Global Navigation Satellite Systems (GNSS) support numerous applications, including mission-critical ones that require high integrity for safe operations such as air, maritime, and land-based navigation. These applications require ensuring the upper bound of the positioning computation, including overbounding any assumptions made in positioning algorithms. One of the main assumptions in the GNSS positioning algorithm is that the error follows a Probability Density Function (PDF), widely assumed to be Gaussian. This assumption should be overbounded to ensure safety. Two mathematical definitions of distribution overbounding have been proposed: Cumulative Distribution Function (CDF) overbounding and paired overbounding. Achieving these definitions has been an open problem for the past 20 years, and to date, no methods have effectively achieved either definition in multimode datasets. This paper proposes the first overbounding method, the Maximum non-Bounded Difference (MnBD) method, capable of achieving both definitions. Its effectiveness is assessed by comparison with the combined CDF bounding and paired overbounding approach. The results show that the MnBD method successfully achieves overbounding in both real datasets and 1000 simulated multimode data, tested on Gaussian and Generalized Extreme Value (GEV) distributions. The latter demonstrates MnBD’s ability to handle asymmetric distributions. The developed approach can be utilized in overbounding the GNSS error at the system level and user level to ensure the system integrity.
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