Enhance Antenna Range Resolution

I have a Python script that controls an antenna array and performs object detection with a basic Hamming-windowed FFT. While it works, the range resolution is still too coarse for my needs. I began experimenting with the MUSIC algorithm and even toyed with the idea of adding a continual-learning loop, but I would like a cleaner, expertly implemented solution—whether that is MUSIC, ESPRIT, a refined windowing strategy, or any other modern signal-processing method you can justify.

Here is the current landscape:
• Language & stack: Python with NumPy, SciPy and Matplotlib.
• Key variable: signal-processing methods drive the entire detection chain, so any change must integrate cleanly with the existing pipeline.
• Desired outcome: a measurable, demonstrable improvement in range resolution without an unacceptable hit to computation time.

What I need from you:
1. Review the present codebase and outline the limitations of the current Hamming approach.
2. Propose and implement an advanced algorithm (MUSIC plus any supporting technique, or a more suitable alternative spcially with AI or machin learning) to tighten range bins.
3. Integrate—or replace—my early continual-learning loop so the system adapts to new data without manual retuning.
4. Provide a concise report that compares “before vs. after” resolution metrics and explains the math behind your improvements.
5. Comment the code clearly so I can maintain it later.

Please focus on your experience with antenna or radar signal processing, sub-space algorithms, and adaptive learning techniques when you reply. Demonstrated results on similar projects will be the deciding factor.