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Theoretical range precision obtained by maximum likelihood estimation in laser radar compared with the Cramer-Rao
Applied Optics
|January 16, 2019
Summary
This study introduces Theoretical Range Precision (TRP) derived from Maximum Likelihood Estimation for signal processing. TRP accurately describes range estimator variance, outperforming the Cramer-Rao Bound (CRB) at low signal-to-noise ratios.
Area of Science:
- Signal Processing
- Statistical Inference
Background:
- Waveform fitting is crucial for extracting objects from signals.
- Noise corruption significantly impacts the precision of range estimation.
Purpose of the Study:
- To derive an analytical solution for Maximum Likelihood Estimation (MLE) of the range estimator.
- To evaluate the performance of the derived estimator against the Cramer-Rao Bound (CRB).
Main Methods:
- Derivation of an analytical solution for the probability density function (PDF) of the range estimator using a Gaussian model.
- Comparison of the variance of the derived PDF (Theoretical Range Precision - TRP) with the CRB.
Main Results:
- The variance of the linear PDF version aligns with the CRB.
- TRP accurately models simulation data variance, while CRB serves as a lower bound.
- TRP remains effective at low signal-to-noise ratios (SNR), whereas CRB becomes too loose for unbiased estimation.
Conclusions:
- Theoretical Range Precision (TRP) offers a more accurate measure of range precision than CRB, especially in noisy conditions.
- The derived analytical solution provides a robust method for range estimation performance evaluation.
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