A novel algorithm is presented for the estimation of spacecraft angular-rate from vector observations. Belonging to the class of Monte Carlo sequential methods, the new estimator is a particle filter that uses approximate numerical representation techniques for performing the otherwise exact time propagation and measurement update of potentially non-Gaussian probability density functions in inherently nonlinear systems. The paper develops the filter and its implementation in the case of a low Earth orbit (LEO) spacecraft, acquiring noisy Geomagnetic field measurements via a three-axis magnetometer (TAM). The new estimator copes with the absence of an exact inertia tensor by employing a second particle filter which computes a minimum mean square error (MMSE) estimate of the tensor of inertia, thus avoiding the need to expand the filter's state. This renders the new estimator highly efficient and enables its implementation with a remarkably small number of particles. The results of a simulation study are presented, in which the new filter is compared to a recently presented conventional extended Kalman filter. The comparison demonstrates the viability and robustness of the new algorithm and its fast convergence rate.