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Updated: Jun 6, 2026
12:14
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in
Ioannis Bertsatos1, Michele Zanolin, Purnima Ratilal
1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
The Journal of the Acoustical Society of America
|November 30, 2010
Summary
This study provides a method to determine the necessary sample size or signal-to-noise ratio (SNR) for accurate parameter estimation in remote sensing. It ensures reliable results by minimizing bias and ensuring covariance is within error thresholds.
Area of Science:
- Signal processing
- Statistical inference
- Remote sensing
Background:
- Accurate parameter estimation is crucial for remote sensing in dynamic environments.
- Maximum likelihood estimates (MLEs) are widely used but their accuracy depends on sample size and signal-to-noise ratio (SNR).
- Fluctuating environments, such as ocean waveguides with internal waves, pose challenges to estimation accuracy.
Purpose of the Study:
- To develop a method for determining necessary conditions on sample size or SNR for accurate parameter estimates.
- To provide analytical expressions for bias and covariance of MLEs.
- To quantify the impact of environmental fluctuations, like internal waves, on estimation accuracy.
Main Methods:
- Expanding bias and covariance of MLEs in inverse orders of sample size or SNR.
- Utilizing the Cramer-Rao lower bound (CRLB) as a first-order covariance term.
- Deriving conditions based on minimizing first-order bias and second-order covariance, and meeting CRLB error thresholds.
- Developing an analytical expression for the second-order covariance of MLEs for complex Gaussian data.
Main Results:
- Established necessary conditions on sample size and SNR for accurate parameter estimation.
- Provided an analytical expression for the second-order covariance of MLEs applicable to Gaussian data.
- Quantified the loss of coherence effects on source localization accuracy in a fluctuating ocean waveguide.
Conclusions:
- The developed method enables determination of optimal sample sizes or SNRs for reliable remote sensing.
- The analytical framework is applicable to various problems involving Gaussian data and parameter-dependent measurements.
- The study highlights the significant impact of environmental fluctuations on estimation accuracy, particularly in underwater acoustics.
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