The invention is a method for improved active sonar using a singular value decomposition filtering and a Volterra-Hermite Basis Expansion to model real active sonar measurements. The fitting model minimizes the sum of the squared errors between a measured channel response, z(t), and model response, y(t), which is a fitted Volterra Series solution. The model requires as input an excitation waveform, x(t), to which is fitted the model response, y(t). A contracted broadband cross-ambiguity function is used to correct the excitation waveform for Doppler and range effects. Once completed, the modeled response can be used to determine the linearity or non-linearity of the channel effects. Appropriate measures can be utilized to reduce these effects on the measured channel response.