169,448 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
Spectral rate theory for projected two-state kinetics
Classical rate theories often fail in cases where the observable(s) or order
parameter(s) used are poor reaction coordinates or the observed signal is
deteriorated by noise, such that no clear separation between reactants and
products is possible. Here, we present a general spectral two-state rate theory
for ergodic dynamical systems in thermal equilibrium that explicitly takes into
account how the system is observed. The theory allows the systematic estimation
errors made by standard rate theories to be understood and quantified. We also
elucidate the connection of spectral rate theory with the popular Markov state
modeling (MSM) approach for molecular simulation studies. An optimal rate
estimator is formulated that gives robust and unbiased results even for poor
reaction coordinates and can be applied to both computer simulations and
single-molecule experiments. No definition of a dividing surface is required.
Another result of the theory is a model-free definition of the reaction
coordinate quality (RCQ). The RCQ can be bounded from below by the directly
computable observation quality (OQ), thus providing a measure allowing the RCQ
to be optimized by tuning the experimental setup. Additionally, the respective
partial probability distributions can be obtained for the reactant and product
states along the observed order parameter, even when these strongly overlap.
The effects of both filtering (averaging) and uncorrelated noise are also
examined. The approach is demonstrated on numerical examples and experimental
single-molecule force probe data of the p5ab RNA hairpin and the apo-myoglobin
protein at low pH, here focusing on the case of two-state kinetics
Technical Report: Compressive Temporal Higher Order Cyclostationary Statistics
The application of nonlinear transformations to a cyclostationary signal for
the purpose of revealing hidden periodicities has proven to be useful for
applications requiring signal selectivity and noise tolerance. The fact that
the hidden periodicities, referred to as cyclic moments, are often compressible
in the Fourier domain motivates the use of compressive sensing (CS) as an
efficient acquisition protocol for capturing such signals. In this work, we
consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS)
estimators when CS is used to acquire the cyclostationary signal assuming
compressible cyclic moments in the Fourier domain. We develop a theoretical
framework for estimating THOCS using the low-rate nonuniform sampling protocol
from CS and illustrate the performance of this framework using simulated data
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