Simultaneous estimation of aerosol cloud concentration and spectral backscatter from multiple-wavelength lidar data

Applied Optics

Volumn 47, Issue 24, 2008, Pages 4309-4320

  Warren, Russell E ^a   Vanderbeek, Richard G ^b   Ben David, Avishai ^b   Ahl, Jeffrey L ^c  

^a EO Stat Inc   (United States)

^b EDGEWOOD CHEMICAL BIOLOGICAL CENTER   (United States)

^c JLA Technology Corp   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSOLS; ATMOSPHERIC AEROSOLS; BACKSCATTERING; CARBON DIOXIDE; ESTIMATION; INFRARED RADIATION; KALMAN FILTERS; MAXIMUM LIKELIHOOD; MAXIMUM LIKELIHOOD ESTIMATION; OPTICAL RADAR;

ATMOSPHERIC BACKSCATTERS; BACKSCATTER COEFFICIENTS; CONCENTRATION DEPENDENCE; MAXIMUM LIKELIHOOD ESTIMATOR; MULTIPLE WAVELENGTHS; SEQUENTIAL ALGORITHM; SIMULTANEOUS ESTIMATION; SPECTRAL DEPENDENCES;

DATA HANDLING;

EID: 53549100191     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.47.004309     Document Type: Article

References (13)

1. The text Elastic Lidar, by V. A. Kovalev and W. E. Eichinger (Wiley, 2004) has an extensive treatment and bibliography of lidar analysis methods for aerosols distributed continuously over extended paths.
2. We are assuming a single aerosol material here. Generalization to more than one material present at a given time and range is currently being investigated.
3. 2/(mg sr). Settingg = 1 of course means that these units no longer apply and, consequently, only relative backscatter and concentration can be estimated by this choice. This is described in more detail in Section 3.
4. B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, 1983).
5. g.
6. Even with the choice of maximum likelihood, there is the decision of whether the estimates should be computed independently for each time step or be processed by a recursive algorithm, such as recursive least squares. We have adopted the former choice here since the estimates are to be used to train and test classifiers for which independent training samples are required. Actual deployment may be better served by a recursive algorithm.
7. A related concern is the huge amount of background data needed to construct suitable sample estimates of the range-covariance matrices. This is not compatible with the limited amount of background data typically available.
8. See S. Mallat, Wavelet Tour of Signal Processing, Section 9.1.3 and Appendix A6, for an excellent discussion of the KL expansion (Academic, 1998).
9. If our covariance function, given by Eq. (14), had circular periodicity, Mallat [8] shows that the Fourier basis would be the KL basis. We cannot claim this, but for target aerosols not close to either end of the sampling range, there is little error in making this assumption.
10. See, for example, F. L. Lewis, Optimal Estimation (Wiley, 1986).
11. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm (with discussion)," J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).
12. R. H. Shumway and D. S. Stoffer, Time Series Analysis and Its Applications (Springer-Verlag, 2000), Chap. 4.
13. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993) has very readable treatments of ML and related topics.