If you can't find your German ancestor that was in the 1820 census but no passenger records in Philadelphia or the Carolinas you might check with HETRINA. This abreviation is for Hessische Truppen im Amerikanischen Unabhängigkeitskrieg.
Many Hessian deserters remained as farmers and married into German-speaking farming families. Even during the Revolution War they settled down to farm without much harrassment. The ones that deserted in the last months of the war were considered immigrants and integrated into the German-speaking community.
HETRINA is a compilation of the names of soldiers by Dr. Inge Auerbach of the Staatsarchiv (State Archives) in Marburg (Hessen) Germany. The soldiers' names were drawn from the "mass und rangierliste" (the regiment lists from 1776 and 1785) and the regiment monthly reports of personnel changes. The information included gives the soldier's name, town, approximate year of birth, rank, regiment, date and type of event. As an example, if the soldier deserted, this would be indicated along with the date of the desertion. The first 4 volumes (organized by regiment) provide the names of the Hessen-Cassel regiments, volume 5, the Waldeck troops and volume 6, those of Hessen-Hanau. The HETRINA series (on microfilm) can be accessed through one of the LDS Family History Centers.
Bd. 1-2 FHL US/CAN Film 1320516 Items 6-7
Bd. 3-5 FHL US/CAN Film 1320542 Items 5-6