Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

Area of Science:

• Signal Processing
• Sensor Networks
• Estimation Theory

Background:

• Sensor placement critically impacts localization accuracy in sensor networks.
• Angle of Arrival (AOA) localization is a key technique for target tracking.
• Gaussian priors represent prior knowledge about target location.

Purpose of the Study:

• To optimize sensor placement in 3D space for AOA target localization.
• To develop a method that leverages the Fisher Information Matrix (FIM) properties.
• To improve the performance of Maximum A Posteriori (MAP) estimation.

Main Methods:

• Formulating the sensor placement optimization under the A-optimality criterion.
• Transforming the problem into a diagonalizing process of the AOA-based FIM.
• Utilizing the 3D rotation invariance property of the FIM for optimal sensor configuration.
• Applying 3D rotation to diagonalize the Gaussian covariance matrix of the FIM.

Main Results:

• The sensor placement optimization problem was successfully reformulated.
• The FIM was shown to be invariant to 3D rotations.
• An optimal sensor placement method using 3D rotation was developed.
• Simulations demonstrated significant improvements in localization accuracy.

Conclusions:

• The proposed 3D rotation-based sensor placement method effectively optimizes AOA localization.
• The method achieves at least a 25% reduction in MSE compared to existing techniques.
• The estimation bias remains minimal, below 0.15 m, ensuring high precision.