27,889 research outputs found
A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements
Multipath propagation causes major impairments to Global
Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step
Scalable Inference for Markov Processes with Intractable Likelihoods
Bayesian inference for Markov processes has become increasingly relevant in
recent years. Problems of this type often have intractable likelihoods and
prior knowledge about model rate parameters is often poor. Markov Chain Monte
Carlo (MCMC) techniques can lead to exact inference in such models but in
practice can suffer performance issues including long burn-in periods and poor
mixing. On the other hand approximate Bayesian computation techniques can allow
rapid exploration of a large parameter space but yield only approximate
posterior distributions. Here we consider the combined use of approximate
Bayesian computation (ABC) and MCMC techniques for improved computational
efficiency while retaining exact inference on parallel hardware
The iterated auxiliary particle filter
We present an offline, iterated particle filter to facilitate statistical
inference in general state space hidden Markov models. Given a model and a
sequence of observations, the associated marginal likelihood L is central to
likelihood-based inference for unknown statistical parameters. We define a
class of "twisted" models: each member is specified by a sequence of positive
functions psi and has an associated psi-auxiliary particle filter that provides
unbiased estimates of L. We identify a sequence psi* that is optimal in the
sense that the psi*-auxiliary particle filter's estimate of L has zero
variance. In practical applications, psi* is unknown so the psi*-auxiliary
particle filter cannot straightforwardly be implemented. We use an iterative
scheme to approximate psi*, and demonstrate empirically that the resulting
iterated auxiliary particle filter significantly outperforms the bootstrap
particle filter in challenging settings. Applications include parameter
estimation using a particle Markov chain Monte Carlo algorithm
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