Precise positioning is needed for applications like tracking people, vehicles, and assets. Current positioning approaches are not accurate enough for many interesting applications. The resolution of time delay estimation, which is key to positioning, depends on bandwidth and signal to noise ratio (SNR) of received signals, but these are limited by spectrum regulations. The proposed approach uses multiband channel sampling and subspace-based estimation along with compressive sensing and software defined radios to achieve high-resolution time delay estimation from low bandwidth and SNR signals, enabling more precise positioning for applications like IoT tracking, healthcare monitoring, autonomous vehicles, and smart cities.