This paper investigates the problem of ground vehicle tracking with a Ground Moving Target Indicator (GMTI) radar. In practice, the movement of ground vehicles may involve several different manoeuvring types (acceleration, deceleration, standstill, etc.). Consequently, the GMTI radar may lose measurements when the radial velocity of the ground vehicle is below a threshold, i.e. falling into the Doppler blind region. In this paper, to incorporate the information gathered from normal measurements and knowledge on the Doppler blindness constraint, we develop an enhanced particle filtering method for which the importance distributions are inspired by a recent noise related doppler blind (NRDB) filtering algorithm for GMTI tracking. Specifically, when constructing the importance distributions, the proposed particle filter takes the advantages of the efficient NRDB algorithm by applying the extended Kalman filter and its generalization for interval-censored measurements. In addition, the linearization and Gaussian approximations in the NRDB algorithm are corrected by the weighting process of the developed filtering method to achieve a more accurate GMTI tracking performance. The simulation results show that the proposed method substantially outperforms the existing methods for the GMTI tracking problem.