Particle filters, was first coined in 1996 by Del Moral, are a set of genetic-type particle Monte Carlo methodologies to solve the filtering problem. It is also known as Sequential Monte Carlo. Particle filters implement the prediction-updating transitions of the filtering equation directly by using a genetic type mutation-selection particle algorithm. Kalman filters have much lower computational requirements than particle filters, but are less flexible. Basically, the math works out so that estimators for this sort of system have a very nice solution.
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