The integration of GPS with an IMU has been widely used in many applications of positioning and orientation. The performance of a GPS-aided inertial integrated navigation system is mainly characterized by the ability of the IMU to bridge GPS outages. This basically depends on the inertial sensor errors that cause a rapid degradation in the integrated navigation solution during periods of GPS outages. The inertial sensor errors comprise systematic and random components. In general, systematic errors (deterministic) can be estimated by calibration and therefore they can be removed from the raw observations. Random errors can be studied by linear or high order nonlinear stochastic processes. These stochastic models can be utilized by a navigation filter such as, Kalman filter, to provide optimized estimation of navigation parameters. Traditionally, random constant (RC), random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in the navigation filters. In this technical note, the inertial sensor errors are introduced and discussed. Subsequently, a six-position laboratory calibrationtest is described. Then mathematical models for RC, RW, GM, and AR stochastic models with associated variances for gyros and accelerometer random errors are presented along with a discussion regarding ongoing research in this field. Also, the implementation of a stochastic model in a loosely coupled INS/GPS navigation filter is explained.