Active sonar systems are plagued by false alarms due to confusion between returns from water-column targets and backscatter from the bottom. Both feature-based and physics-based classifiers are notoriously susceptible to mismatch of the environment used for training and/or modeling active sonar returns. In this paper, in order to achieve more robust classification, uniformly sub-sampled DFT-coefficients from a single snapshot of the wideband active sonar return are used to define a waveguide-invariant spectral density matrix (WI-SDM). The WI-SDM facilitates adaptive matched-filtering based approaches for target depth estimation, where the waveguide invariant property is exploited to obtain uncorrelated snapshots without inflating covariance matrix rank. Depth classification is then performed by designing a waveguide-invariant minimum variance filter (WI-MVF) with adaptive weights which minimize ambiguous depth sidelobes. Simulation and real data results in a shallow-water Mediterranean environment are presented to illustrate the approach. [Work sponsored by ONR.]