Riassunto analitico
In this work the filtering and smoothing problems for state space models are analysed from a factor graph perspective. First, it is shown how factor graphs can be used to represent filtering and marginalized particle filtering. Then, a method for developing novel filtering algorithms through the parallel concatenation of two (constituent) Bayesian filters is illustrated. The description of this method, called turbo filtering for its conceptual resemblance to the turbo decoding of concatenated channel codes, is based on a novel graphical model; this allows to efficiently describe both the processing accomplished by each constituent filter and the interactions between them. This model is exploited to develop two new filtering algorithms, called turbo filters, for conditionally linear Gaussian systems. Finally, the same conceptual approach is adopted to develop a new class of smoothing algorithms, called turbo smoothers. A turbo smoother combines a turbo filter, employed in its forward pass, with the parallel concatenation of two backward information filters in its backward pass. As a specific application of this general theory, a detailed derivation of two turbo smoothing algorithms for conditionally linear Gaussian systems is illustrated.
Numerical results for a specific dynamic system evidence that the developed algorithms can achieve a better complexity-accuracy tradeoff than other well known filtering and smoothing techniques available in the technical literature.
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