The stochastic Cramér-Rao bound for source localization and medium tomography using vector sensors

Area of Science:

• Signal Processing
• Estimation Theory
• Array Processing

Background:

• The stochastic Cramér-Rao bound (CRB) is crucial for assessing the fundamental limits of parameter estimation accuracy.
• Existing formulations can be computationally intensive, especially for complex sensor arrays and signal models.
• Applications span radar, sonar, seismics, and oceanography, requiring robust estimation techniques.

Purpose of the Study:

• To introduce a direct and simplified formulation for the stochastic CRB applicable to Gaussian signals with additive Gaussian noise.
• To generalize the CRB formulation for vector observations from multiple sources, including partially coherent signals.
• To enable efficient performance studies for signal localization and tomographic parameters.

Main Methods:

• Developed a direct formulation for the stochastic CRB for Gaussian signals and noise.
• Utilized a general embedding using a Green's function vector for various parameters (localization, tomographic).
• Derived simplified CRB expressions using three quadratic forms involving the Green's function and noise covariance.

Main Results:

• The new formulation yields simplified stochastic CRB expressions.
• Computational efficiency is improved by inverting the noise covariance only once.
• The method is validated with applications to vector sensors in jamming scenarios, showing analytical and numerical results.

Conclusions:

• The proposed direct CRB formulation offers a computationally efficient approach for performance analysis.
• It provides a unified framework for diverse sensor systems and estimation problems.
• The results facilitate more accessible and scalable performance studies in signal processing applications.