Abstract
Recently, a novel method for developing filtering algorithms, based on the interconnection of two Bayesian filters and called double Bayesian filtering, has been proposed. In this manuscript we show that the same conceptual approach can be exploited to devise a new smoothing method, called double Bayesian smoothing. A double Bayesian smoother combines a double Bayesian filter, employed in its forward pass, with the interconnection of two backward information filters used in its backward pass. As a specific application of our general method, a detailed derivation of double Bayesian smoothing algorithms for conditionally linear Gaussian systems is illustrated. Numerical results for two specific dynamic systems evidence that these algorithms can achieve a better complexity-accuracy tradeoff and tracking capability than other smoothing techniques recently appeared in the literature.
Highlights
The problem of Bayesian smoothing for a state space model (SSM) concerns the development of recursive algorithms able to estimate the probability density function of the model state on a given observation interval, given a batch of noisy measurements acquired over it [1], [2]; the estimated pdf is known as a smoothed or smoothing pdf
In that manuscript, we focus on conditionally linear Gaussian models, but assume that the forward pass is accomplished by marginalized particle filtering (MPF; known as Rao-Blackwellized particle filtering); in other words, Bayesian filtering is based on the interconnection of a particle filter with a bank of Kalman filters
Is the acceleration due to a force applied to the agent, a0 is a scale factor, d0 is a reference distance, and np,k is an additive Gaussian noise (AGN) vector characterized by the covariance matrix σp2 I2 and accounting for model inaccuracy
Summary
The problem of Bayesian smoothing for a state space model (SSM) concerns the development of recursive algorithms able to estimate the probability density function (pdf) of the model state on a given observation interval, given a batch of noisy measurements acquired over it [1], [2]; the estimated pdf is known as a smoothed or smoothing pdf. 2) Different approximations can be used for the predicted/filtered/smoothed pdfs computed in the message passing on each of the two sub-graphs and for the involved Markov/observation models For this reason, generally speaking, the two interconnected filtering/BIF/smoothing algorithms are not required to be of the same type. Iterative message passing on the devised graphical model involves both the couple of measurement updates and the backward prediction accomplished in each of the interconnected backward information filters This should allow each filter to progressively refine the nuisance substate density employed in its second measurement update and backward prediction, and improve the quality of the pseudo-measurements exploited in its first measurement update. We first describe the graphical models on which these algorithms are based; we provide a detailed description of the computed messages and their scheduling in a specific case
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