Networks of neurons perform complex calculations using distributed, parallel computation, including dynamic “real-time” calculations required for motion control. The brain must combine sensory signals to estimate the motion of body parts using imperfect information from noisy neurons. Models and experiments suggest that the brain sometimes optimally minimizes the influence of noise, although it remains unclear when and precisely how neurons perform such optimal computations. To investigate, we created a model of velocity storage based on a relatively new technique–“particle filtering”–that is both distributed and parallel. It extends existing observer and Kalman filter models of vestibular processing by simulating the observer model many times in parallel with noise added. During simulation, the variance of the particles defining the estimator state is used to compute the particle filter gain. We applied our model to estimate one-dimensional angular velocity during yaw rotation, which yielded estimates for the velocity storage time constant, afferent noise, and perceptual noise that matched experimental data. We also found that the velocity storage time constant was Bayesian optimal by comparing the estimate of our particle filter with the estimate of the Kalman filter, which is optimal. The particle filter demonstrated a reduced velocity storage time constant when afferent noise increased, which mimics what is known about aminoglycoside ablation of semicircular canal hair cells. This model helps bridge the gap between parallel distributed neural computation and systems-level behavioral responses like the vestibuloocular response and perception.