Systematic and random errors inherently present in all inertial sensors contribute to the long-term divergence of the navigation solution of an Inertial Navigation System (INS). To keep such long-term divergence under control while taking advantage of their excellent short-term performance, an INS is often combined with information from other navigation aids. However, the improvements due to external aiding are limited by the type, accuracy and update period of the information provided by the aid(s). In the case where an INS is aided by GPS, only the long-term inertial errors are suppressed while the short-term inertial errors essentially remain unaffected. A better navigation solution can therefore be expected if most of the short-term inertial sensor noise is reduced prior to data integration. This paper describes a method of inertial data pre-filtering over the frequency band of interest, i.e. between the measurement period of external aiding with GPS and the edge of the motion band. A model for the short-term inertial errors in this band is introduced as a combination of a broad band signal with noise possessing self-similarities over several decades of frequency. The model is defined in the frequency and wavelet domains. A technique for adaptive estimation of the model parameters is introduced. This method is based on an analysis of a short portion of data above the band of interest. Once the model parameters are estimated for a specific system and time-period, the noise distribution is predicted within the band of interest and the signals are de-noised. This filtering methodology is tested using different navigation-grade strapdown inertial systems and the results are presented. A 20% improvement in the attitude determination has been observed under the dynamic conditions with respect to an independent reference.