Sigma Point Belief Propagation

The sigma point (SP) filter, also known as unscented Kalman filter, is an attractive alternative to the extended Kalman filter and the particle filter. Here, we extend the SP filter to nonsequential Bayesian inference corresponding to loopy factor graphs. We propose sigma point belief propagation (SPBP) as a low-complexity approximation of the belief propagation (BP) message passing scheme. SPBP achieves approximate marginalizations of posterior distributions corresponding to (generally) loopy factor graphs. It is well suited for decentralized inference because of its low communication requirements. For a decentralized, dynamic sensor localization problem, we demonstrate that SPBP can outperform nonparametric (particle-based) BP while requiring significantly less computations and communications.Comment: 5 pages, 1 figur

Scaled unscented transform Gaussian sum filter: theory and application

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf ... This work is on the construction of the Gaussian sum filter based on the scaled unscented transform

Statistical Inference in the Duffing System with the Unscented Kalman Filter

We investigate the accuracy of inference in a chaotic dynamical sys- tem (Duffing oscillator) with the Unscented Kalman Filter, and quantify the dependence on the sample size, the signal to noise ratio and the initialization

Automated weighing by sequential inference in dynamic environments

We demonstrate sequential mass inference of a suspended bag of milk powder from simulated measurements of the vertical force component at the pivot while the bag is being filled. We compare the predictions of various sequential inference methods both with and without a physics model to capture the system dynamics. We find that non-augmented and augmented-state unscented Kalman filters (UKFs) in conjunction with a physics model of a pendulum of varying mass and length provide rapid and accurate predictions of the milk powder mass as a function of time. The UKFs outperform the other method tested - a particle filter. Moreover, inference methods which incorporate a physics model outperform equivalent algorithms which do not.Comment: 5 pages, 7 figures. Copyright IEEE (2015