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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 817–826

Cramér–Rao analysis of orientation estimation: influence of target model uncertainties

David R. Gerwe, Jennifer L. Hill, and Paul S. Idell  »View Author Affiliations

JOSA A, Vol. 20, Issue 5, pp. 817-826 (2003)

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We explore the use of Cramér–Rao bound calculations for predicting fundamental limits on the accuracy with which target characteristics can be determined by using imaging sensors. In particular, estimation of satellite orientation from high-resolution sensors is examined. The analysis role that such bounds provide for sensor/experiment design, operation, and upgrade is discussed. Emphasis is placed on the importance of including all relevant target/sensor uncertainties in the analysis. Computer simulations are performed that illustrate that uncertainties in target features (e.g., shape, reflectance, and relative orientation) have a significant impact on the bounds and provide considerable insight as to how details of the three-dimensional target structure may influence the estimation process. The simulations also address the impact that a priori information has on the bounds.

© 2003 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(100.3190) Image processing : Inverse problems
(100.5010) Image processing : Pattern recognition
(110.3000) Imaging systems : Image quality assessment

David R. Gerwe, Jennifer L. Hill, and Paul S. Idell, "Cramér–Rao analysis of orientation estimation: influence of target model uncertainties," J. Opt. Soc. Am. A 20, 817-826 (2003)

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  1. D. R. Gerwe, D. J. Lee, and J. D. Barchers, “Supersampling multiframe blind deconvolution resolution enhancement of adaptive optics compensated imagery of low earth orbit satellites,” Opt. Eng. 41, 2238–2251 (2002).
  2. J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE 3170, 2–15 (1997).
  3. T. Schulz, J. Miller, and B. Stribling, “Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope,” Opt. Express 1, 355–362 (1997).
  4. J. B. West and D. Utley, “Radiance map improvement in AEOS LWIR Images,” in Prceedings of the 2001 AMOS Technical Conference, P. Kervin, L. Bragg, and S. Ryan, eds. (Maui Economic Development Board, Kihei, Maui, HI, 2001), pp. 542–550.
  5. X. Du, S. Ahalt, and B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
  6. J. Zhao, S. Ahalt, and C. B. Stribling, “3-D orientation vector estimation from satellite imagery,” in Signal Processing, Sensor Fusion, and Target Recognition V, I. Kadar and V. Libby, eds., Proc. SPIE 2755, 472–483 (1996).
  7. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  8. D. R. Gerwe, P. S. Idell, and J. Vaughn, “Cramer–Rao bound analysis of target characterization accuracy limits for imaging,” in Dual Use Technologies for Space Surveillance and Assessment II, P. Idell, ed., Proc. SPIE 4490, 245–255 (2001).
  9. U. Grenander, M. I. Miller, and A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
  10. M. I. Miller, U. Grenander, J. A. O’Sullivan, and D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
  11. A. D. Lanterman, M. I. Miller, and D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
  12. J. Kostakis, M. Cooper, T. J. Green, Jr., M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, and D. L. Snyder, “Multispectral sensor fusion for ground-based target orientation estimation: FLIR, LADAR, HRR,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE 3718, 14–24 (1999).
  13. U. Grenander, A. Srivastava, and M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
  14. M. L. Cooper and M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000).
  15. H. Hendriks, “A Cramér–Rao type lower bound for estimators with values in a manifold,” J. Multivar. Anal. 38, 245–261 (1991).
  16. D. L. Snyder, A. M. Hammoud, and R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
  17. D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, and R. L. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272–283 (1995).
  18. R. E. Blahut, Principles and Practice of Information Theory (Addison-Wesley, Reading, Mass., 1987).
  19. A. Hero and J. A. Fessler, “A recursive algorithm for computing Cramer–Rao-type bounds on estimator covariance,” IEEE Trans. Inf. Theory 40, 1205–1210 (1994).
  20. Note that although newer versions of the rendering code support computation of the fractional unobscured area of each facet by comparing the mutual overlap of all facets, the version used for this paper effectively rounded this fraction to 0 or 1. Also, in the version of the code used for this paper, only Lambertian BRDFs were supported.
  21. D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, and B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini and R. K. Tyson, eds., Proc. SPIE 3353, 160–170 (1998).

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