This publication proposes a parametric data model and a gradient-based maximum likelihood estimator suitable for the description of delay-dispersive responses of multiple dynamic ultrawideband (UWB)-radar targets. The target responses are estimated jointly with the global target parameters range and velocity. The large relative bandwidth of UWB has consequences for model-based parameter estimation. On the one hand, the Doppler effect leads to a dispersive response in the Doppler spectrum and to a coupling of the target parameters that both need to be considered during modeling and estimation. On the other hand, the shape of an extended target results in a dispersive response in range, which can be resolved by the radar resolution. We consider this extended response as a parameter of interest, e.g., for the purpose of target recognition. Hence, we propose an efficient description and estimation of it by a finite impulse response (FIR) structure only imposing a restriction on the target’s dispersiveness in range. We evaluate the approach on simulations, compare it to state-of-the-art solutions, and provide a validation of the FIR model on measurements of a static scenario.