Abstract

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

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  1. D. R. Gerwe, D. J. Lee, 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).
    [CrossRef]
  2. J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
    [CrossRef]
  3. T. Schulz, J. Miller, B. Stribling, “Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope,” Opt. Express 1, 355–362 (1997).
    [CrossRef] [PubMed]
  4. J. B. West, D. Utley, “Radiance map improvement in AEOS LWIR Images,” in Prceedings of the 2001 AMOS Technical Conference, P. Kervin, L. Bragg, S. Ryan, eds. (Maui Economic Development Board, Kihei, Maui, HI, 2001), pp. 542–550.
  5. X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
    [CrossRef]
  6. J. Zhao, S. Ahalt, C. B. Stribling, “3-D orientation vector estimation from satellite imagery,” in Signal Processing, Sensor Fusion, and Target Recognition V, I. Kadar, V. Libby, eds., Proc. SPIE2755, 472–483 (1996).
    [CrossRef]
  7. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  8. D. R. Gerwe, P. S. Idell, 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. SPIE4490, 245–255 (2001).
    [CrossRef]
  9. U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
    [CrossRef]
  10. M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
    [CrossRef] [PubMed]
  11. A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
    [CrossRef]
  12. J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
    [CrossRef]
  13. U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
    [CrossRef]
  14. M. L. Cooper, M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000).
    [CrossRef]
  15. H. Hendriks, “A Cramér–Rao type lower bound for estimators with values in a manifold,” J. Multivar. Anal. 38, 245–261 (1991).
    [CrossRef]
  16. D. L. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
    [CrossRef] [PubMed]
  17. D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, R. L. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272–283 (1995).
    [CrossRef]
  18. R. E. Blahut, Principles and Practice of Information Theory (Addison-Wesley, Reading, Mass., 1987).
  19. A. Hero, J. A. Fessler, “A recursive algorithm for computing Cramer–Rao-type bounds on estimator covariance,” IEEE Trans. Inf. Theory 40, 1205–1210 (1994).
    [CrossRef]
  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, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
    [CrossRef]

2002 (1)

D. R. Gerwe, D. J. Lee, 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).
[CrossRef]

2000 (2)

U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
[CrossRef]

M. L. Cooper, M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000).
[CrossRef]

1998 (2)

X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
[CrossRef]

U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
[CrossRef]

1997 (3)

M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
[CrossRef] [PubMed]

A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
[CrossRef]

T. Schulz, J. Miller, B. Stribling, “Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope,” Opt. Express 1, 355–362 (1997).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

A. Hero, J. A. Fessler, “A recursive algorithm for computing Cramer–Rao-type bounds on estimator covariance,” IEEE Trans. Inf. Theory 40, 1205–1210 (1994).
[CrossRef]

1993 (1)

1991 (1)

H. Hendriks, “A Cramér–Rao type lower bound for estimators with values in a manifold,” J. Multivar. Anal. 38, 245–261 (1991).
[CrossRef]

Ahalt, S.

X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
[CrossRef]

J. Zhao, S. Ahalt, C. B. Stribling, “3-D orientation vector estimation from satellite imagery,” in Signal Processing, Sensor Fusion, and Target Recognition V, I. Kadar, V. Libby, eds., Proc. SPIE2755, 472–483 (1996).
[CrossRef]

Barchers, J. D.

D. R. Gerwe, D. J. Lee, 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).
[CrossRef]

Blahut, R. E.

R. E. Blahut, Principles and Practice of Information Theory (Addison-Wesley, Reading, Mass., 1987).

Cooper, M.

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

Cooper, M. L.

M. L. Cooper, M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000).
[CrossRef]

Du, X.

X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
[CrossRef]

Ellerbroek, B. L.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

Faisal, M.

Fessler, J. A.

A. Hero, J. A. Fessler, “A recursive algorithm for computing Cramer–Rao-type bounds on estimator covariance,” IEEE Trans. Inf. Theory 40, 1205–1210 (1994).
[CrossRef]

Ford, S.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Gerwe, D. R.

D. R. Gerwe, D. J. Lee, 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).
[CrossRef]

D. R. Gerwe, P. S. Idell, 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. SPIE4490, 245–255 (2001).
[CrossRef]

Green, T. J.

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

Grenander, U.

U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
[CrossRef]

U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
[CrossRef]

M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
[CrossRef] [PubMed]

Hammoud, A. M.

Helstrom, C. W.

Hendriks, H.

H. Hendriks, “A Cramér–Rao type lower bound for estimators with values in a manifold,” J. Multivar. Anal. 38, 245–261 (1991).
[CrossRef]

Hero, A.

A. Hero, J. A. Fessler, “A recursive algorithm for computing Cramer–Rao-type bounds on estimator covariance,” IEEE Trans. Inf. Theory 40, 1205–1210 (1994).
[CrossRef]

Hunt, B.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Idell, P. S.

D. R. Gerwe, P. S. Idell, 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. SPIE4490, 245–255 (2001).
[CrossRef]

Johnston, D. C.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Kostakis, J.

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

Lanterman, A. D.

A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
[CrossRef]

D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, R. L. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272–283 (1995).
[CrossRef]

Lee, D. J.

D. R. Gerwe, D. J. Lee, 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).
[CrossRef]

Miller, J.

Miller, M.

M. L. Cooper, M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000).
[CrossRef]

Miller, M. I.

U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
[CrossRef]

U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
[CrossRef]

A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
[CrossRef]

M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
[CrossRef] [PubMed]

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

O’Sullivan, J. A.

M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
[CrossRef] [PubMed]

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

Paxman, R. G.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

Reiley, M. F.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

Roggemann, M.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Schulz, T.

T. Schulz, J. Miller, B. Stribling, “Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope,” Opt. Express 1, 355–362 (1997).
[CrossRef] [PubMed]

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Schulze, K.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Seldin, J.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Seldin, J. H.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

Shapiro, J. H.

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

Sheppard, D.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Snyder, D. L.

A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
[CrossRef]

M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
[CrossRef] [PubMed]

D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, R. L. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272–283 (1995).
[CrossRef]

D. L. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
[CrossRef] [PubMed]

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
[CrossRef]

Srivastava, A.

U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
[CrossRef]

U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
[CrossRef]

Stribling, B.

X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
[CrossRef]

T. Schulz, J. Miller, B. Stribling, “Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope,” Opt. Express 1, 355–362 (1997).
[CrossRef] [PubMed]

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Stribling, B. E.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

Stribling, C. B.

J. Zhao, S. Ahalt, C. B. Stribling, “3-D orientation vector estimation from satellite imagery,” in Signal Processing, Sensor Fusion, and Target Recognition V, I. Kadar, V. Libby, eds., Proc. SPIE2755, 472–483 (1996).
[CrossRef]

Tyler, D.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Utley, D.

J. B. West, D. Utley, “Radiance map improvement in AEOS LWIR Images,” in Prceedings of the 2001 AMOS Technical Conference, P. Kervin, L. Bragg, S. Ryan, eds. (Maui Economic Development Board, Kihei, Maui, HI, 2001), pp. 542–550.

van Kampen, W.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

Vaughn, J.

D. R. Gerwe, P. S. Idell, 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. SPIE4490, 245–255 (2001).
[CrossRef]

Welsh, B.

D. Tyler, S. Ford, B. Hunt, M. Roggemann, T. Schulz, K. Schulze, J. Seldin, D. Sheppard, B. Stribling, W. van Kampen, B. Welsh, “Comparison of image reconstruction techniques using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–170 (1998).
[CrossRef]

West, J. B.

J. B. West, D. Utley, “Radiance map improvement in AEOS LWIR Images,” in Prceedings of the 2001 AMOS Technical Conference, P. Kervin, L. Bragg, S. Ryan, eds. (Maui Economic Development Board, Kihei, Maui, HI, 2001), pp. 542–550.

White, R. L.

Zhao, J.

J. Zhao, S. Ahalt, C. B. Stribling, “3-D orientation vector estimation from satellite imagery,” in Signal Processing, Sensor Fusion, and Target Recognition V, I. Kadar, V. Libby, eds., Proc. SPIE2755, 472–483 (1996).
[CrossRef]

IEEE Trans. Image Process. (1)

M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (3)

U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000).
[CrossRef]

M. L. Cooper, M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000).
[CrossRef]

A. Hero, J. A. Fessler, “A recursive algorithm for computing Cramer–Rao-type bounds on estimator covariance,” IEEE Trans. Inf. Theory 40, 1205–1210 (1994).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups for ATR,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–802 (1998).
[CrossRef]

J. Multivar. Anal. (1)

H. Hendriks, “A Cramér–Rao type lower bound for estimators with values in a manifold,” J. Multivar. Anal. 38, 245–261 (1991).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (3)

D. R. Gerwe, D. J. Lee, 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).
[CrossRef]

A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997).
[CrossRef]

X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998).
[CrossRef]

Opt. Express (1)

Other (9)

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[CrossRef]

J. Kostakis, M. Cooper, T. J. Green, M. I. Miller, J. A. O’Sullivan, J. H. Shapiro, 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. SPIE3718, 14–24 (1999).
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J. B. West, D. Utley, “Radiance map improvement in AEOS LWIR Images,” in Prceedings of the 2001 AMOS Technical Conference, P. Kervin, L. Bragg, S. Ryan, eds. (Maui Economic Development Board, Kihei, Maui, HI, 2001), pp. 542–550.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Image Reconstruction and Restoration II, T. J. Schulg, ed., Proc. SPIE3170, 2–15 (1997).
[CrossRef]

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.

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Figures (7)

Fig. 1
Fig. 1

Noise sources and uncertainties regarding the target/sensor system that are not included in the forward model on which the CRLB calculations are based can cause the resulting bound to be optimistically low.

Fig. 2
Fig. 2

Hypothetical example of how CRLB calculations might compare against performance accuracy of optimal estimators and operational codes.

Fig. 3
Fig. 3

3-D plot of the centers of the facets used to tessellate a target’s exterior. The number of points in the model shown here has been reduced for purpose of illustration.

Fig. 4
Fig. 4

Image at orientation A ( θ R = 0 , θ P = 0 , θ Y = 0 ).

Fig. 5
Fig. 5

Image at orientation B ( θ R = 0 , θ P = 90 , θ Y = 0 ).

Fig. 6
Fig. 6

Image at orientation C ( θ R = 45 , θ P = 45 , θ Y = 0 ).

Fig. 7
Fig. 7

Increase in the calculated CRLB as additional nuisance parameters are included in the analysis (i.e., added to ξ). The parameters associated with particularly large jumps are called out. The satellite orientation is as in Fig. 4.

Tables (5)

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Table 1 Imaging Conditions Used for This Study

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Table 2 Effects of Choice of Uncertainties Included in ξ for the CRLB Calculation at Orientation A

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Table 3 Effects of Choice of Uncertainties Included in ξ for the CRLB Calculations at Orientation B

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Table 4 Effects of Choice of Uncertainties Included in ξ for the CRLB Calculations at Orientation C

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Table 5 Portion of the (Normalized) Fisher Information Matrix That Indicates Why Uncertainties in the Solar Panel Position ( x s ) Strongly Influence Estimation of the Satellite’s Roll Euler Angle θ R Even Though the Correlation between the Influence of These Parameters on the Image Measurement Is Weak

Equations (16)

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[ ξ ^ k - ξ k ] 2 CRLB { ξ k | ξ } [ F D - 1 ( ξ ) ] kk ,
[ F D ( ξ ) ] kl = - 2 ln   p ( d | ξ ) ξ k ξ l =   ln   p ( d | ξ ) ξ k   ln   p ( d | ξ ) ξ l .
( ξ ^ k - ξ k ) 2 [ { F D ( ξ ) + F P ( ξ ) } - 1 ] kk ,
[ F P ( ξ ) ] kl = - 2 ln   p ( ξ ) ξ k ξ l =   ln   p ( ξ ) ξ k   ln   p ( ξ ) ξ l .
p ( ξ ) = [ ( 2 π ) N / 2 | Λ ξ | 1 / 2 ] - 1 exp [ - 1 2 ( ξ - ξ T Λ ξ - 1 ( ξ - ξ ) ] ,
d q ( x ¯ ) = Poisson { g q ( x ¯ ,   ξ ) } + n σ q ( x ¯ , ξ ) .
d q ( x ¯ ) Poisson { g q ( x ¯ ,   ξ ) + σ x ¯ , q 2 } - σ x ¯ , q 2 .
p ( d + σ ¯ 2 | ξ )
q x ¯ F q  
× exp [ - ( g q ( x ¯ | ξ ) + σ ¯ x ¯ , q 2 ) ] [ g q ( x ¯ | ξ ) + σ ¯ x ¯ , q 2 ] d q ( x ¯ ) + σ ¯ x ¯ , q 2 [ d q ( x ¯ ) + σ ¯ x ¯ , q 2 ] ! .
 
[ F D ( ξ ) ] kl q x ¯ F q g q ( x ¯ | ξ ) ξ k g q ( x ¯ | ξ ) ξ l g q ( x ¯ | ξ ) + σ ¯ x ¯ , q 2 .
[ F D ( ξ ) ] kl = q x ¯ F q g q ( x ¯ | ξ ) ξ k g q ( x ¯ | ξ ) ξ l σ ¯ x ¯ , q 2 .
CRLB = 1 ( F data + F a priori ) 1 / 2 ,
CRLB 1 [ max ( F data , F a priori ) ] 1 / 2 .
CRLB 1 ( 2 F data ) 1 / 2 1 ( 2 F a priori ) 1 / 2 .

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