A21-12 in The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1776.
B-784 and B-785 in The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1776.
Rus14-22 in The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1776.
Family #45 in the 1775 Grimm census.
Family #76 in the 1798 Grimm census.
According to the German Origins Project, Johann Ludwig David Kaiser was born in Württemberg and lived in Frankenbach before immigrating to Denmark. 
He arrived in the City of Schleswig, Schleswig Royal Duchy, in May 1761.  Information in this same source says he left Denmark in May 1765, but that is probably when he requested permission to leave Denmark and immigrate to Russia. The Kulberg Reports show he arrived in Russia on July 4, 1766.
The German Origins Project also show his name as J. Ludewig David Kayser.  The J most likely stands for Johann and confirms that he is the Johann Kaiser listed in the Transport of the Volga Germans from Oranienbaum to the Colonies on the Volga.  The spelling of the last name as Kayser was probably an error due to the input taker spelling the name phonetically. His surname is listed under multiple spellings in The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1766 where is name is also given as Johann Ludewig David.
The Kulberg Reports also show that Ludwig, a Lutheran, was a farmer from Hessen, Germany. Frankenbach is in what is now the State of Hesse. 
The Germans in Denmark who decided to go on to Russia were transported separately from those listed in the Kulberg Reports. They arrived before 1766 and were placed in a temporary village until the rest of the Volga villages were ready for the main group of German colonists. To my knowledge, a list of these immigrants is not available to current researchers, if it exists at all. Since Ludwig appears to be listed both in Denmark records and the Kulberg Reports, it's possible that he left Denmark and returned to Germany before deciding to emigrate to Russia in 1766. This would result in him being listed in documentation for both groups.
By the time he immigrated to Russia, he was married with two children. At that time, he said his last previous home was in Frankenbach, Hesse. His transport document number was 2424.  He departed Luebeck on the Galliot "Die Fortuna," with the skipper Peter Stahl.  They arrived in Oranienbaum on July 4, 1766.  They remained there for approximately one year before traveling to Grimm in July of 1767. 
In The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1766, his age is given as 21 in 1761.  That would make his birth year 1740. This source also lists him as single,  but we know from the Volga German Transportation List and Kulberg Reports that he was married with two children in 1767.   He must have married in Denmark shortly after his arrival, which allowed for him to have a child born in 1759. This child would have been 7 years old in 1766, when the Kulberg Reports were originally created.  The list also includes the name of his wife, Susanna, and two daughters, Margaretha, 8, and Maria, 2. 
The Volga German transport list, however, does not list Margaretha, the oldest daughter who at this time would have been nine years old.  It's possible she died in Oranienbaum, but we cannot be sure from these records. The transport list adds a son, Johann Kaeyser, who was 1 year 3 months old and died enroute to Grimm.  Daughter Maria also perished before reaching Grimm. 
According to Dr. Brent Mai, many Germans perished on the journey to their new colonies along the Volga. There were also deaths from raiding Mongols and other nomadic tribes who lived in the Volga area and battled the settlers for their land.
By 1770, Ludwig Kaiser had married Eva Maria Reisig and their first child was born in 1771.
1775 Grimm Census 
1798 Grimm Census 
Ludwig Kaiser does not appear in the 1834 Grimm census, and the most likely explanation is that he was deceased. Had he survived, he would have been 92 years old.
There is an Eleonora Kaiser who appears in the 1798 census with a given age of 18, making her birth year around 1780. There is no indication in the 1798 census that she was from another Volga German colony, so she was born in Grimm to one of the two Kaiser families:
She was born after the 1775 census, but married before the 1798 census, meaning that she never appeared in a census with her birth parents. It is virtually impossible to identify her lineage using census records. What we can do, however, is check to see how close she lived to both Kaiser families in each census, since Volga German families tended to live near each other and/or marry people who lived close to them.
I reviewed the census records and noted the household numbers for each family during the 1798 and 1834 censuses.
A comparison of these numbers shows that Eleonora Kaiser Bürkheim lived closer to Ludwig Kaiser and his children during the time between the 1798 and 1834 censuses. This is the only clue we have to discovering who her parents were. Studying the maternal haplogroup of Eleonora's female descendants and/or knowing the haplogroup of her mother could also help narrow down her maternal ancestry possibilities.
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