Inverse Synthetic Aperture Radar (ISAR) imaging presents a formidable challenge when it comes to small everyday objects due to their limited Radar Cross-Section (RCS) and the inherent resolution constraints of radar systems. Existing ISAR reconstruction methods including backprojection (BP) often require complex setups and controlled environments, rendering them impractical for many real-world noisy scenarios. In this paper, we propose a novel Analysis-through-Synthesis (ATS) framework enabled by Neural Radiance Fields (NeRF) for high-resolution coherent ISAR imaging of small objects using sparse and noisy Ultra-Wideband (UWB) radar data with an inexpensive and portable setup. Our end-to-end framework integrates ultra-wideband radar wave propagation, reflection characteristics, and scene priors, enabling efficient 2D scene reconstruction without the need for costly anechoic chambers or complex measurement test beds. With qualitative and quantitative comparisons, we demonstrate that the proposed method outperforms traditional techniques and generates ISAR images of complex scenes with multiple targets and complex structures in Non-Line-of-Sight (NLOS) and noisy scenarios, particularly with limited number of views and sparse UWB radar scans. This work represents a significant step towards practical, cost-effective ISAR imaging of small everyday objects, with broad implications for robotics and mobile sensing applications.