1. P.1 JAMES S. Bethel Wonjo Jung Geomatics Engineering School of Civil Engineering Purdue University APR-30-2008 Sensor Modeling and Triangulation for an Airborne Three Line Scanner

2. P.2 Outline 1.Introduction 2.Dataset –Camera Design –Flight and observations (3-OC Atlanta, GA) 3.Sensor Model 4.Trajectory Model 5.Pseudo Observation Equations 6.Data Ajustment 7.Implementation 8.Results 9.Conclusions 10.Future plans

3. P.3 1. Introduction MAIN OBJECTIVE Developing an algorithm to recover orientation parameters for an airborne three line scanner

4. P.4 1. Introduction - Types of three line scanners Lens Linear arrays on the same focal plane Three separate cameras

5. P.5 1. Introduction Instantaneous gimbal rotation center flight trajectory While ADS40, TLS and JAS placed CCD arrays on the focal plane in a single optical system, 3-DAS-1 and 3-OC use three optical systems, rigidly fixed to each other. For this reason, we need to develop a photogrammetirc model for three different cameras moving together along a single flight trajectory

6. P.6 1. Introduction Parameters to be estimated –Exterior orientation parameters 6 parameters per an image line –Additional external parameters Translation vector between a gimbal center to perspective centers Rotation angles between gimbal axis and sensor coordinate systems –Interior orientation parameters Focal lengths Principal points Radial distortions

7. P.7 1. Introduction There have been two kinds of approaches. –Reducing number of unknown parameters Piece-wise polynomials –Providing fictitious observations in addition to the real observations Stochastic models

8. P.8 1. Introduction Reducing number of unknown parameters –Piecewise polynomials given estimated 1000×6=6000 3×6=18

9. P.9 1. Introduction Providing fictitious observations in addition to the real observations –1 st -Order Gauss-Markov Model given estimated observations

10. P.10 1. Introduction Self-calibration –Partial camera calibration information is provided. focal length, aperture ratio, shift of the distortion center, radial distortion –Coordinates of projection center of the camera relative to the gimbal center is not measured. Just design values are provided. –Need to refine some of the parameters

11. P.11 2. DATASET Camera Design (3-OC)

12. P.12 2. DATASET Strip IDHeadingAltitude 2E 5,500ft 3W 4E 5W 6S 8N 9S 10N 11S 10,500ft 12N 13S 14N 15E 16W 17E 18W : 20 GCPs : 8Check points

13. P.13 3. Sensor Model Collinearity Equation – a line scanner Ground scan line Perspective Center flight direction Sensor Coordinate System (SCS) row column SCS

14. P.14 3. Sensor Model Collinearity Equation - oblique camera Ground scan line perspective Center flight direction

15. P.15 3. Sensor Model Collinearity in a three line scanner flight direction gimbal center plumb line F N B three angles should be considered

16. P.16 4. Trajectory Model 1 st order Gauss-Markov trajectory model –Probability density function f(x(t)) at a certain time is dependent only upon previous point –Probability density function is assumed to be Gaussian –Autocorrelation function becomes

17. P.17 4. Trajectory Model 1 st order Gauss-Markov trajectory model Parameters are highly correlated! autocorrelation function

18. P.18 5. Pseudo Observation equations t autocorrelation function One-sided equation Symmetric pseudo observation equation

19. P.19 6. Data Adjustment the Unified Least Squares Adjustment

20. P.20 7. Implementation To reduce the number of parameters, only the parameters of lines containing image observations are implemented. For the memory management, IMSL Ver. 6.0 library is used. IMSL contains a sparse matrix solver. riptide.ecn.purdue.edu –Red Hat Enterprise Linux 4 operating systems –16 multi core processors –64GB of system memory

21. P.21 8. Results Processing time : 49 seconds (16 core x86_64 Linux with 64GB ram) Number of iteration : 7 Converged at 0.58 pixels RMSE : 1.08 pixels for 8 check points

22. P.22 8. Results Interior Orientation parameters are self- calibrated

23. P.23 9. Conclusions We could successfully recover the orientation parameters using stochastic trajectory model Interior orientation parameters of three cameras can be refined through the self calibration process

24. P.24 9. Future Plans Analysis on the model properties Adding pass points Automated passpoints generation