Bayesian Inference in Dynamic Models - Minka, Tom (2007)
The following algorithms all try to infer the hidden state of a dynamic model from measurements. The input is a dynamic model and a measurement sequence and the output is an approximate posterior distribution over the hidden state at one or many times. Only discrete-time models are discussed here. Inferring only the most recent hidden state is known as filtering; inferring past states is known as smoothing. Most filtering methods are on-line, which means they process each measurement exactly once, after which it can be discarded. This allows them to operate with a fixed amount of memory. The opposite of on-line is off-line or batch. There are standard ways to turn an on-line filtering algorithm into a batch filtering or smoothing algorithm. Therefore, the overview is divided into two parts: on-line filtering and batch filtering/smoothing. Some of these algorithms are general algorithms for approximate Bayesian inference and others are specialized for dynamic models. With the description of each algorithm is a partial list of references. I've included more references for algorithms which are less well-known.