An Analysis of Error Distributions in Navigation

Abstract

This paper first presents some of the results of my recent work on error distributions in navigation which may be worth summarizing for navigation practitioners. Some further explanations and insights in the second part may be useful for future studies on the subject.Discussion on this subject was initiated by E. W. Anderson who questioned the adequacy of the gaussian distribution as the probability model for navigational position errors. He observed that empirical position error distributions are usually long-tailed (i.e. with raised skirts) compared to the gaussian and have a strong tendency to form an exponential function of error magnitude, especially in the far tail-region. Attempts to explain this phenomenon have been made by Abbott, Crossley, Lloyd, Parker, Lord, O. D. Anderson, etc., based on various aspects of navigation performance. To provide a general structure for characterizing the error distributions, Anderson and Ellis made a significant step forward in suggesting ‘Student's t’ distributions as error models. As pointed out by Parker, however, this suggestion has to be taken with reservation and requires further verification based upon empirical data. My own recent work has indeed taken the direction advocated by Parker and has attempted to fill a theoretical deficiency in Anderson and Ellis's work, to provide examples of empirical model fitting and to discuss the merits of Student's t distributions relative to the double exponential model. The main findings are summarized below.