15,661 research outputs found
Trajectory Synthesis for Fisher Information Maximization
Estimation of model parameters in a dynamic system can be significantly
improved with the choice of experimental trajectory. For general, nonlinear
dynamic systems, finding globally "best" trajectories is typically not
feasible; however, given an initial estimate of the model parameters and an
initial trajectory, we present a continuous-time optimization method that
produces a locally optimal trajectory for parameter estimation in the presence
of measurement noise. The optimization algorithm is formulated to find system
trajectories that improve a norm on the Fisher information matrix. A
double-pendulum cart apparatus is used to numerically and experimentally
validate this technique. In simulation, the optimized trajectory increases the
minimum eigenvalue of the Fisher information matrix by three orders of
magnitude compared to the initial trajectory. Experimental results show that
this optimized trajectory translates to an order of magnitude improvement in
the parameter estimate error in practice.Comment: 12 page
Cosmology with anisotropic galaxy clustering from the combination of power spectrum and bispectrum
The apparent anisotropies of the galaxy clustering in observable redshift
space provide a unique opportunity to simultaneously probe cosmic expansion and
gravity on cosmological scales via the Alcock--Paczynski effect and
redshift-space distortions. While the improved theoretical models have been
proposed and developed to describe the apparent anisotropic clustering at
weakly non-linear scales, the applicability of these models is still limited in
the presence of the non--perturbative smearing effect caused by the randomness
of the relative velocities. Although the cosmological constraint from the
anisotropic clustering will be certainly improved with a more elaborate
theoretical model, we here consider an alternative way by using the statistical
power of both the power spectrum and bispectrum at large scales. Based on the
Fisher matrix analysis, we estimate the benefit of combining the power spectra
and bispectra, finding that the constraints on the cosmic expansion and growth
of structure will be improved by a factor of two. This compensates for the loss
of constraining power using the power spectrum alone due to the randomness of
the relative velocities.Comment: 11 pages, 8 figures, preprint number YITP-15-
Adaptive Designs for Optimal Observed Fisher Information
Expected Fisher information can be found a priori and as a result its inverse
is the primary variance approximation used in the design of experiments. This
is in contrast to the common claim that the inverse of observed Fisher
information is a better approximation to the variance of the maximum likelihood
estimator. Observed Fisher information cannot be known a priori; however, if an
experiment is conducted sequentially (in a series of runs) the observed Fisher
information from previous runs is available. In the current work two adaptive
designs are proposed that use the observed Fisher information from previous
runs in the design of the current run.Comment: 19 pages, 2 figure
Determine measurement set for parameter estimation in biological systems modeling
Parameter estimation is challenging for biological systems modelling since the model is normally of high dimension, the measurement data are sparse and noisy, and the cost of experiments is high. Accurate recovery of parameters depend on the quantity and quality of measurement data. It is therefore important to know what measurements to be taken, when and how through optimal experimental design (OED). In this paper we present a method to determine the most informative measurement set for parameter estimation of dynamic systems, in particular biochemical reaction systems, such that the unknown parameters can be inferred with the best possible statistical quality using the data collected from the designed experiments. System analysis using matrix theory is introduced to examine the number of necessary measurement variables. The priority of each measurement variable is determined by optimal experimental design based on Fisher information matrix (FIM). The applicability and advantages of the proposed method are illustrated through an example of a signal pathway model
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Motion Planning for Optimal Information Gathering in Opportunistic Navigation Systems
Motion planning for optimal information gathering in an opportunistic navigation (OpNav)
environment is considered. An OpNav environment can be thought of as a radio
frequency signal landscape within which a receiver locates itself in space and time by extracting
information from ambient signals of opportunity (SOPs). The receiver is assumed
to draw only pseudorange-type observations from the SOPs, and such observations are
fused through an estimator to produce an estimate of the receiver’s own states. Since
not all SOP states in the OpNav environment may be known a priori, the receiver must
estimate the unknown SOP states of interest simultaneously with its own states. In this
work, the following problem is studied. A receiver with no a priori knowledge about its
own states is dropped in an unknown, yet observable, OpNav environment. Assuming that
the receiver can prescribe its own trajectory, what motion planning strategy should the
receiver adopt in order to build a high-fidelity map of the OpNav signal landscape, while
simultaneously localizing itself within this map in space and time? To answer this question,
first, the minimum conditions under which the OpNav environment is fully observable are
established, and the need for receiver maneuvering to achieve full observability is highlighted.
Then, motivated by the fact that not all trajectories a receiver may take in the
environment are equally beneficial from an information gathering point of view, a strategy
for planning the motion of the receiver is proposed. The strategy is formulated in a
coupled estimation and optimal control framework of a gradually identified system, where
optimality is defined through various information-theoretic measures. Simulation results
are presented to illustrate the improvements gained from adopting the proposed strategy
over random and pre-defined receiver trajectories.Aerospace Engineering and Engineering Mechanic
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