The close approach of the asteroid that we have all read about in the newspapers represents something of a coincidence for me as I prepare for the data assimilation workshop in Banff this coming week. Gauss invented data assimilation as we know it for the purpose of calculating asteroid orbits. The orbit of an asteroid around the sun is determined by six parameters. Given observations of an asteroid, he chose the parameters that would minimize the sum of squared differences between the observed and predicted values. I don’t know whether he considered more complicated orbital calculations that would have taken the gravity fields of Jupiter or Mars into account. Why Gauss would have spent his time doing this I don’t know. Two centuries later, most data assimilation systems still rely on least squares.
Some may question Gauss’ title as inventor of data assimilation, as Legendre did at the time. Eric Temple Bell, in one of his books, described an exchange of letters between Gauss and Legendre, in which Legendre pointed out that he had published the least squares method before Gauss’ paper on asteroid orbits appeared. Legendre humbly asked Gauss to acknowledge his proudest achievement. Surely Gauss, for all his great accomplishments, could acknowledge what Legendre described in a charming biblical reference as “My one ewe lamb.” Gauss refused, saying that he had, in fact, formulated the least squares method independently before Legendre. This turned out to be true. The least squares method appeared in Gauss’ notebooks before Legendre’s paper, but Legendre published first.
It’s likely, though not certain, that the accounts in the media of the asteroid that recently passed within the orbits of our geostationary satellites are based on least squares calculations. There are alternatives. Someone once told me that the trajectory of the European Space Agency’s Ariane launch vehicle is calculated by probabilistic methods based on the theory of stochastic differential equations. I asked him how they did that, and he laughed and said “Oh, they will not tell you.” However they do it, it’s a hard calculation, probably impossible without electronic computing machinery, even given Gauss’ legendary calculating abilities.
College of Earth, Ocean, and Atmospheric Sciences
Oregon State University