A study on the performance of covariance matrix estimators

Abstract

This is a statistical study conducted to determine reliable and efficient accuracy measures that will summarize uncertainty of multidimensional fixes.

We assume that a mass of position data, such as that obtained through a positioning system, has somehow been recorded at a location. Then the problem at issue is to determine a statistical quantity that will summarize the degree of scatter shown by the data and appraise and validate the positioning system's performance. Six covariance matrix estimators have been identified. Their performance in terms of efficiency, reliability, and flexibility has been assessed using three‐dimensional GPS position data under various distributional situations.

All in all, robust covariance matrix estimators, such as Huber's and Campbell's M‐estimators, satisfy global requirements of good efficiency, reliability, and flexibility.

Keywords:

• covariance matrix estimators
• robust statistics
• GPS
• accuracy evaluation