653 research outputs found
Computable infinite dimensional filters with applications to discretized diffusion processes
Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved
signal (xn) is a Markov chain and the observed component is such that, given
the whole sequence (xn), the random variables (yn) are independent and the
conditional distribution of yn only depends on the corresponding state variable
xn. The main problems raised by these observations are the prediction and
filtering of (xn). We introduce sufficient conditions allowing to obtain
computable filters using mixtures of distributions. The filter system may be
finite or infinite dimensional. The method is applied to the case where the
signal xn = Xn is a discrete sampling of a one dimensional diffusion process:
Concrete models are proved to fit in our conditions. Moreover, for these
models, exact likelihood inference based on the observation (y0,...,yn) is
feasable
Computing aspects of problems in non-linear prediction and filtering
Imperial Users onl
Some results on Tchebycheffian spline functions
AbstractThis report derives explicit solutions to problems involving Tchebycheffian spline functions. We use a reproducing kernel Hilbert space which depends on the smoothness criterion, but not on the form of the data, to solve explicitly Hermite-Birkhoff interpolation and smoothing problems. Sard's best approximation to linear functionals and smoothing with respect to linear inequality constraints are also discussed. Some of the results are used to show that spline interpolation and smoothing is equivalent to prediction and filtering on realizations of certain stochastic processes
Analytic Moment-based Gaussian Process Filtering
We propose an analytic moment-based filter for nonlinear stochastic dynamic systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction step and the filter step, where an additional Gaussian assumption is exploited in the latter case. Our filter does not require further approximations. In particular, it avoids finite-sample approximations. We compare the filter to a variety of Gaussian filters, that is, the EKF, the UKF, and the recent GP-UKF proposed by Ko et al. (2007). copyright 2009
A Bayesian Filtering Algorithm for Gaussian Mixture Models
A Bayesian filtering algorithm is developed for a class of state-space
systems that can be modelled via Gaussian mixtures. In general, the exact
solution to this filtering problem involves an exponential growth in the number
of mixture terms and this is handled here by utilising a Gaussian mixture
reduction step after both the time and measurement updates. In addition, a
square-root implementation of the unified algorithm is presented and this
algorithm is profiled on several simulated systems. This includes the state
estimation for two non-linear systems that are strictly outside the class
considered in this paper
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