About Sargent there's so much that can be said. He was close to Lucas and those people. Sargent and Sims' works are tightly interrelated, however it's hard to see Sims as subscribing to Sargent's insistence on micro-foundations. Sims seems to me a more pragmatic, salt-water type, and micro-foundations probably seem to him as trying to based astrophysics on the principles of quantum mechanics. Telegraphically: Before the Stokey, Lucas, and Prescott book was published, Sargent's macro books were *the* intro grad textbooks in macro. He got curious about the 1980s "complexity" project (along with Arrow) but then he dropped out. His book with Lars Ljungqvist (not to be confused with Lars Hansen) on recursive macro will now get more recognition. In it, he emphasized the mathematical unity of VARs, dynamic programming (Newton's variational calculus reworked as a recursive procedure that is more convenient with discrete data), and the Kalman filter. I think this is neat. Geometrically, regressing estimated y = X b is the same as taking the projection X (X′X)^{-1} X′ on y, the actual observed y. So you can interpret Kalman as recursive projection. The mathematical trick to Kalman is the state-space specification ("representation") of the system.
If you have intro training in econometrics, here is an easy way to view the Kalman filter. By contrast with the simplest model, y_t = b0 + b1 x_1t + e_t, where the b0, b1, and e_t are all fixed parameters to be estimated, the Kalman filter allows one to specify the model as y_t = b0_t + b1_t x_1t + e_t and squeeze information from the data to update the value of the parameters over time. I myself used the filter (in a paper co-authored with my friends Jason Hecht and Mihail Velikov, http://www.opf.slu.cz/kfi/icfb/proc2009/pdf/15_Huato.pdf) to generate time series for the forex betas on main currencies for over a thousand European firms. The dataset on forex betas is unused as the three of us moved on to other things.