Ridge Regression: A Cautionary Note

James L. Farrell

Abstract:	Investigation of the Ridge formulation applied to navigation with poor geometry has identified conditions for which significant limitations arise. The reason is directly traceable to its intentional retardation of excursions allowed in the solution when residuals, inflated by HDOP, are large. That feature appears as a benefit when inflation by HDOP is the sole orprinzaly reason why the residuals are large. As with any filtering operation, the “flip side” involves responsiveness to large residuals that are bona fide. The expression for the ridge estimator is applied to a straightforward example with poor geometry and the results are expanded for further scrutiny. Analysis reveals the type of scenario wherein the limitations are encountered, and computational results are shown to confirm the analytical investigation. These results are not intended to deny the potential benefits of using total mean squared error (rather than variance) as a performance criterion. Rather than an attempt to invalidate other results previously presented in other literature, results and suggestions presented herein should be viewed as efforts to balance the perspective and to steer the development of the ridge formulation as applied to navigation. Results presented elsewhere have emphasized conditions of inflated HDOP as the sole or predominant cause of large residuals. By giving increased attention to a more general class of conditions, a better overall assessment will result.
Published in:	Proceedings of the 46th Annual Meeting of The Institute of Navigation (1990) June 26 - 28, 1990 Atlantic City, NJ
Pages:	131 - 138
Cite this article:	Farrell, James L., "Ridge Regression: A Cautionary Note," Proceedings of the 46th Annual Meeting of The Institute of Navigation (1990), Atlantic City, NJ, June 1990, pp. 131-138.
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