Calibration and orientation of airborne image and laser scanner data using GPS and INS

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(1)75,7$*(2)272 ,661 ,651.7+56(. &DOLEUDWLRQDQG2ULHQWDWLRQRI$LUERUQH ,PDJHDQG/DVHU6FDQQHU'DWD8VLQJ *36DQG,16 'LVVHUWDWLRQ. +HOpQ%XUPDQ. ___________________________________________________________________________________ Royal Institute of Technology Department of Geodesy and Photogrammetry Stockholm, Sweden April 2000. Fotogrammetriska Meddelanden Photogrammetric Reports No 69 ISSN 0071-8068.

(2) © Helén Burman Royal Institute of Technology Department of Geodesy and Photogrammetry Stockholm, Sweden ISBN 91-7170-565-1 TRITA-GEOFOTO 2000:11 ISSN 1400-3155 ISRN KTH/GEOFOTO/R--00/11--SE Photogrammetric Reports No 69 ISSN 0071-8068.

(3) $%675$&7 GPS and INS measurements provide positions and attitudes that can be used for direct orientation of airborne sensors. This research improves the final results by performing simultaneous adjustments of GPS, INS and image or laser scanner data. The first part of this thesis deals with in-air initialisation of INS attitude using GPS and INS velocity difference. This is an improvement over initialisation on the ground. Even better results can probably be obtained if accelerometer biases are modelled and horizontal accelerations made larger. The second part of this thesis deals with GPS/INS orientation of aerial images. Theoretical investigations have been made to find the expected accuracy of stereo models and orthophotos oriented by GPS/INS. Direct orientation will be compared to block triangulation. Triangulation can to greater extent model systematic errors in image and GPS-coordinates. Further, the precision in attitude after triangulation is better than that found in present INS performance. On the other hand, direct orientation can provide more effective data processing, since there is no need for finding or measuring tie points or ground control points. In strip triangulation, the number of ground control points can be reduced, since INS attitude measurements control error propagation through the strip. Even if consecutive images are strongly correlated in direct orientation, it is advisable to make a relative orientation to minimise stereo model deformations. The third part of this thesis deals with matching laser scanner data. Both elevation and intensity data are used for matching and the differences between overlapping strips are modelled as exterior orientation errors. Special attention is paid to determining misalignment between the INS and the laser scanner coordinate systems. We recommend flying in four different directions over an area with elevation and/or intensity gradients. In this way, misalignment can be found without any ground control. This method can also be used with other imaging sensors, HJ an aerial camera. .H\ZRUGV Airborne, Camera, Laser scanner, GPS, INS, Adjustment, Matching.. i.

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(5) $&.12:/('*(0(176 I would like take this opportunity to express gratitude to my supervisor, Professor Kennert Torlegård, for his support and guidance during my studies. I have greatly appreciated his understanding during this period for my situation, when I have had to combine doctoral studies with the birth of three children. I would also like to thank my second supervisor, Peter Axelsson, for his support and the fruitful discussions we had on a daily bases. Thanks to Håkan Sterner and others at Topeye AB for their enthusiasm and willingness to support my research in different ways. I'd also like to thank Lewis Lebolt for proof reading this thesis. Thanks to my former and present colleagues at the Department of Geodesy and Photogrammetry, for all the practical jokes, laughs and spiritual discussions during our coffee breaks. Special thanks to my parents Gerd and Egon my mother-in-law Eva and my late fatherin-law Finn, for helping out in critical situations. There would not have been any thesis without your help. Finally, I would like to express my gratitude and love to Tobbe and my children Henrik, Rickard and Marcus. Through late evenings and deadline agonies, you have continued to show me love and support. This research was made possible by financial support from the Swedish Research Council for Engineering Sciences and the Swedish National Space Board.. iii.

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(7) &217(176 $%675$&7 L $&.12:/('*(0(176 LLL &217(176 Y /,672)7$%/(6 YLL /,672)),*85(6L[ /,672)$%%5(9,$7,216[L . ,1752'8&7,21 1.1 1.2 1.3 1.4. . 6(162525,(17$7,21 2.1 2.2 2.3 2.4 2.5. . BACKGROUND ........................................................................................................1 RELATED WORK .....................................................................................................2 RESEARCH OBJECTIVES ..........................................................................................3 OUTLINE OF THE THESIS .........................................................................................3 GEOREFERENCING OF AIRBORNE IMAGING SENSORS .............................................5 GPS........................................................................................................................6 INS.........................................................................................................................7 GPS AND INS INTEGRATION ..................................................................................8 THE TOPEYE LASER SCANNING SYSTEM ..............................................................11. ,1$,5$77,78'(,1,7,$/,6$7,21 3.1 THE METHOD .......................................................................................................14 3.2 PRACTICAL TEST IN FINLAND ...............................................................................16 5HVXOWV 3.3 SUMMARY AND CONCLUSIONS .............................................................................20. . ,0$*(25,(17$7,21%<*36$1',16 4.1 MATHEMATICAL MODEL ......................................................................................22 *36DQG,166XSSRUWHG%ORFN7ULDQJXODWLRQ 'LUHFW,PDJH2ULHQWDWLRQE\*36DQG,16 $FFXUDF\0HDVXUHV 4.2 THEORETICAL TEST ..............................................................................................31 ,QYHVWLJDWHG&DVHV 5HVXOWRIWKH7KHRUHWLFDO7HVW 2UWKRSKRWR3UHFLVLRQ 'LVFXVVLRQDQG&RQFOXVLRQ 4.3 PRACTICAL TEST - BORLÄNGE .............................................................................41 7KH'DWD6HW &DPHUD&DOLEUDWLRQ 5HVXOWVRIWKH3UDFWLFDO7HVW%RUOlQJH 'LVFXVVLRQWKH%RUOlQJH7HVW 4.4 PRACTICAL TEST - FREDRIKSTAD .........................................................................46 v.

(8) 7HVW&RQILJXUDWLRQ 5HVXOWV(YDOXDWLQJ*36,160HDVXUHPHQWV 5HVXOWV'LUHFW2ULHQWDWLRQE\*36,16 5HVXOWV6WULS7ULDQJXODWLRQ 5HVXOWV&RUUHODWLRQ 'LVFXVVLRQ7HVW)UHGULNVWDG 4.5 SUMMARY AND CONCLUSIONS .............................................................................58 . $'-8670(172)/$6(5'$7$ 5.1 MODELLING LASER SHOTS ...................................................................................59 5.2 ALIGNMENT..........................................................................................................68 7HVW&RQILJXUDWLRQ 2EVHUYDWLRQ:HLJKWLQJ &KRRVLQJD0DWFKLQJ$UHD 5.3 STRATEGY ............................................................................................................80 5.4 CONTROLLED TESTS .............................................................................................81 7HVW$UHDV 5HVXOWV 5.5 DISCUSSION ..........................................................................................................87. . 6800$5<$1'&21&/86,216 6.1 6.2 6.3 6.4. IN-AIR ATTITUDE INITIALISATION ........................................................................89 GPS/INS ORIENTED IMAGES ...............................................................................89 ADJUSTMENT OF LASER SCANNER DATA .............................................................90 FUTURE DEVELOPMENT .......................................................................................91. 5()(5(1&(6 $33(1',; . vi.

(9) /,672)7$%/(6 Table 2-1 Specifications for the Topeye laser scanning system ...................................12 Table 3-1 Differences between uncorrected and corrected laser elevations.................18 Table 4-1 Mean precision in new points computed with different methods. The X-axis is in the flight direction and the Y-axis across the flight direction. The precision of GPS measurements (σGPS) is of the same magnitude as the precision of standard error of unit weight times the image scale, 1.0(σim ∗ image scale). .................................................................................................40 Table 4-2 Camera calibration adjustment conditions ...................................................43 Table 4-3 Camera calibration results. The calibrated parameters are described in Equations 4-3 and 4-4...................................................................................44 Table 4-4 Differences between camera exterior orientation parameters derived from triangulation, and exterior orientation parameters derived from GPS/INS measurements. ..............................................................................................44 Table 4-5 Root Mean Square (RMS) values of the differences between geodetically and photogrammetrically measured ground point coordinates. ...................45 Table 4-6 Standard deviations of different observation groups based on Förstner’s variance component analysis method...........................................................49 Table 4-7 Standard deviations of different observation groups based on Förstner’s variance component analysis after strip-wise shift and drift correction of GPS/INS measurements. ..............................................................................49 Table 4-8 Result from direct orientation by GPS/INS..................................................53 Table 4-9 Strip triangulation (strip 1-4 = S.1-S.4) with full ground control at the ends of the strip, either without GPS/INS observations, with GPS position observation and shift (gps1) or shift/drift parameters (gps2) and/or with INS attitudes and shift (ins1) or shift/drift parameters (ins2). .............................55 Table 5-1 Result from matching test area 1. Mean elevation discrepancies after adjustment are found in G=. ..........................................................................83 Table 5-2 Results from matching test area 2. Mean elevation discrepancies after adjustment are found in G=. ..........................................................................85 Table 5-3 Results from matching test area 3. Mean elevation discrepancies after adjustment are found in G=. ..........................................................................86 Table B- 1 Table B- 2 Table B- 3 Table B- 4. Block triangulation .....................................................................................101 Strip triangulation.......................................................................................101 Direct orientation........................................................................................102 Direct orientation........................................................................................102. Table C- 1 Differences between triangulated and GPS/INS measured attitudes. ........103 Table C- 2 Differences between triangulated and GPS/INS measured attitudes after strip-wise correction for shift and drift.......................................................103 Table C- 3 Comparing triangulation result of camera projection centre positions with GPS-measured positions.............................................................................103 Table C- 4 Comparing triangulation results with INS attitudes. Numbers in arcseconds. ....................................................................................................................104 Table C- 5 Comparing the result of ground point coordinates from triangulation with check point coordinates. .............................................................................104. vii.

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(11) /,672)),*85(6 Figure 2-1. Figure 2-2 Figure 2-3. Figure 2-4 Figure 2-5 Figure 2-6 Figure 3-1 Figure 3-2 Figure 3-3 Figure 3-4. Figure 3-5. Figure 3-6. Figure 3-7 Figure 4-1 Figure 4-2. Figure 4-3. Figure 4-4. Figure 4-5 Figure 4-6 Figure 4-7. An example of the difference between INS and GPS positions in the global frame using a stand-alone INS with ring laser gyros. The vertical position is probably afflicted with an erroneous input of gravity. The helicopter made two turns, which caused the trend change in horisontal position error. .............................................................................................................8 GPS and INS positions before adjustment...................................................9 GPS and INS positions after having applied a 3rd degree polynomial adjustment to two seconds of INS positional information, matching the GPS positions...............................................................................................9 GPS aided by INS. dv=acceleration, df=angular velocity, r=position, v=velocity, w=attitude ...............................................................................10 Loosely coupled system / decentralised Kalman filtering .........................10 Tightly coupled system / centralised Kalman filtering. .............................11 An attitude error results in erroneous (N,E,D) components.......................13 Adjusting a 2nd degree curve to the first 20 measurements improves estimation of the initial attitude. Attitude changes converge on zero. .......15 Incremental calculation of attitudes. ..........................................................16 Laser data ground classification (light grey). Only laser points on the ground were compared to photogrammetric reference DEM (dark squares). Dark grey points are laser points classed as non-ground, in this case primarily trees. ...........................................................................................17 Flightline 1 (1f18) across the strip before (light grey) and after (dark grey) re-initialisation of INS attitude. Dark squares are photogrammetric reference elevations....................................................................................18 Flightline 1 (1f18) along the strip before (light grey) and after (dark grey) re-initialisation of INS attitude. Dark squares are photogrammetric reference elevations....................................................................................18 Cross sections of laser strip before and after correction of attitudes. ........19 Probability α and β depending on the critical value k and the noncentrality parameter δ0 in data-snooping....................................................30 Precision in ground coordinates depending on precision in attitude and a correlation between attitude errors of 0.8 . GPS-precision = 1.0 [σim ∗ image scale]................................................................................................33 Precision in ground coordinates depending on precision in attitude and a correlation between attitude errors of 1.0 . GPS-precision = 1.0 [σim ∗ image scale]................................................................................................33 Standard deviation in model coordinates due to errors in image coordinates and image orientations. The different layers represent different correlation factors (ρ = 0, 0.2, …, 1.0) between orientation parameters in the two images, the highest correlation giving the lowest standard deviation in model..........................................................................................................34 Precision in model coordinates, in millimetres, dependent on correlation between the orientation error in two images. .............................................34 Precision in ground points dependent on precision in attitude. The accuracy of the GPS-measurement is 1.0 [σim ∗ image scale]...................35 Precision in ground coordinates, separated into X, Y and Z, dependent on precision in GPS/INS position and attitude. ..............................................36. ix.

(12) Figure 4-8 Figure 4-9. Figure 4-10. Figure 4-11 Figure 4-12 Figure 4-13 Figure 4-14 Figure 4-15 Figure 4-16 Figure 4-17 Figure 4-18 Figure 4-19 Figure 5-1 Figure 5-2 Figure 5-3 Figure 5-4 Figure 5-5 Figure 5-6 Figure 5-7 Figure 5-8 Figure 5-9 Figure 5-10 Figure 5-11 Figure 5-12 Figure 5-13. Figure 5-14. Figure 5-15 Figure 5-16. x. Precision in ground points after block triangulation dependent on precision in GPS positions.........................................................................................37 Precision in pixels in ground scale for an image of 0.23x0.23 meter depending on the precision of exterior orientation (0.2 m in position and 10’’ in attitude) and the DEM (2.5 m in elevation).....................................38 Precision in pixels in ground scale for an image of 0.23x0.23 meter depending on the precision of exterior orientation (0.2 m in position and 45’’ in attitude) and the DEM (2.5 m in elevation).....................................39 Control points (asterisks) and tie points (dots) in the test area. .................42 One of the images of the test area, which is dominated by a large crossroad. ...................................................................................................42 Comparing triangulation position results with GPS/INS position measurements.............................................................................................47 Comparing triangulation attitude results with GPS/INS measurements. ...48 Remaining differences between triangulated and GPS/INS measured positions after strip-wise shift and drift correction. ...................................50 Differences after strip-wise shift and drift correction of INS attitude. ......51 Difference in check points after GPS/INS-supported triangulation without ground control points. ................................................................................52 Difference in check points after direct orientation of images by GPS/INS. ....................................................................................................................54 Auto-correlation (ρ) of GPS/INS observations over time based on data from the Fredrikstad-block.........................................................................57 Elevation data (left) and intensity data (right) from the same laser strip...59 One laser shot (Xl,Yl,Zl) related to a regular grid. .....................................61 Configuration for alignment procedure solving dr in flat areas with only one strip available. .....................................................................................69 Configuration for solving all misalignment angles with only one strip.....70 Configuration for solving all misalignment angles with only one strip.....71 Configuration for solving dr in an alignment procedure with two strips in opposite directions. ....................................................................................72 Configuration for solving all misalignment angles with two strips. ..........74 Configuration for solving all misalignment angles with two strips. ..........75 Recommended configuration for the alignment procedure........................79 Test area 1, elevations on the left and intensity data on the right. .............82 Test area 2, elevation data on the left and intensity data on the right. .......82 Test area 3, elevation data on the left and intensity data on the right. .......82 Interest points for matching elevation values (left) and intensity values (center). The right image shows flat areas suitable for measuring elevation differences due to misalignment in the roll angle. .....................................83 Interest points for matching elevation values and intensity values. Top flat areas suitable for measuring elevation differences due to errors in roll. Center - interest points for elevation matching. Bottom - interest points for intensity matching. .....................................................................................84 Profiles of the building in test area 2, before (left) and after (right) laser data adjustment. .........................................................................................85 Interest points for matching elevation and intensity. Top - flat areas suitable for measuring elevation differences due to errors in roll. Center interest points for elevation matching. Bottom - interest points for intensity matching.....................................................................................................86.

(13) /,672)$%%5(9,$7,216 GPS (N,E,D) (r,p,h) AGNES CATNET DEM DPW DTG FOG GCP GP CP IMU INS IR ISPRS NIJOS nIR NLH OEEPE RLG RMS SAR Seuw Stdv SWEPOS MSE. Global Positioning System North, east, down Roll, pitch , heading Austrian net of stationary GPS receiver stations Catalonean net of stationary GPS receiver stations Digital Elevation Model Digital photogrammetric workstation Dynamically Tuned Gyro Fibre Optic Gyro Ground control point Ground point Check points Inertial Measuring Unit Inertial Navigation System Infrared International Society for Photogrammetry and Remote Sensing Norwegian Institute of Land Inventory Near infrared Agricultural University of Norway European Organisation for Experimental Photogrammetric Research Ring laser Gyro Root Mean Square Synthetic Aperture Radar Standard error of unit weight Standard deviation Swedish net of stationary GPS receiver stations Mean square error. xi.

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(15) 1 INTRODUCTION. ,1752'8&7,21 %DFNJURXQG When using an imaging sensor on an airborne moving platform it is essential to reference the collected data to a ground coordinate system. In the past, this has mainly been done by connecting the images to features on the ground, either by visual or digital correlation. In recent years, satellite positioning systems has become a powerful tool for planning and navigation of flight missions and the positioning of airborne platforms. As the development of inertial navigation and its integration with GPS has led to systems of lower cost and higher precision, it has become profitable to invest in INS for a more efficient collection of remotely sensed data. Platform orientation is needed for many applications. One is navigation and its special interest for the military has been a great source of development. Many of these techniques have become more or less available on the open market and can be used for navigation, positioning and orientation of both stationary and moving objects. One area of use is in orienting airborne sensor platforms. Examples of sensors are cameras, pushbroom scanners, laser scanners, interferometric SAR, etc. Adding INS measurements to the georeferencing procedure gives new conditions for data processing. For some types of sensors, like push-broom or laser scanners, the GPS/INS technique is necessary for an operational system and efficient data processing, as each row of pixels or each laser shot has its own set of orientation parameters. For full frame cameras, the GPS/INS technique enables in principle direct georeferencing, without ground control or block triangulation. There is a great international interest in using GPS/INS for georeferencing, which is reflected in ongoing projects in international organisations. One example of this is the European organisation OEEPE (European Organisation for Experimental Photogrammetric Research), which has an ongoing project called "Integrated Sensor Orientation". In this project, the performance of GPS/INS in aerial photography is investigated. Another project example is that the international organisation ISPRS (International Society for Photogrammetry and Remote Sensing) has a working group, WG III/1, called “Integrated Sensor Calibration and Orientation”, which held a workshop in November 1999 entitled “Direct Versus Indirect Methods of Sensor Orientation”. This workshop dealt with GPS/INS georeferencing techniques. The present attitude performance of GPS/INS, 15-25 arcseconds in roll and pitch and 30-60 arcseconds in heading (Colomina, 1999) is sufficient for many applications but not comparable to the capability of photogrammetric block triangulation, <10 arcsec. Recent scientific output indicates a performance of 3-10 arcseconds (Skaloud, 1999a). This does not necessarily mean that it can compete with block triangulation. Instead, the necessity of a thoroughly calibrated system is emphasised, as the possibility to correct for systematic errors by additional parameters or shift and drift parameters is limited.. 1.

(16) 1 INTRODUCTION. 5HODWHG:RUN The Department of Geomatics Engineering at the University of Calgary has presented a number of reports on integration of GPS and INS. They have been using this technique in connection with various applications, HJ aerial photography (Cannon, 1991; Schwarz, 1995; Skaloud HW DO., 1996; Skaloud & Schwarz, 1998), (Skaloud, 1999a,b), airborne digital camera (Mostafa HW DO 1998) and mobile mapping (El-Sheimy & Schwarz, 1995). The Department of Photogrammetry and the Department of Navigation, both at the University of Stuttgart, introduced the method of using shift and drift parameters in GPS-supported block triangulation (see e.g. Friess (1990) and Ackermann (1992)). The department is continuing to develop aerial photography by adding INS to the system (Cramer & Haala, 1999). Other applications have been laser scanning (Kilian HW DO 1996; Schiele, 1999) and pushbroom scanning (Haala HWDO 1997). The Center for Mapping at Ohio State University has announced its ambition to develop methods for direct orientation using GPS/INS. This has resulted in the Mobile Mapping System GPSVanTM (Bossler & Toth, 1996) and the Airborne Integrated Mapping System AIMSTM (Toth, 1998) for example combined with combined with CCD arrays (Toth, 1999). Directly GPS/INS oriented digital images have been combined with lidar data for improved DEM extraction (Toth and Grejner-Brzezinska, 1999). The Department of Environmental Engineering and Geodetic Science at the same university has presented accuracy investigations of the GPS/INS oriented push-broom scanner (Habib HWDO 1998) and of GPS/INS oriented images (Schenk, 1999). Others have reported on the accuracy of GPS/INS camera orientation, such as Jacobsen (1999), Andersen (1999) and Gajdamowicz (1999). The most commonly used system for GPS/INS orientation in aerial applications is the Applanix Position and Orientation System (POS). Principles and performance of this system have been presented in a number of reports HJ Reid HWDO (1996), Scherzinger (1997) and Lithopoulos (1999). The accuracy of airborne laser scanning has been evaluated by HJ Kilian HWDO (1996), Axelsson & Willén (1997), Lemmens (1997), Kraus & Pfeifer (1998), Huising & Pereira (1998) and Schaochuang HWDO. (1999). An automatic position reference system, combining measurements from differential GPS, inertial systems an laser altimeter was presented by Budde (1995). Kilian HWDO (1996) presented a method for adjusting laser strips to control DEMs by correcting the exterior orientation of the laser scanner. The differences between the ground truth and the laser strips were measured by matching. The method is similar to the one presented in this thesis for laser data adjustment. Attitude can also be measured using multi-antenna GPS systems (Schade HWDO 1993; Lu & Cannon, 1994), but the method has limited use as the accuracy proved to be rather poor (0.2-0.3 gon for applications in air).. 2.

(17) 1 INTRODUCTION. 5HVHDUFK2EMHFWLYHV The main objective of this research is to develop methods of processing GPS/INS positions and attitudes together either with image measurements or laser scanner data in order to attain precise orientation. This includes simultaneous adjustment of GPS and INS data, simultaneous adjustment of GPS/INS positions and attitudes with image or laser scanner data, calibration of systems with emphasis on the alignment between INS and the sensor, and an analysis of the accuracy of the results. No attempt will be made to present a fully developed system for GPS and INS integration, nor will the major tool for such an integration, Kalman filtering, be described in any detail. This research emphasises instead the next step, the integration of GPS/INS positions and attitudes with image or laser scanner data.. 2XWOLQHRIWKH7KHVLV The first part includes a general discussion of georeferencing of airborne sensors and provides an overview of GPS and INS and their performance. The second part is a study of INS and GPS data, which will show how simultaneous adjustment of the two data sets can improve final results. In the study, the attitude is reinitialised in the air by comparing GPS and INS velocities. In chapter four, GPS and INS data are used for image orientation and the accuracy of ground points is evaluated both in theoretical and practical tests. Different block configurations, drift parameters and ground control configurations will be tested and evaluated. Chapter five deals with the adjustment of laser scanner data so that the sensor’s orientation is measured using GPS and INS. We will show that he orientation parameters are improved through an adjustment process based on discrepancies in overlapping strips. Both laser elevations and the intensity of reflectance data are used in this adjustment. Finally, chapter six comprises a summary together with conclusions drawn from the results presented in the former chapters.. 3.

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(19) 2 SENSOR ORIENTATION. 6(162525,(17$7,21 *HRUHIHUHQFLQJRI$LUERUQH,PDJLQJ6HQVRUV Rapid development in computer performance has led to an increase in digital processing. Even though the most common type of airborne imaging sensor is the film camera, photographs are often digitised and processed in digital photogrammetric workstations. There is also an increasing use of digital sensors, like frame-grabbers, line scanners, pushbroom scanners and swath scanners. They can not compete with the high geometric resolution or coverage of photography but they are useful in other respects, thanks to their faster processing and multispectral resolution. Methods of georeferencing have changed to reflect this development in imaging sensors. The block triangulation method was developed early on to densify the net of ground control points when taking blocks of images. It started as a mechanical adjustment, but developed into a numerical procedure, which is well suited to the digital environment. This method is still the most commonly used together with ground control points for georeferencing of aerial imagery. In the 1980’s, GPS-supported block triangulation became operational. Systematic errors in GPS-positions are modelled by a set of shift and drift parameters for each strip. By using crossing strips at the ends of the block, the number of control points was reduced to three in each corner of the block. Identification and measurement of the connection points in the triangulation procedure is time-consuming and faster methods would be desirable. Digital photogrammetric workstations make more efficient and partly automated triangulation procedure possible. A recent OEEPE/ISPRS test (Heipke, 1999) investigated the performance of automatic aerial triangulation. It showed that a large number of connection points are necessary to achieve reliability, which is hard to do in forested or mountainous terrain. Problems with single stereo models can be corrected for using a strong connection the surrounding images, but larger areas create problems that require manual interaction. The optimal solution would be to have a system that measures both the position and attitude of the imaging sensor directly. This is done using GPS together with an inertial system. The accuracy is not yet as high as in block triangulation using control points, but sufficient for applications where the accuracy demand can be met by the GPS/INS/sensor system. One important aspect of using GPS/INS is that no ground control is necessary for orienting single stereo models or single strips. For line-scanners or swath-scanners, GPS/INS is the only way to create operational systems, since each line or each pixel has its own set of orientation parameters. The inertial system also captures velocities with a high degree of accuracy (Cannon, 1994), which is necessary when processing Interferometric SAR. Block triangulation is a well-developed method for georeferencing aerial photography. It has the strength of correcting for many systematic image errors through the use of additional parameters (self-calibration) and reliability is improved by its use of strong geometry from the connection point measurements. Errors in the camera constant and the principal point are partly corrected for by allowing the projection centres to move. The datum problem is solved with ground control points. In GPS-supported triangulation, shift- and drift-parameters eliminate some systematic errors in the GPS5.

(20) 2 SENSOR ORIENTATION measurements and in the transformation of GPS coordinates to the local coordinate system. Kruck HWDO (1996) presented a method combining blockadjustment with GPS data, where there is no need for shift and drift parameters. When using directly referenced images, systematic errors in the image or in the camera are extrapolated to ground coordinates and there is no way to correct for systematic errors in either GPS/INS measurements or datum transformation. Hence, a reliable use of directly referenced images requires a high level of internal calibration of each sensor, as well as positional and temporal calibrations. The reliability of direct georeferencing depends to a great extent on the GPS and INS measurements. It would be desirable to get continuous accuracy measurements of GPS/INS positions and attitudes. These measurements should include both precision and reliability, in order to be able to estimate the final accuracy in ground coordinates. Time synchronisation error of camera exposure and GPS/INS is often constant and can be calibrated for, HJ by comparing triangulated and GPS/INS measured positions and attitude. The translation offset between the imaging sensor and GPS-antenna and between the sensor and IMU (Inertial Measuring Unit) can be measured by terrestrial methods or estimated by taking the difference between the triangulated and GPS/INS measured position. Misalignment between the IMU and the imaging sensor can be calibrated for by comparing triangulated and GPS/INS measured attitudes. In laser scanning, the misalignment can be calibrated for by comparing ground truth with laser data or by comparing different laser strips (Fritsch & Kilian, 1994; Kilian HWDO 1996; Schiele, 1999). Another operational aspect is to design the sensor system so as to minimise the effect of errors in the GPS antenna vector and differential movements between sensors. As georeferencing is more sensitive to attitude errors, the optimal placement of the IMU is close to or on the imaging sensor. The GPS antenna should be placed as close to the other sensors as possible to minimise the effect of offset error. It has been shown (Mostafa HWDO., 1998) that mounting the IMU and sensor on a vibration damper can reduce velocity noise by about 50%.. *36 To get the submeter precision necessary for most georeferencing applications, dual frequency measurements and differential positioning to correct for ionospheric and tropospheric disturbance are necessary. When dealing with operational aspects, the preferred procedure is to use permanent reference receivers, which are available through established national networks such as SWEPOS (in Sweden), AGNES (in Austria) or CATNET (in Catalonia). Multiple reference receivers can be used for improving the accuracy of GPS positioning (Talaya, 1999). There are various indications of the importance of distance to the reference receivers. Some results show that distances up to 300 kilometres can be used with precision maintained (Ackermann, 1996; Cramer, 1999). This result can only be obtained using precise post-mission satellite orbits and correct modelling of atmospheric delay. Other error sources are cycle slips, multi-path and loss-of-lock on the satellite signal. The chance of discovering and correcting for such errors increases by integrating inertial data with GPS observables. To get absolute coordinates with high precision, the correct ambiguity resolution must be determined. This can be done while standing still on the ground before take-off and then maintain 6.

(21) 2 SENSOR ORIENTATION contact with the satellites during the rest of the flight. This has been difficult to achieve as it becomes critical to keep the airplane as horizontal as possible throughout the entire mission, in order to keep from disturbing the satellite signal. Instead, on-the-fly ambiguity resolutions have been developed and small errors in ambiguity have been compensated for by shift and drift parameters. This method is impossible to implement if no control points exist. Including inertial data increases the chance of maintaining the correct ambiguity resolution throughout the flight, which produces a high degree of accuracy in absolute position.. ,16 An IMU (Inertial Measuring Unit) consists of three accelerometers and three gyroscopes. The accelerometers measure acceleration on three orthogonal axes and the gyroscopes measures angular rates around these axes. The IMU is often embedded in an INS (Inertial Navigation System), which processes raw IMU data to provide navigational information. There are various types of INS. Some of them keep their axes oriented in a global reference frame; these are called gimballed systems. Other systems, more commonly used for georeferencing of airborne sensors, have their accelerometers and gyroscopes fixed to the platform and are called strapdown systems. They measure acceleration and angular rates in the body frame. From these observables, the differential equations describing the trajectory model are formulated.   [& H   Y H      Y& H  =  5HE I E − 2Ω LHH Y H + J H   &   HE  5HE   5HE Ω E . [H YH 5HE IE ΩHLH JH ΩEHE. SRVLWLRQUHODWLYHWRWKHHDUWKIUDPH YHORFLW\UHODWLYHWRWKHHDUWKIUDPH ERG\WRHDUWKURWDWLRQPDWUL[ ,08PHDVXUHGVSHFLILFIRUFH HDUWKURWDWLRQUDWH JUDYLW\YHFWRU ,08PHDVXUHGURWDWLRQUDWHFRUUHFWHGIRUHDUWKURWDWLRQUDWH. To solve for the unknowns: position, velocity and attitude, the gravity vector, JH, and the earth rotation, ωHLH, must be used together with initial position, velocity and attitude. These equations should give all the necessary information for rigid body motion in three-dimensional space, but the IMUs are afflicted with unmodelled errors which cause severe time dependent drifts (see Figure 2-1 for a typical example). These errors include non-orthogonality between body axes, scale factor errors in the gyros or accelerometers, constant gyro drift and other gyro drifts like random walk or white noise (Skaloud & Schwarz, 1998). Some errors can be modelled and solved if reference data, e.g. GPS data, is available. This is most commonly done through Kalman filtering, typically using a minimum of 15 state variables modelling three position errors, three velocity errors, three attitude errors, three accelerometer biases and three gyro drifts.. 7.

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(24) )LJXUH $Q H[DPSOH RI WKH GLIIHUHQFH EHWZHHQ ,16 DQG *36 SRVLWLRQV LQ WKH JOREDOIUDPHXVLQJDVWDQGDORQH,16ZLWKULQJODVHUJ\URV7KHYHUWLFDOSRVLWLRQ LVSUREDEO\DIIOLFWHGZLWKDQHUURQHRXVLQSXWRIJUDYLW\7KHKHOLFRSWHUPDGHWZR WXUQVZKLFKFDXVHGWKHWUHQGFKDQJHLQKRULVRQWDOSRVLWLRQHUURU. The cost of an INS differs widely but is relative to the performance of the system. The difference in price depends for the most part on the type of hardware used and especially the type of gyroscopes. There are mainly three groups of gyroscopes: precise or tactical grade; high precision or navigational grade; and very high precision or strategic grade. Two types of gyros often used for airborne applications are the DTG (Dry or Dynamically Tuned Gyro), and the FOG (Fibre Optic Gyro) which are usually regarded as tactical grade gyros. Another gyro often used is the RLG (Ring Laser Gyro) which like the FOG is an optical gyro. Its performance is navigational grade. More information on gyroscopes can be found in Smith and Weyrauch (1990).. *36DQG,16,QWHJUDWLRQ There are many ways to treat GPS and INS data. The simplest way is to use GPS observations to derive the sensor position and INS attitude observations to derive the tilt of the sensor, without any other integration than having the same time reference. The high data rate and short-time accuracy of the INS position measurements can however be used if the INS-drift is checked against the long-time accuracy of the GPS. A simple way to do this is by polynomial fitting of INS to GPS positions (for an example see Figures 2-2 and 2-3).. 8.

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(26). 2 SENSOR ORIENTATION. 680 660 640 620 600 580 560 540 295075. INS 50 Hz GPS 2 Hz. 295077. 295079. 295081. 295083. 295085. 7LPH V

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(28). )LJXUH*36DQG,16SRVLWLRQVEHIRUHDGMXVWPHQW. 555 553 551 549 547 545 295075 295077 295079 295081 295083 295085. INS 50 Hz GPS 2 Hz. 7LPH V

(29) )LJXUH *36 DQG ,16 SRVLWLRQV DIWHU KDYLQJ DSSOLHG D UG GHJUHH SRO\QRPLDO DGMXVWPHQWWRWZRVHFRQGVRI,16SRVLWLRQDOLQIRUPDWLRQPDWFKLQJWKH*36SRVLWLRQV. The INS can be used for cycle slip detection (if the GPS observable are carrier phase measurements) and multi-path detection. Lost satellite lock can also be compensated for by using INS as a single measuring unit until the GPS has locked back onto track again. This break cannot go on too long, if INS drift is to be kept to a minimum. By integrating GPS and INS, positions, velocities, accelerations and attitudes can be determined to a higher degree of accuracy than if either system were used alone (Napier HW DO 1987; Schwarz HWDO 1993). The common method of integrating GPS and INS observations is via Kalman filtering. Kalman filtering is a real-time optimal estimation method. It provides the optimal estimate of the system based on all past and present information. Block diagrams of typical integration methods are shown in Figures 2-4 - 2-6. Figure 2-4 shows GPS aided 9.

(30) 2 SENSOR ORIENTATION by INS, which is the simplest type of integration. If separate filters (decentralised Kalman filtering) are used for GPS and INS, results from the GPS filter can be used for updating INS, so-called loosely coupled system (Figure 2-5). In a fully integrated (tightly coupled) system, both GPS and INS data are fed to a common filter, so-called centralised Kalman filtering (Figure 2-6), (Brown HW DO 1992; Schwarz, 1990). A closed loop system feeds back sensor error estimates to correct the measurement while a loose loop system does not. The closed loop system is preferable due to better performance. Loosely coupled systems have been prevalent, but the rapid increase in computational power is facilitating a move towards tightly coupled systems.. INS. INS NAV. dv,df. INS r,v,w. GPS NAV. GPS receiver. GPS Kalman. )LJXUH *36 DLGHG E\ ,16 GY DFFHOHUDWLRQ GI DQJXODU YHORFLW\ U SRVLWLRQY YHORFLW\Z DWWLWXGH. INS. dv,df. INS NAV INS Kalman GPS NAV. GPS receiver. GPS Kalman. )LJXUH/RRVHO\FRXSOHGV\VWHPGHFHQWUDOLVHG.DOPDQILOWHULQJ. 10.

(31) 2 SENSOR ORIENTATION. INS. dv,df. INS NAV INS Kalman. GPS receiver. )LJXUH7LJKWO\FRXSOHGV\VWHPFHQWUDOLVHG.DOPDQILOWHULQJ. 7KH7RSH\H/DVHU6FDQQLQJ6\VWHP Much of the data used in this research was captured with the Topeye system. This system is equipped with a Laser Range Finder, a Trimble dual frequency receiver, a Honeywell H-764 INS and an optional digital frame camera. The scanner has one scanning mirror controls the side swath and one pitch mirror that adjusts the inclination angle of the laser beam relative to the ground in order to compensate for tipping of the helicopter. Specifications for the Topeye system are listed in Table 2-1.. 11.

(32) 2 SENSOR ORIENTATION 7DEOHSpecifications for the Topeye laser scanning system 6ZDWKDQJOH. 20 degrees stabilised / 40 degrees fixed wing. $OWLWXGH. 60 - 960 m. /DVHU5DQJH)LQGHU. . PRF : 7000 Hz Number of echoes: 4 with minimum 2 m object separation in slope distance Strength : 128 levels (nIR) Beam divergence : 1, 2 or 4 mrad. $EVROXWH DFFXUDF\ GHSHQGHQW RQ 10-30 cm in Z DOWLWXGH

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(34). . dual frequency (L1/L2). 2SWLRQDO'LJLWDOFDPHUD. . 2x3 K, 24x36 mm chip 48 bit RGB or 64 bit CMYK 1 image / 1.5 s Camera house: Hasselblad 555 ELD, 50 mm FLE lens. 12.

(35) 3 IN-AIR ATTITUDE INITIALISATION. ,1$,5$77,78'(,1,7,$/,6$7,21 The strapdown INS can be used for determining attitude and the main sensor for this is the gyro that measures angular rates, i.e. changes in attitude over time. For this, the initial attitude has to be known. This is done on the ground before the flight while the platform is standing still. In this procedure, the gyros and the accelerometers are calibrated for their biases and drifts. During the subsequent flight mission, approximate position of the INS must be determined, since attitude is related to the earth’s surface. If no auxiliary information is used, position is calculated from the raw INS measurements. After flying awhile, the accuracy in attitudes will decrease due to drift in gyros and accelerometers. The measured accelerations include not only platform motion but also gravitational force and forces created by the earth’s rotation. These latter forces have to be factored out to determine platform motion correctly. This means that gravitational anomalies can constitute a source of errors. Gravity can also be used for alignment, as it is much larger than forces caused by the platform motion. An error in the direction of the plumb line will cause acceleration errors in all three axes of the ground coordinate system (Figure 3-1).. North Erroneous east component East. Erroneous down component Actual gravity (Correct down component) Attitude error. Down. )LJXUH$QDWWLWXGHHUURUUHVXOWVLQHUURQHRXV 1('

(36) FRPSRQHQWV. 13.

(37) 3 IN-AIR ATTITUDE INITIALISATION. 7KH0HWKRG The difference between GPS and INS acceleration (∆a) in the navigation frame can be estimated (Equation 3-1). INS accelerations in the inertial frame can be rotated to determine accelerations in the global frame by the using roll, pitch and heading angles (Equation 3-2). The GPS accelerations are treated as true values and by adding the differences, ∆a, to the INS accelerations, corrections to the roll, pitch and heading angles can be calculated (Equation 3-3). ∆D ( = ∆D 1 = ∆D ' =. ∆Y*36 ( − ∆Y ,16 (. ∆W ∆Y*36 1 − ∆Y ,16 1. ∆W ∆Y*36 ' − ∆Y ,16 '. (1'

(38) ∆Y ∆D ∆W. ∆W. (DVW1RUWKDQG'RZQFRPSRQHQWVLQWKHQDYLJDWLRQIUDPH GLIIHUHQFHLQYHORFLW\EHWZHHQ*36DQG,16 GLIIHUHQFHLQDFFHOHUDWLRQEHWZHHQ*36DQG,16 HODSVHGWLPH. D [   I1       I (  = 5 (U , S, K) *  D \  D   I '   ]. D I 5 USK. 14.

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(40) DWWLWXGHUROOSLWFKDQGKHDGLQJDQJOHV. D [  D [   I 1 + ∆D 1        + ∆ = + I D 5 * 5 * D G ( ( \   D \    D  D   I ' + ∆D '   ]  ]. 5 G5.

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(44) 3 IN-AIR ATTITUDE INITIALISATION In order to decrease noise and improve estimates of the first attitude, a 2nd degree curve was adjusted to the 20 first measurements, Figure 3-2.. Delta Roll. Delta Pitch. 0.005. 0.05. 0. 0. Delta Pitch (rad). Delta Roll (rad). -0.005. -0.01. -0.015. -0.05. -0.1. -0.02. -0.15 -0.025. -0.03 4.2252 4.2252 4.2252 4.2252 4.2252 4.2252 4.2252 4.2253 4.2253 4.2253 4 Time (s) x 10. -0.2 4.2252 4.2252 4.2252 4.2252 4.2252 4.2252 4.2252 4.2253 4.2253 4.2253 4 Time (s) x 10. Delta Heading 0.035 0.03. )LJXUH$GMXVWLQJD GHJUHH FXUYHWRWKHILUVWPHDVXUHPHQWV LPSURYHVHVWLPDWLRQRIWKHLQLWLDO DWWLWXGH$WWLWXGHFKDQJHVFRQYHUJH RQ]HUR QG. Delta Heading (rad). 0.025 0.02 0.015 0.01 0.005 0 -0.005 4.2252 4.2252 4.2252 4.2252 4.2252 4.2252 4.2252 4.2253 4.2253 4.2253 4 Time (s) x 10. When new values for the initial attitude have been calculated, the sequential attitudes, accelerations and velocities are calculated through incremental calculations (appendix A). After this, the difference between GPS and INS accelerations are calculated again and the whole procedure is repeated until convergence is achieved, Figure 3-3. It normally takes about three iterations for the adjustment to converge.. 15.

(45) 3 IN-AIR ATTITUDE INITIALISATION. GPS. INS. Φ0 = (r0,p0,h0). (N,E,D)GPS. v = v0 +∫a d = d0 + ∫v Φ = Φ0 + ∫ω. ∆d/∆t. r0+=∆r p0+=∆p h0+=∆h. (vN,vE,vD)GPS. ∆v/∆t. R∗[ax,ay,az]. (aN,aE,aD)GPS. âGPSâINS. (aN,aE,aD)INS. ∆r,∆p,∆h < 10-6. No. Yes. Incremental calculation of attitudes. )LJXUH,QFUHPHQWDOFDOFXODWLRQRIDWWLWXGHV. 3UDFWLFDO7HVWLQ)LQODQG The Saab Topeye system was used on test flights in Finland for the Finnish Road Administration. The quality of the first test flight was greatly reduced by gross errors in attitude angles caused by INS drift. The quality of the gyros in this system is very high with a drift of approximately 0.001 degrees per hour, so the main source of error was the accelerometer drift. According to the original plan, raw gyro measurements (angular velocity) and GPS measurements of velocity and position were to be used. This proved to be impossible, as there had not been a continuous recording during the entire flight due to limitations in computer storage capacity. There were only recordings of INS data. 16.

(46) 3 IN-AIR ATTITUDE INITIALISATION during active laser scanning. This means that the attitude initialisation had been lost. To be able to recover data, the attitude had to be re-initialised for every continuous laser strip. The method described above was used to make the reintitialisations.. . 5HVXOWV. In order to evaluate accuracy, the laser strips were compared to a photogrammetrically measured DEM. Estimated accuracy of the photogrammetrically measured elevations was 0.20 meter. To be able to compare the two data sets, the non-ground laser points had to be excluded. Terra Modeller software and its built-in ground classification algorithm were used for this (for more information see www.terrasolid.fi), see Figure 3-4.. )LJXUH/DVHUGDWDJURXQGFODVVLILFDWLRQ OLJKWJUH\

(47) 2QO\ODVHUSRLQWVRQWKH JURXQGZHUHFRPSDUHGWRSKRWRJUDPPHWULFUHIHUHQFH'(0 GDUNVTXDUHV

(48) 'DUN JUH\SRLQWVDUHODVHUSRLQWVFODVVHGDVQRQJURXQGLQWKLVFDVHSULPDULO\WUHHV. For all laser points within half a meter horizontal radius from a reference point the elevation difference was calculated. This was done for each laser strip both before and after reinitialisation of the attitude. The result is listed in Table 3-1.. 17.

(49) 3 IN-AIR ATTITUDE INITIALISATION 7DEOHDifferences between uncorrected and corrected laser elevations. Strip. Original orientation # RMS Stdv [m] [m]. Mean [m]. Max [m]. After corrected attitude # RMS Stdv Mean [m] [m] [m]. 1.68. -0.3. -6.12. 2055. 1.46. 1.42. 0.36. 16.91. 11.24 11.25. -3.94. -23.80. 26. 0.53. 0.40. -0.35. -1.31. 1.70. Max [m]. 1f16. 708. 1f18. 8. 2f10a. 599. 5.99. 5.66. 1.96. 16.41. 595. 2.29. 2.15. 0.79. 12.71. 2f10b. 758. 6.05. 5.42. 2.70. 17.13. 503. 1.33. 1.29. 0.33. 7.89. 7f08. 482. 4.36. 4.26. -0.97. 11.87. 262. 1.12. 1.05. 0.39. -5.31. 8f08. 1411. 4.15. 3.90. 1.42. 16.59. 819. 1.92. 1.92. -0.04. 14.94. Σ. 3966. 4.65. 4.51. 1.14. -23.80. 4260. 1.66. 1.62. 0.34. 16.91. )LJXUH)OLJKWOLQH I

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(56) 3 IN-AIR ATTITUDE INITIALISATION. %HIRUHFRUUHFWLRQ. $IWHUFRUUHFWLRQ. Strip 1f16. Strip 1f16. Strip 1f18. Strip 1f18. Strip 2f10. Strip 2f10. Strip 7f08. Strip 7f08. Strip 8f08 Strip 8f08 )LJXUHCross sections of laser strip before and after correction of attitudes.. 19.

(57) 3 IN-AIR ATTITUDE INITIALISATION Even if the result has been greatly improved, there are still discrepancies between the laser measurements and the reference DEM (Figures 3-5, 3-6, 3-7 and Table 3-1). This can be explained by persistent errors in INS velocities, which in this case directly effected attitude measurements.. 6XPPDU\DQG&RQFOXVLRQV By adding GPS velocity to INS calculations, attitude can be reinitialised while in the air. Horizontal accelerations are needed to resolve heading error, as this error in itself does not influence the down component. In this case there were some horizontal accelerations due to helicopter dynamics, even though data was captured only along more or less straight laser strips. Since this method depends on GPS velocity, INS velocity and gravity force, measurement errors in any of them will effect the result. GPS velocities have to be smoothed prior to comparison with INS velocities, which was done in this case. INS velocities are disturbed by accelerometer biases and errors in assumed gravity. These errors have not been modelled in this investigation and negatively effect the result. Cramer HW DO (1999) and Skaloud (1999b) presented the same principle for in-air alignment in an aeroplane. They used turning manoeuvres to provoke horizontal accelerations and their results show considerable improvement of attitude accuracy by implementing in-air attitude initialisation instead of transfer (on-the-ground) attitude initialisation.. 20.

(58) 4 IMAGE ORIENTATION BY GPS AND INS. ,0$*(25,(17$7,21%<*36$1',16 GPS and INS provide all the information, positions and attitudes, necessary for image orientation. Ground control points and triangulation become redundant if we know the internal positions and attitudes for GPS, INS and the camera system. While providing more efficient data processing, this system also has the advantage of requiring a reduced number of ground control points, especially in single stereo models and strips. In traditional photogrammetric triangulation and GPS-supported block triangulation, the projection centres are treated as unknowns. Small errors in the camera constant and in the principal are modelled in this case as a translation of the projection centre. If GPS and INS are used for georeferencing, these errors will be extrapolated to the ground coordinates. In stereo measurements, this results in systematic errors in elevation and plane (Schenk, 1999). In orthophoto production, it leads to horizontal displacement. Errors in interior orientation will directly effect the ground coordinates and camera calibration becomes critical when georeferencing by GPS and INS. To investigate the accuracy of GPS/INS oriented images, theoretical and practical tests have been performed and evaluated. Aspects of calibration methods have also been considered. When dealing with the accuracy of photogrammetric methods, it becomes necessary to refer to the accuracy of either the final ground coordinates or the exterior orientation. Since the accuracy of the final coordinates is of primary interest, this is used most often when presenting the performance of the block triangulation method. The accuracy in ground coordinates after block triangulation and GPS-supported block triangulation is well known from earlier investigations, see for example Stark (1973); Förstner (1985); Friess (1990); Ackermann (1992); Burman (1992); Blankenberg & Övstedahl (1993) and Burman & Torlegård (1994). These different sources agree that the precision of new points is about 1.0(σim ∗ image scale) in plane and 1.5(σim ∗ image scale) in elevation for traditional block triangulation. GPS-supported block triangulation will produce an accuracy of 1.5(σim ∗ image scale) in plane and 2.0(σim ∗ image scale) in elevation (where σim = precision in image coordinates measurements). For greater reliability, measuring pairs of tie points and using groups of control points in multiple image overlap is advisable. The accuracy of GPS/INS orientation is often presented as differences between GPS/INS measurements and triangulated orientation parameters or as differences between calculated and geodetically measured check points, as presented in Cannon & Schwarz (1990), Scherzinger (1997), Toth (1998), Andersen (1999) and Cramer & Haala (1999). Many of these investigations found discrepancies between direct orientation and triangulation with the ground control that could be explained by datum transformation errors or errors in the interior orientation of the camera, which underlines the importance of system calibration. In this chapter, the following methods for image orientation were investigated: • Direct image orientation by GPS/INS • GPS/INS supported strip triangulation • GPS/INS supported block triangulation Direct image orientation by GPS/INS is likely to be used under operational conditions. The same holds true for GPS/INS strip triangulation, since attitude measurements can 21.

(59) 4 IMAGE ORIENTATION BY GPS AND INS replace the need for ground control points along the strip by controlling the error propagation that otherwise occurs. However, GPS/INS supported block triangulation has only limited uses since the attitudes are determined in the triangulation procedure. This method can nevertheless be used to resolve misalignment between the camera and INS, or when attempting to determine the accuracy of the GPS/INS measurements. GPS/INS observations can make triangulation procedures more effective by reducing the requisite number of tie-points and by providing initial values for automatic matching. To treat image, GPS, INS and ground control measurements jointly, a bundle block adjustment program was developed in C++. It resolves shift and drift parameters in both GPS and INS measurements as well as camera calibration parameters. It also provides iterative variance component estimation for the different observation groups. This adjustment program was used both for analysis of real test data and for calculations of simulated blocks.. 0DWKHPDWLFDO0RGHO . *36DQG,166XSSRUWHG%ORFN7ULDQJXODWLRQ. All orientation methods are based on the relation between the image and the ground coordinate system, as established by a three dimensional Helmert transformation.. ;  ;0   [′         <  =  <0  + V ⋅ 5 ⋅  \ ′  =  =  − F    0   >;<=@ >; < = @ V 5 . . . >[¶\¶@ F.

(60). JURXQGFRRUGLQDWHV SURMHFWLRQFHQWUHFRRUGLQDWHV VFDOHIDFWRU URWDWLRQ PDWUL[ EHWZHHQ WKH LPDJH DQG JURXQG FRRUGLQDWH V\VWHP LPDJHFRRUGLQDWHV FDPHUDFRQVWDQW. From this, collinearity equations can be derived. [’= −F. \ ’= −F. U I. LM. [FRUU. 22. I. U11 (; − ; 0 ) + U21 (< − <0 ) + U31 (= − = 0 ) + I [ −FRUU U13 (; − ; 0 ) + U23 (< − <0 ) + U33 (= − = 0 ) U12 (; − ; 0 ) + U22 (< − <0 ) + U32 (= − = 0 ) + I \ −FRUU U13 (; − ; 0 ) + U23 (< − <0 ) + U33 (= − = 0 ). \FRUU. . . FRHIILFLHQW LM

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(63) 4 IMAGE ORIENTATION BY GPS AND INS The correction terms (I I ) are of two kinds. The first kind compensates for remaining errors in radial/tangential distortion, as well as affinity due to film shrinkage (I I ). The second kind (I I ) is for camera calibration, which includes principal point and radial/tangential distortion. In this second case, the camera constant, F, (in Equation 4-2) is also treated as an unknown parameter. [FRUU. [BFRUUB. \BFRUUB. \FRUU. [BFRUUB. \BFRUUB. I [ _ FRUU _ 1 = D UDG [(U 2 − U02 ) + EUDG [ (U 4 − U04 ) + D DII [ ’−EDII \ ’ I \ _ FRUU _ 1 = D UDG \ (U 2 − U02 ) + EUDG \ (U 4 − U04 ) + D DII \ ’+EDII [ ’ I I D E D E [BFRUUB UDG DII. \BFRUUB. UDG. DII.

(64). LPDJHFRRUGLQDWHFRUUHFWLRQWHUPVQR XQNQRZQFRHIILFLHQWVIRUUDGLDOGLVWRUWLRQ XQNQRZQFRHIILFLHQWVIRUDIILQLW\. I [ _ FRUU _ 2 = SS [ + D UDG [(U 2 − U02 ) + EUDG [(U 4 − U04 ) + + D tan ( U 2 + 2 [ 2 ) + Etan (2 [\ ) I \ _ FRUU _ 2 = SS \ + D UDG \ ( U 2 − U02 ) + EUDG \ (U 4 − U04 ) +. .

(65). + D tan ( 2 [\ ) + Etan (U 2 − 2 \ 2 ). I I SS SS D E [BFRUUB [. WDQ. \BFRUUB. \. WDQ. LPDJHFRRUGLQDWHFRUUHFWLRQWHUPVQR SULQFLSDOSRLQWFRRUGLQDWHV XQNQRZQFRHIILFLHQWVIRUWDQJHQWLDOGLVWRUWLRQ. The primary observation equations for traditional bundle adjustments are the collinearity equation and the observation equation for ground control points: ; = ;J < = <J.

(66). = = =J. >;<=@ >; < = @ J. J. J. XQNQRZQJURXQGSRLQWFRRUGLQDWHV JLYHQFRQWUROSRLQWFRRUGLQDWHV. In GPS-supported block triangulation, GPS observations of the photo station positions supplement the image coordinate and control point coordinates. GPS-observations are often calibrated by including shift and time dependent drift parameters:. 23.

(67) 4 IMAGE ORIENTATION BY GPS AND INS. ; *36 L = ; 0 L + VKLIW ; 6 + W L ⋅ GULIW ; 6 <*36 L = <0 L + VKLIW<6 + W L ⋅ GULIW<6.

(68). = *36 L = = 0 L + VKLIW = 6 + W L ⋅ GULIW = 6 >; < VKLIW GULIW *36. *36. =. @. *36. *36REVHUYDWLRQ³L³RIWKHSKRWRVWDWLRQ XQNQRZQVKLIWSDUDPHWHULQ;<DQG=IRUVWULS³V´ XQNQRZQWLPHGHSHQGHQWGULIWSDUDPHWHULQ;<DQG=IRU VWULS³V´ WLPHWDJRIREVHUYDWLRQ³L´. L. ;<=V ;<=V. W. L. The shift and drift parameters are optional, so any of the following options may be chosen: (a) Both shift and drift parameters (b) Only shift parameters (c) Neither shift nor drift parameters In GPS and INS supported block triangulation, both GPS observations of photo station positions and INS observations of the photo station attitudes are included in the bundle adjustment. INS observations are formulated in the same way as GPS observations, i.e. as direct observations of the attitude with optional shift and time dependent drift parameters.. ω. ,16 L. φ. ,16 L. κ. ,16 L. = ω + VKLIWω 6 + W ⋅ GULIWω 6 L. L. = φ + VKLIWφ6 + W ⋅ GULIWφ6 L. L.

(69). = κ + VKLIWκ 6 + W ⋅ GULIWκ 6 L. L. The shift parameters are especially useful for system calibration, when determining misalignment between the INS and camera coordinate systems.. . 'LUHFW,PDJH2ULHQWDWLRQE\*36DQG,16. The measured positions and attitudes can be used for direct image orientation. If images are used for stereo measurements, the coordinates in object space can be calculated using the collinearity equation, which defines the direct relationship between the object point, image measurements and image orientations (Torlegård, 1999).. ; = ; 01 +. 24. [1 ]1. [2 ( = 02 − = 01 ) ]2 [1 [ 2 − ]1 ] 2. ; 02 − ; 01 −.

(70).

(71) 4 IMAGE ORIENTATION BY GPS AND INS [   ; 02 − ; 01 − 2 ( = 02 − = 01 )   ]2  < + \1   01 ]1  [1 [ 2 −   ]1 ] 2 1  <=   [ 2 ; 02 − ; 01 − 1 ( = 02 − = 01 )   ]1  + < + \2  02   [1 [ 2 ]2 −   ]1 ] 2  . [1 [2 = 01 − = ]1 ] 2 02 [1 [2 − ]1 ]2.

(72). ; 02 − ; 01 + = =. ;<= ; < = [ \ ] L. L. L. L. L. L.

(73). JURXQGSRLQWFRRUGLQDWHV SURMHFWLRQFHQWUHIRULPDJHL PRGHOFRRUGLQDWHVIRULPDJHL. where.  1  [1      \1  =  Gκ 1     − Gφ1  ]1 . − Gκ 1 1 Gω1. Gφ1   [ ’− [ ’0    − Gω1   \ ’− \ ’0    1   − F1 .  1  [2      \ 2  =  Gκ 2     − Gφ2  ]2 . − Gκ 2 1 Gω 2. Gφ2   ["− [" 0    − Gω 2   \"− \" 0    1   − F2 . [ \. [. \. [ \. [. \. F . . L. . .

(74). LPDJHFRRUGLQDWHVLPDJH LPDJHFRRUGLQDWHVLPDJH SULQFLSOHSRLQWLPDJH SULQFLSOHSRLQWLPDJH FDPHUDFRQVWDQWIRULPDJHL. if ω ≈ 0 , ϕ ≈ 0 and κ ≈ 0 .. Differentiation with respect to the exterior orientation elements yields:. 25.

(75) 4 IMAGE ORIENTATION BY GPS AND INS. ; ;  G; = 1 − G; 01 + G; 02 + % %  ; ( ; − %) (G= 02 − G= 01 ) + + %+ +. ;<  ;  1 −  Gω 1 − +  %  ; 2  ; ;  − + 1 + 2 1 − Gφ1 − < 1 − Gκ 1 − % %   +  −. G< =.

(76). ;<  ;  1 −  Gω 2 − +  % ;< ;+  ( ; − %) 2  1 + Gφ 2 − Gκ 2 − 2 % %  + . G<01 + G<02 < + (G; 02 − G; 01 ) + % 2 %  < ; −  2 +  (G= 01 − G= 02 ) + %+ + <2  %  +  −  ; −  Gω 1 + 2   2 +%  ; <2  < +2 + ;2 ;  Gκ 1 + +  − Gφ1 +  + + % %  2 2 + <2  %  +  +  ; −  Gω 2 − 2   2 +%  + 2 + ( ; − %) 2 ; − %   Gφ 2 + + % 2    ; −% <2  Gκ 2 +  − %   2. < − +. 26.

(77).

(78) 4 IMAGE ORIENTATION BY GPS AND INS G= =. + + G; 01 − G; 02 + % % ; ; −% + G= 01 − G; 02 + % % ;< +< +2 + ;2 + Gω 1 − Gφ1 − Gκ 1 − % % % ( ; − % )< − Gω 2 + % +< + 2 + ( ; − %) 2 + Gφ 2 + Gκ 2 % %. + %.

(79). IOLJKWDOWLWXGH SKRWRJUDPPHWULFEDVH GLVWDQFHEHWZHHQSURMHFWLRQFHQWUHV

(80). These equations show the model deformation caused by errors in exterior orientation. A shorthand form of this is:. ε; = I H ε< = I H ε = = I H ;. ε. 2U HO. <. 2U HO. =. 2U HO. RU ε = I H. 2U HO.

(81). HUURULQJURXQGFRRUGLQDWHV. ;<=. where I is a 3*12 matrix with coefficients and H is a column vector with the ”true” errors for the 12 exterior orientation elements. With Q points this becomes: =. ).

(82). 2U .HO .. QQ The error of each orientation element unknown. So the above formulae can only suggest the type of error or deformation that will be introduced in the stereo model. Variances of functions of model coordinates can be estimated, keeping in mind the need to include covariances, LH a strict application of the general law of error propagation. &RY ;<=

(83) = ) &RY. 2U HO. ). 7. Reasonable estimates of the values for variance-covariance matrix (&RY are taken from empirical investigations (chapter 4.4.5)..

(84) 2UHO. ) elements. If the image is used for RUWKRSKRWR production, the relation between ground and image coordinates is established by the collinearity equation. Image orientation (X0, Y0, Z0, ω,. 27.

(85) 4 IMAGE ORIENTATION BY GPS AND INS φ, κ) is derived from GPS and INS measurements and elevation is derived from a DEM. Errors in the orthophoto are caused by errors in exterior orientation and the DEM: [ ’ = I [ ’ H 2U .HO .+ + \ ’ = I \ ’ H 2U .HO .+ +. RU = I LP.FRRUG . H 2U .HO .+ +. .

(86). is a 2*7 matrix with coefficients and H is a column vector containing the whereI ”true” errors of 6 exterior orientation elements plus the error in DEM elevation. Variances of functions of image coordinates are based on the general law of error propagation. LPFRRUG. &RY [’, \ ’

(87) = )LP.FRRUG . &RY 2U .HO .+ + ) .

(88). 7. LP . FRRUG .. In case the covariances are known they can be included in the error propagation. In the case studied here, the covariances are unknown and no covariances have been included in the orientation elements or between the DEM and the orientation elements. To calculate the variance in image coordinates in the absence of covariance, we apply the following formula: 2. 2. 2.  ∂[’   ∂[’  ∂[’  σ =   σ;2 0 +  σ<20 +   σ=20 +  ∂;0   ∂<0   ∂=0  2 [’. 2. 2. 2. 2. 2. 2. 2. 2.  ∂[’   ∂[’  ∂[’   ∂[’ +  σω20 +  σφ20 +   σκ20 +   σ+2  ∂+   ∂ω0   ∂φ0   ∂κ0  2.

(89)  ∂\’  σ\2’ =   σ;2  ∂;0 . 0.  ∂\’   ∂\’ +   σ<20 +   σ=20 +  ∂=0   ∂<0 . 2.  ∂\’   ∂\’  ∂\’   ∂[’ +  σω20 +  σφ20 +   σκ20 +   σ+2  ∂+   ∂ω0   ∂φ0   ∂κ0 . . 2. $FFXUDF\0HDVXUHV. The SUHFLVLRQ of the estimated unknown is derived from the adjustment by extracting its corresponding element in the covariance matrix: σ = Σ = σ0 ⋅ 4 L. σ. L. 28. LL. [[LL. VWDQGDUGGHYLDWLRQRIYDULDEOHQXPEHUL.

(90).

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