He was the only child of Georg Friedrich Kellner , a baker from the village of Arnstadt in Thuringia , and Barbara Wilhelmine Vaigle from Bissingen . Kellner was the only child of Georg Friedrich Kellner , a baker and confectioner from the town of Arnstadt in Thuringia , and Barbara Wilhelmine Vaigle from Bietigheim-Bissingen near Ludwigsburg .