This paper introduces a new methodology to account for Doppler blind zone constraints, arising, for example, in ground moving target indicator (GMTI) tracking applications. In such problems, target measurements are suppressed when the range rate (Doppler) of the target drops below a specified threshold in magnitude (the minimum detectable velocity). The proposed method, employing Gaussian mixture approximations to the filtering density, differs from earlier Gaussian mixture approaches in the way missed measurements are modelled. The distinctive feature of the algorithm, as compared with other Gaussian mixture filters, is that it is based on an exact calculation of the filtering density when a measurement is not recorded. Algorithms that result from applying this methodology are simple to implement and computationally undemanding. Simulation results indicate a uniform improvement in estimation accuracy over that of earlier proposed analytic techniques, and a tracking performance comparable to that of state-of-the-art particle filters.