Reliability Criteria in Sequential Least-Squares Adjustment

Abstract

This paper examines the reliability criteria in sequential least-squares adjustment. Sequential least-squares techniques are widely implemented to effectively use adjustment processes. We use the reliability concept to quantify the potential for detecting blunders and to estimate their impact on the adjusted parameters. To gain additional insight into sequential least squares, we address internal and external reliability for recursive least squares (RLS) and two-step least squares (TSLS). After a short introduction to RLS, TSLS, and the concept of reliability, the paper describes the theoretical tools we developed to exploit the benefits of reliability criteria in sequential least-squares adjustment. Finally, the paper presents the results of a of two numerical example, indicating that the reliability can also be used effectively in sequential least-squares adjustment.