22,338 research outputs found
Evaluating Data Assimilation Algorithms
Data assimilation leads naturally to a Bayesian formulation in which the
posterior probability distribution of the system state, given the observations,
plays a central conceptual role. The aim of this paper is to use this Bayesian
posterior probability distribution as a gold standard against which to evaluate
various commonly used data assimilation algorithms.
A key aspect of geophysical data assimilation is the high dimensionality and
low predictability of the computational model. With this in mind, yet with the
goal of allowing an explicit and accurate computation of the posterior
distribution, we study the 2D Navier-Stokes equations in a periodic geometry.
We compute the posterior probability distribution by state-of-the-art
statistical sampling techniques. The commonly used algorithms that we evaluate
against this accurate gold standard, as quantified by comparing the relative
error in reproducing its moments, are 4DVAR and a variety of sequential
filtering approximations based on 3DVAR and on extended and ensemble Kalman
filters.
The primary conclusions are that: (i) with appropriate parameter choices,
approximate filters can perform well in reproducing the mean of the desired
probability distribution; (ii) however they typically perform poorly when
attempting to reproduce the covariance; (iii) this poor performance is
compounded by the need to modify the covariance, in order to induce stability.
Thus, whilst filters can be a useful tool in predicting mean behavior, they
should be viewed with caution as predictors of uncertainty. These conclusions
are intrinsic to the algorithms and will not change if the model complexity is
increased, for example by employing a smaller viscosity, or by using a detailed
NWP model
The path inference filter: model-based low-latency map matching of probe vehicle data
We consider the problem of reconstructing vehicle trajectories from sparse
sequences of GPS points, for which the sampling interval is between 10 seconds
and 2 minutes. We introduce a new class of algorithms, called altogether path
inference filter (PIF), that maps GPS data in real time, for a variety of
trade-offs and scenarios, and with a high throughput. Numerous prior approaches
in map-matching can be shown to be special cases of the path inference filter
presented in this article. We present an efficient procedure for automatically
training the filter on new data, with or without ground truth observations. The
framework is evaluated on a large San Francisco taxi dataset and is shown to
improve upon the current state of the art. This filter also provides insights
about driving patterns of drivers. The path inference filter has been deployed
at an industrial scale inside the Mobile Millennium traffic information system,
and is used to map fleets of data in San Francisco, Sacramento, Stockholm and
Porto.Comment: Preprint, 23 pages and 23 figure
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