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This paper introduces a new methodology to take account of the Doppler blind zone arising, for example, in GMTI tracking. Here, the measurements are suppressed, when the range-rate of the target drops below a specified threshold. Algorithms based on the new methodology are easy to implement, robust to choice of initial distributions and computationally efficient. Simulations have been conducted for a number of scenarios featuring in earlier comparative exercises. The new techniques exhibit a uniform improvement in estimation accuracy, as compared with -earlier proposed approximate analytic techniques.