A primary cause of degraded performance in pointing and tracking systems is the jitter in its line-of-sight. This jitter is caused by the residual angular motion of the stabilized platform within the system. A major contributor to this residual motion if the gyroscope noise. Thus, to further reduce angular jitter, lower noise gyroscopes need to be selected, generally at a premium cost. Another approach is to electronically enhance the accuracy of the gyroscopes (by suppressing measurement noise) before their outputs are fed into the stabilized platform control system. Optimal filtering techniques can be used for this purpose. The goal is to estimate the platform motion so that the calculated value is closer to the actual value than the measurement is. Enhanced performance is obtained at the expense of added complexity, but in many cases this approach may prove to be more economical than resorting to more precise and costly lower-noise gyroscopes. This paper presents a novel Kalman filtering method that provides more accurate angular motion estimates than the measured values. The effectiveness of this method is evaluated through a computer simulation case study. The simulation demonstrates that the new approach yields excellent 3D angular velocity estimates, very small mean-square-estimation errors, and over a 5 to 1 improvement (in the mean-square sense) over angular velocity measurements obtained from 3 orthogonal gyroscopes. The enhanced 3D angular velocity estimates can be fed into the platform stabilization control system, rather than feeding raw gyroscope measurements, significantly reducing the contribution of gyroscope noise toward the overall jitter in a stabilized platform. This would permit a relaxation on gyroscope noise specifications, which could lead to substantial savings, while maintaining the same error budget.