Three-dimensional dislocations in a uniform linear array's isotropic sensors-Direction finding's hybrid Cramér-Rao...

Area of Science:

• Signal Processing
• Array Signal Processing
• Acoustic and Electromagnetic Wave Propagation

Background:

• Linear arrays are typically used for univariate direction finding, estimating source direction-of-arrival (DOA).
• Real-world conditions, such as ocean waves and currents, can cause sensor dislocation, deviating from the ideal linear geometry.
• This dislocation can potentially compromise the accuracy of direction-finding algorithms.

Purpose of the Study:

• To analyze the impact of three-dimensional random sensor dislocation on the direction-finding accuracy of a nominally linear array.
• To derive a closed-form expression for the hybrid Cramér-Rao bound (HCRB) of the arrival-angle estimate under dislocation.
• To investigate the conditions under which sensor dislocation might improve or degrade DOA estimation accuracy.

Main Methods:

• Development of a theoretical framework to model sensor dislocation in a linear array.
• Derivation of the hybrid Cramér-Rao bound (HCRB) for the arrival-angle estimation error.
• Analysis of the derived HCRB in terms of sensor dislocation statistics, arrival angle, and signal-to-noise ratio (SNR).

Main Results:

• A closed-form expression for the HCRB was derived, quantifying the impact of sensor dislocation.
• Contrary to expectations, sensor dislocation does not always degrade HCRB; it can improve it under certain conditions.
• The effect of dislocation on HCRB is dependent on dislocation variances, source arrival angle, and SNR.

Conclusions:

• The assumption that sensor dislocation solely degrades direction-finding accuracy is not universally true.
• Optimal array design and performance analysis must consider the interplay between dislocation statistics and source characteristics.
• This study provides a more nuanced understanding of DOA estimation accuracy in practical, non-ideal array scenarios.