A Least-Squares Normalized Error Regression Algorithm with Application to the Allan Variance Noise Analysis Method

Brian E. Grantham and Mark A. Bailey

Abstract:	Over the last decade, extensive advances in digital computing have enabled the integration of navigation aids into tightly coupled navigation systems. These systems often include an error model of the inertial system that is continuously updating and compensating for inertial system error parameters. In these systems, inertial sensor random noise often becomes the limiting factor in performance. Therefore, it is more critical than ever to have accurate characterization of sensor random noise. This paper documents a specialized form of the weighted leastsquares error regression algorithm that results in a least-squares normalized-error (LSNE) regression. This algorithm weights the error from the curve fit by the reciprocal of the value of the curve fit. This fitting method is applied to the Allan variance method of noise analysis to arrive at five typical noise coefficients including random walk and bias instability. The fit technique presented is less complex, requires less computation time, and does not have convergence issues compared to iterative logarithmic methods that are typically used for fitting Allan variance data. Random noise coefficients estimated using this method are compared against other regression methods with good agreement. The authors’ form of implementation is presented. An easyto- use graphical user interface (GUI) application was developed to generate the Allan variance cluster data and calculate the curve fit from time domain data, while providing a visual presentation of the data and a simple means of fit parameter adjustment.
Published in:	Proceedings of IEEE/ION PLANS 2006 April 25 - 27, 2006 Loews Coronado Resort Hotel San Diego, CA
Pages:	750 - 756
Cite this article:	Grantham, Brian E., Bailey, Mark A., "A Least-Squares Normalized Error Regression Algorithm with Application to the Allan Variance Noise Analysis Method," Proceedings of IEEE/ION PLANS 2006, San Diego, CA, April 2006, pp. 750-756. https://doi.org/10.1109/PLANS.2006.1650671
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