Compressive time delay estimation off the grid.

Area of Science:

• Signal Processing
• Acoustics
• Information Theory

Background:

• Traditional time delay estimation (TDE) relies on discretized grids, leading to reconstruction errors when actual delays fall between grid points.
• Compressive sensing (CS) offers a sparse signal reconstruction approach for TDE, but standard methods suffer from basis mismatch due to grid limitations.

Purpose of the Study:

• To develop an off-the-grid compressive sensing (CS) technique for time delay estimation (TDE) in the continuous time domain.
• To address the reconstruction degradation caused by the mismatch between actual and discretized time delays in conventional CS-TDE.

Main Methods:

• Formulating TDE as a sparse signal reconstruction problem solvable with CS.
• Adapting an off-the-grid CS framework, inspired by direction of arrival (DOA) estimation, to overcome basis mismatch.
• Applying the proposed method to real-world data from a water tank experiment.

Main Results:

• The off-the-grid CS TDE method successfully estimates the channel impulse response in a continuous time domain.
• Demonstrated super-resolution capabilities, allowing for the distinction of closely spaced arrivals.
• Validation of the technique using experimental data, confirming its effectiveness.

Conclusions:

• The proposed off-the-grid CS TDE technique significantly improves upon traditional methods by avoiding basis mismatch.
• This advanced TDE approach offers enhanced accuracy and super-resolution for channel impulse response estimation.
• The method shows practical applicability and effectiveness, as evidenced by water tank experiment results.