<p>Earth-orbiting space debris poses a severe threat to current and future space missions. To combat the dangers of debris, countries (and companies) perform collision avoidance using catalogs of space objects. Better technology has also led to the detection of more space objects, increasing the amount of data in these catalogs. With this increase in data comes a greater need for a single comprehensive catalog without duplicates, and this work proposes two methods of catalog correlation to address this need. These methods are tested using the publicly available Space-Track (US) and Vimpel (Russian) catalogs. The first method, called direct catalog comparison, directly correlates the Space-Track and Vimpel catalogs to determine the same objects between them. This method is validated using the datefirst.txt file – a file from Vimpel which lists Space-Track and Vimpel object pairs. When correlating the Vimpel objects in the datefirst.txt file to the Space-Track catalog, the direct catalog comparison method produces over 90\% of these pairs. It is also found that the datefirst.txt file pairing for Vimpel 92400 should be NORAD 42075 and not NORAD 41879. The second method, arc correlation, uses optical observations received from the Purdue Optical Ground Station and the German Aerospace Center to correlate optical observations to both of the catalogs. By matching observations to objects in the catalogs, these catalog objects are indirectly correlated to each other. This method is validated using tracking data messages containing observation sets of tasked Space-Track objects in various orbits. For all tasked Space-Track objects, even ones in a cluster, the tracking data messages are appropriately matched to the Space-Track catalog. For the cases where Vimpel objects are associated with these Space-Track objects – as claimed by the datefirst.txt file (except for the case listed above) – the appropriate Vimpel objects are matched to the tracking data messages. When observation sets of unknown objects are tested, the arc correlation method produces distinct and viable candidate matches for both catalogs. Overall, the direct catalog combination and arc correlation methods can be used together to effectively correlate the Space-Track and Vimpel catalogs, aiding the development of a comprehensive catalog of space objects.</p>