Abstract: The limited number of snapshots and environmental parameter mismatch in active detection significantly constrain the performance of matched-field depth estimation. This paper proposes a method for estimating the depth of targets using active sonar in shallow water, based on frequency-domain subsampling of wideband echoes and a Riemannian distance processor. The method involves performing a short-time Fourier transform on the received wideband target echoes. By leveraging the property that the waveguide invariant in shallow water is approximately equal to 1, it efficiently acquires multi-snapshot wideband echo data within fewer transmission cycles, enabling robust estimation of the cross-spectral density matrix. Additionally, the Riemannian distance metric is introduced into matched-field processing to better quantify the correlation between the received signal matrix and the replica field matrix. Simulation results demonstrate that the proposed algorithm enhances depth estimation performance under low signal-to-noise ratio conditions and exhibits improved robustness against environmental mismatch. This approach provides a practical solution for shallow-water target localization with limited observational data and parameter uncertainties.