Statistical Distribution Analysis of Navigation Positioning System Errors-Issue of the Empirical Sample Size

Area of Science:

• Navigation Systems
• Statistical Analysis
• Geomatics Engineering

Background:

• Statistical analysis of positioning systems assumes normal distribution of position errors.
• Iterative methods in positioning systems cause 'Position Random Walk' (PRW).
• PRW leads to empirical error distributions inconsistent with normal distribution, even with thousands of measurements.

Purpose of the Study:

• Determine the representative length of measurement sessions for positioning systems.
• Establish criteria for statistically reliable sample sizes for accuracy verification.
• Investigate the impact of PRW on accuracy overestimation in navigation systems.

Main Methods:

• Analysis of empirical measurement data from GPS, DGPS, EGNOS, and Decca Navigator systems.
• Statistical evaluation of position errors (latitude and longitude) to identify PRW.
• Comparison of accuracy overestimation from short vs. long measurement sessions.

Main Results:

• All researched positioning systems (GPS, DGPS, EGNOS, Decca Navigator) demonstrate PRW.
• PRW causes empirical error distributions to deviate from normal distribution.
• Short measurement sessions (e.g., 1000 GPS fixes) significantly overestimate accuracy (by 109.1%).

Conclusions:

• Position Random Walk is a characteristic of modern positioning systems.
• Representative measurement session length varies by system and must be determined individually.
• Accurate accuracy assessment requires statistically representative measurement data, accounting for PRW.