Tropospheric Spectrum Estimations Comparing Maximum Likelihood with Expectation Maximization Solutions and Fast Fourier Transforms
The FIRST program (Far Infrared Spectroscopy in the Troposphere) was created as an Instrument Incubator Program (IIP) by NASA Langley to demonstrate improved technology readiness levels (TRLs) for two technologies needed in the design of new imaging Fourier transform spectrometers (IFTS). The IIP IFTS was developed at the Space Dynamics Laboratory and ?own to an altitude of 103,000 feet on an instrumented NASA balloon payload. The sensor collected approximately 15,000 interferograms during its 6-hour ?ight. Fourier transforms (FFT) produced acceptable results except for noise equivalent temperature di?erences (NETD) that were ?ve times higher than goal and inconclusive transforms at seven strong absorption features. An alternate transform technique, maximum likelihood estimation (MLE), was implemented to improve spectral estimations at the absorptions and to improve the NETD for the sensor. Iterative expectation-maximization (EM) algorithms provide numerical solutions for the MLE. Four combinatorial forms of the EM algorithm were developed. Forms of the EM algorithm were developed to optimize amplitude estimations as a function of assumed noise distributions. "Direct" and "indirect" EM forms were developed to process the asymmetrical interferograms recorded by the FIRST sensor. The direct method extends the standard even (cosine) EM algorithm to simultaneously transform both the sine and cosine components of the interferogram. The indirect method, uses Fourier and inverse Fourier transforms as pre-processors to convert the measured asymmetrical interferograms to even (cosine) interferograms. Using the indirect Gaussian EM form improved the measured NETD by approximately twenty percent between 100 and 700 wavenumbers. For wavenumbers less than 100 or greater than 700, the improvement increased to a factor of at least two out to 1500 wavenumbers. The indirect Gaussian produced inconclusive results in the areas of high absorption because of large bias errors introduced by the FFT/IFFT pre-processing. The indirect method was found to be inadequate for estimating spectra at the deep absorptions. The direct EM method, on the other hand, has the potential to produce improved amplitude estimations at the absorptions since there are no inherent biases in the algorithm's initial conditions at a cost in computer resources and execution times that are four times those needed for the indirect method.
School:Utah State University
School Location:USA - Utah
Source Type:Master's Thesis
Keywords:tropospheric fast fourier transforms
Date of Publication:05/01/2007