654 research outputs found
On Approximate Nonlinear Gaussian Message Passing On Factor Graphs
Factor graphs have recently gained increasing attention as a unified
framework for representing and constructing algorithms for signal processing,
estimation, and control. One capability that does not seem to be well explored
within the factor graph tool kit is the ability to handle deterministic
nonlinear transformations, such as those occurring in nonlinear filtering and
smoothing problems, using tabulated message passing rules. In this
contribution, we provide general forward (filtering) and backward (smoothing)
approximate Gaussian message passing rules for deterministic nonlinear
transformation nodes in arbitrary factor graphs fulfilling a Markov property,
based on numerical quadrature procedures for the forward pass and a
Rauch-Tung-Striebel-type approximation of the backward pass. These message
passing rules can be employed for deriving many algorithms for solving
nonlinear problems using factor graphs, as is illustrated by the proposition of
a nonlinear modified Bryson-Frazier (MBF) smoother based on the presented
message passing rules
Quadrature filters for one-step randomly delayed measurements
In this paper, two existing quadrature filters, viz., the GaussāHermite filter (GHF) and the sparse-grid GaussāHermite filter (SGHF) are extended to solve nonlinear filtering problems with one step randomly delayed measurements. The developed filters are applied to solve a maneuvering target tracking problem with one step randomly delayed measurements. Simulation results demonstrate the enhanced accuracy of the proposed delayed filters compared to the delayed cubature Kalman filter and delayed unscented Kalman filter
Estimating model evidence using data assimilation
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual modelāwhich corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurredāand a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensembleāDA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble fourādimensional variational smoother (Enā4DāVar), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated timeādependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz threeāvariable convection model (L63), and (ii) the Lorenz 40āvariable midlatitude atmospheric dynamics model (L95). The numerical results of these three DAābased methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DAābased methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution
Computational guidance using sparse Gauss-Hermite quadrature differential dynamic programming
This paper proposes a new computational guidance algorithm using differential dynamic programming and sparse Gauss-Hermite quadrature rule. By the application of sparse Gauss-Hermite quadrature rule, numerical differentiation in the calculation of Hessian matrices and gradients in differential dynamic programming is avoided. Based on the new differential dynamic programming approach developed, a three-dimensional computational algorithm is proposed to control the impact angle and impact time for an air-to-surface interceptor. Extensive numerical simulations are performed to show the effectiveness of the proposed approach
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