- A novel algorithm is presented for the estimation of the 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. This paper develops the filter and its implementation in the case of a low Earth orbit spacecraft, acquiring noisy geomagnetic field measurements via a three-axis magnetometer. Because the effective measurement noise in this case is time correlated, a special procedure is developed to account for that correlation in the particle filter implementation. The new estimator copes with the absence of an exact inertia tensor by employing a secondary particle filter that computes a maximum-likelihood estimate of the tensor of inertia, thus avoiding the need to expand the primary 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.