A Fast, Parallel Algorithm for Fully Overlapped Allan Variance and Total Variance for Analysis and Modeling of Noise in Inertial Sensors

Modeling stochastic noise in inertial sensors-particularly those used in guidance, navigation, and control applications-involves characterizing the underlying noise process by inferring parameters such as random walks and drift rates from the Allan deviation plots. Fully overlapped Allan variance (FOAV) and total variance (TV) are two methods that accurately derive these parameters by observing all possible time averages, but existing implementations are computationally expensive: They require Θ(N
³
) time for processing N data points (see Section III). Thus, several methods have been developed to trade accuracy in parameter estimates for reduced computational effort, including not fully overlapping AV (NFOAV), which runs in Θ(N
²
) time. Our key contribution is a fast, parallelizable algorithm (Algorithm 1) to calculate FOAV and TV for generating smooth Allan deviation plots whose serial running time is Θ(N
²
), and we demonstrate improved execution times with parallel implementations. Our fast algorithm thus enables FOAV and TV to be the norm for estimating AV parameters efficiently and with high confidence.