- Extending and consolidating the recently introduced quaternion particle filter for a spacecraft's attitude estimation and its companion, the angular-rate particle filter, this paper presents a novel algorithm for the estimation of both a spacecraft's attitude and 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 spacecraft, acquiring noisy Geomagnetic field measurements via a three-axis magnetometer. The new estimator copes with the curse of dimensionality related to the particle filtering technique by introducing innovative procedures that permit a significant reduction in the number of particles. This renders the new estimator computationally efficient and enables its implementation with a remarkably small number of particles (relative to the dimension of the state). The results of a simulation study demonstrate the viability and robustness of the new filter and its fast convergence rate.