This paper describes the effects of measurement errors on the distribution of relative vertical distances (RVD) from which we may estimate the probability of vertical overlap of an aircraft pair. As typical examples of probability density functions, the double exponential distribution and the double double exponential distribution are assumed for height keeping errors. First, theoretical probability density functions (pdf) of RVD are derived for the both cases assuming that the pdfs of measurement errors are normally distributed. Then theoretical pdfs are compared with the empirical distribution generated by computer simulation in order to verify the theoretical values. Finally, some numerical examples for pdf of RVD are shown for several cases. Numerical examples suggest that the frequency in the central part (the core region) of RVD distribution in the presence of measurement errors becomes slightly less than that for the case that the measurement errors are not taken into account. On the other hand, the frequency in the tail region becomes slightly greater because of the presence of measurement errors. As a result, an estimate of the probability of vertical overlap for a given separation minimum (e.g., 1, 000ft or 2, 000ft) based on the RVD distributions would give a conservative value because of effects of measurement errors.
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