An optimization iterative algorithm based on nonnegative constraint with application to Allan variance analysis technique

• A highly performance method is proposed for estimating the Allan parameters.
• The estimation process with the method avoids the nearly singular matrix issues.
• An equation is provided to evaluate the duration of static data collection.
• An equation is given to calculate the common ratio of the coefficient sequence.

It is well known that inertial integrated navigation systems can provide accurate navigation information. In these systems, inertial sensor random error often becomes the limiting factor to get a better performance. So it is imperative to have accurate characterization of the random error. Allan variance analysis technique has a good performance in analyzing inertial sensor random error, and it is always used to characterize various types of the random error terms. This paper proposes a new method named optimization iterative algorithm based on nonnegative constraint applied to Allan variance analysis technique to estimate parameters of the random error terms. The parameter estimates by this method are nonnegative and optimal, and the estimation process does not have matrix nearly singular issues. Testing with simulation data and the experimental data of a fiber optical gyro, the parameters estimated by the presented method are compared against other excellent methods with good agreement; moreover, the objective function has the minimum value.