Low-cost inertial measurement units (IMUs) are increasingly becoming commercially available and the use of IMUs in autonomous vehicle applications has increased rapidly in the past decade. IMUs are subject to various errors, such as biases, drifts, nonlinearities, scale factors and noise. The noise is produced by various sources, such as thermal and vibrational disturbances. Noise estimation is critical in accurate inertial navigation systems (INS). The main contribution of this paper is that a noise analysis of the raw accelerations measured by IMUs during signal presence (i.e, an acceleration caused by a specific force) or absence (when the IMU undergoes constant velocity) is carried out to reduce these noise components, which corrupt the inertial data. After noise reduction, multi-aiding information from odometry, a single-axis gyroscope and vehicle constraints is utilized to bound the error growth of the inertial data and produce a reliable outdoor localization system. Experimental results are presented to show the effectiveness of the noise reduction method and the improved accuracy of the multi-aided INS.