- A novel algorithm is presented for the estimation of spacecraft attitude quaternion from vector observations in gyro-equipped spacecraft. 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 new method can be applied using various kinds of vector observations. In this paper, the case of a low-Earth-orbit spacecraft, acquiring noisy geomagnetic field measurements via a three-axis magnetometer, is considered. A genetic algorithm is used to estimate the gyro bias parameters, avoiding the need to augment the particle filter's state and rendering the estimator computationally efficient. Contrary to conventional filters, which address the quaternion's unit norm constraint via special (mostly ad hoc) techniques, the new filter maintains this constraint naturally. An extensive simulation study is used to compare the new filter to three extended Kalman filters and to the unscented Kalman filter in Gaussian and non-Gaussian scenarios. The new algorithm is shown to be robust with respect to initial conditions and to possess a fast convergence rate. An evaluation of the Cramer-Rao estimation error lower bound demonstrates the filter's asymptotic statistical efficiency and optimality.