude data from a sesor with the stored digital elevatio map (DE)[5] regardless of outside disturbace sigals, has bee recetly studied as a alterative method for correctio. hus, this techique ca be used whe GPS is ot available or jammed. here are two processig methods for a RN system[]. Oe is a sequetial processig method such as SIAN (Sadia Iertial errai- Aided Navigatio), which compares oe measuremet data with the stored DE at the time whe the sesor measures altitudes. he other is a batch processig such as Digital Scee atchig Area Correlator (DSAC), which compares betwee sesed images ad stored referece images to determie positio measuremets through the best match locatio of the image, ad errai Cotour atchig (ERCO), which obtais the measuremets through correlatig a sesed terrai profile to a stored map terrai profile. o measure the altitude data for RN, a pressure altimeter, a radar altimeter ad a LiDAR (Light Detectio ad Ragig) are eeded. Comparig with the radar altimeter, the LiDAR has several advatages i that it ca measure large areas that are difficult to approach with higher resolutios i a shorter period of time ad costruct a digital elevatio map. he costructed DE ca be used for hazard avoidace as well as RN. herefore, this paper proposes the RN system usig the LiDAR i order to compesate for errors. Sectio describes the sequetial processig method based o the LiDAR measuremets ad system ad measuremet modelig. Sectio 3 discusses the batch processig method with cross correlatio matchig. Sectio 4 explais EKF algorithm. Sectio 5 gives results of the simulatios cosisted of two differet eviromets ad compariso. Fially, sectio 6 gives coclusio. 1

2 Yeoha Hwag, i-jea ah Sequetial processig method his sectio explais SIAN as a sequetial processig method ad describes the system model..1 SIAN SIAN[] is a sequetial processig method which meas whe the sesor measures a altitude, the positio of UAV is derived by correlatig the altitude to the stored DE at the time. A icliatio of terrai is iput ito a Exteded Kalma filter (EKF) which updates the UAV s F G where, W meas radom white oise of..3 easuremet model[4] (3) he terrai-clearace measuremet equatio is a oliear fuctio of x, y, z coordiates. o apply the EKF, the liearizatio of the measuremet equatio is eeded. z= yˆ - y hˆ ( ˆ, ˆ) hdb x y ylidar ˆ h y pressure (4). system model Fig. 1. SIAN system he states of system model are defied as 6 error states expressed the positio ad the velocity of UAV. x [ x y h v v v ] (1) x y h where, x, y, h are the errors of x, y ad z coordiates. v x, v y, vz are the errors of the velocities of UAV. his error states are used i idirect alma filter for correctio. Equatio () ad (3) are error state equatios. () x FxGW H hdb hdb 1 x y (5) 1 where, yˆ ad y describe the estimated measuremets ad true measuremets of z coordiate. h ˆ is estimated altitude ad h ( ˆ, ˆ ) DB x y is a elevatio obtaied i DE whe x ad y coordiates are ( xˆ, y ˆ). ylidar is a measuremet by LiDAR ad y pressure is a measuremet by pressure altimeter. Fially, H is a measuremet sesitivity matrix ad the first ad secod rows mea the terrai slops of x ad y coordiates. 3 Batch processig method his sectio discusses DSAC method ad cross correlatio. 3.1 DSAC DSAC[3] is origially used for omahaw cruise missile i order to provide a reliable ad precise measuremet of locatio. Durig the missile flyig, the curret locatio of

3 ERRAIN REFERENCEDD UAV NAVIGAION WIH LIDAR A COPARISON OF SEQUENAIL PROCESSING AND BACH PROCESSING ALGORIH missile where the most well matched is determied by acquired images of the groud comparig with a existig image that is stored. I this paper, as previously metioed, altitude measureme ts obtaied from the sesors suchh as LiDAR ad pressure altimeter are used for geeratig terrai elevatio map istead of images ad compares with DE i order to estimate the curret positio. (a) template widow (b) search widoww ad matchig widow Fig 4. Cocept of Cross-Correlatio matchig Fig. DSAC operatio he first picture p (a) is a template widoww through LiDAR. he secod picture (b) is a search widow i DE ad red areas mea a matchig widow. Cross-correlatio coefficiet (, 1 1) is defied as equatio (8). m i1 j1 m i 1 j1 ( h (, ) xi y j h)( h( xi, yj) h ) ( h ( xi, yj) h) m 1 m 1 m i1 j1 ( h ( x, y ) h ) i j m 1 (8 ) Fig 3. DSAC system 3. Cross-Correlatio matchig[1] Area-based matchig techique is used to extract the most similar parts by aalyzig the similarity betwee elevatios measured by the LiDAR sesor ad DE. I other words, terrai elevatio map geerated by LiDAR is defied as a template widow ad the, the size of a search widow is set as much as icludig the emplate widow. While the template widoww is movig withi the search widow, the most well matched areas are foud. his paper uses cross-correla atio matchig techique for area- based matchig techique. where, is covariace betwee a template widow ad a matchig widow ad ad are the stadard deviatios of the t template widow ad the t matchig widow. Cross-correlatio coefficiet hass a statistical characteristic so that the maximum cross correlatio coefficiet does ot mea the best matched. hus, whe the crosss correlatio coefficiet iss deoted as a three-dimesioal curved surface, the positio where the partial derivative iss zero i the three-dimesioal curved surface is the best well-matched. his positio ca be b the locatio of UAV estimated cx 1 cx y cxy 3 cxy 4 3 c5x cxy 6 cxy 7 c8 xy 3 c9x c1xy c11xy c1 xy 3 c c yc y c y (9) 3

4 Yeoha Hwag, i-jea ah Usig the three-dimesioal surface approximatio equatio (9), the pixel positio ad ay polyomial coefficiets ca express the cross correlatio coefficiet (1) x x y x y y c x x y x y y c x x y x y y c 16 (1) hrough pseudo iverse, the polyomial coefficiets ca be obtaied. he threedimesioal surface approximatio equatio ca be calculated by substitutig the polyomial coefficiets for c1, cc 16. he equatio (11) is for fidig the sub-pixel positio whe a partial differetial of threedimesioal surface approximate equatio is zero. d dx dy x x (11) where, x ˆ, y ˆ, h ˆ are x, y ad z coordiates by. x, y are x ad y coordiates by usig cross-correlatio matchig. h pressure is the altitude measured by pressure altimeter. he true measuremet is used i alma filter. 4 Exteded Kalma Filter his sectio describes the EKF[4] used for this research simulatio. Kalma filter is origially used i liear system. However, whe alma filter is applied to oliear system, exteded alma filter (EKF) is eeded i istead of Kalma fitler. he filter method has two stages: oe is a state propagatio step, the other is a state update step. he equatio (6) represets the propagatio step for error states ad error covariace. xˆ ˆ ˆ f ( x 1) 1x1 ˆ ˆ P 1P111GQ1G 1t I Ft 1 (6) ˆ x where, xˆ is a priori estimated error state ad is a posterior estimated error state. P ˆ represets a error state covariace. Q 1 represets a oise covariace matrix of. 1 is a state trasitio matrix.. he equatio (7) represets the update step for error states ad error covariace. Fig 5. Positio of maximum coefficiet of correlatio 3.3 easuremet model rue measuremet of the x ad y coordiates is calculated by Cross-Correlatio matchig usig LiDAR. z= yˆ - y xˆ x ˆ y y ˆ h hpressure (1) zˆ H ˆ x ˆ ˆ 1 K P H (HP H R ) (7) xˆ ˆ ( z zˆ x K ) ˆ ( H ) ˆ P I K P ( I KH ) KR K where, z is errors of true measuremets which are itroduced earlier i sectio.3 ad ẑ is the estimated measuremets. H is measuremet sesitivity matrix. After obtaiig alma gai, xˆ ad Pˆ are calculated by substitutig the alma gai i equatio (7). Idirect alma filter is used alog with EKF so that xˆ 1 is zero vector every steps. 4

5 ERRAIN REFERENCED UAV NAVIGAION WIH LIDAR A COPARISON OF SEQUENAIL PROCESSING AND BACH PROCESSING ALGORIH 5 Simulatio results 5.1 Simulatio eviromet his sectio aalyzes the simulatio results of RN system of UAV. he speed of UAV is set 9m/s. HG 17 is used as the sesor of IU ad the oise of LiDAR ad pressure altimeter are assumed each 5m. Error-y [m] /DSAC 5. Example 1 I this study, simulatios perform by cosiderig two differet situatios that iitial positio errors have small or large values. DSAC ad SIAN methods are compared to each other with the two differet situatios. If the iitial positio error is bigger tha 9m, the positio could have divergece because the grid size of DE is 9m ad the terrai icliatio varies discretely. I this sectio, x, y ad z coordiates errors are assumed 1m, 5m, ad m. Error-h [m] Fig 7. Y coordiate error history /DSAC /DSAC ime [sec] Fig 8. Z coordiate error history Error-x [m] Fig 6. X coordiate error history Latitude [deg] Logitude [deg] Fig 9. Start ad Ed locatio of simulatio Figure 6-8 are SIAN ad DSAC performace. he positios through SIAN ad DSAC follow referece positios with small or large errors. he results represet a disadvatage of SIAN[] which is high probability of divergece due to the highly oliear characteristic of terrai ad use of 5

6 Yeoha Hwag, i-jea ah oly oe measuremet. o mae sure to compare to each methods, mea values of errors are represeted i table 1. able 1. ea for RN with iitial small errors x(m) y(m) z(m) SIAN DSAC Error-H [m] Averagely, the errors of SIAN are see to be larger tha the errors of DSAC accordig to table Example. I this sectio, x, y ad z coordiates errors are assumed 15m, 1m, ad m. Error-X [m] /DSAC /DSAC ime [sec] Fig 1. Z coordiate error history Figure 1-1 are SIAN ad DSAC performace with large error. As show i figures, the SIAN performace with large errors is showed a tedecy of divergece ad it is more distict tha the SIAN performace with small errors. able represets the errors meas for RN with iitial large errors. able. ea for RN with iitial large errors x(m) y(m) z(m) SIAN DSAC Coclusio Error-Y [m] Fig 1 X coordiate error history his research carries out to verify the performace betwee the two methods (sequetial processig ad batch processig) for iitial error coditios to aalyze each method is more useful i each specific eviromet. hrough the simulatios, the batch processig method has a better performace tha the sequetial processig method i the whole simulatio whe the iitial errors of the are small or large. -8 /DSAC Fig 11.. Y coordiate error history Refereces [1] Bo-mi lee errai Refereced Navigatio usig Area-based atchig Algorithm, Egieerig aster's hesis, Uiversity of Seoul, 9 [] aarte Uijt de Haag Applicatio of Laser Rage Scaer Based errai Refereced Navigatio Systems for Aircraft Guidace, Proceedigs of the 6

7 ERRAIN REFERENCED UAV NAVIGAION WIH LIDAR A COPARISON OF SEQUENAIL PROCESSING AND BACH PROCESSING ALGORIH hird IEEE Iteratioal Worshop o Electroic Desig, est ad Applicatios(DELA 6) 5 [3] Frederic W. Guidace ad Navigatio i the Global Egagemet Departmet, JOHNS HOPK APL ECHNICAL DIGES, VOLUE 9, NUBER, 1 [4] Sughoo o, H.C.Bag A Performace Aalysis of Usceted Kalma Filter Based errai Refereced Navigatio, KSAS, P551-P556 [5] he CGIAR Cosortium for Spatial Iformatio (CGIAR-CSI) Copyright Statemet he authors cofirm that they, ad/or their compay or orgaizatio, hold copyright o all of the origial material icluded i this paper. he authors also cofirm that they have obtaied permissio, from the copyright holder of ay third party material icluded i this paper, to publish it as part of their paper. he authors cofirm that they give permissio, or have obtaied permissio from the copyright holder of this paper, for the publicatio ad distributio of this paper as part of the ICAS1 proceedigs or as idividual off-prits from the proceedigs. 7