5,957 research outputs found
A cloudy Vlasov solution
We propose to integrate the Vlasov-Poisson equations giving the evolution of
a dynamical system in phase-space using a continuous set of local basis
functions. In practice, the method decomposes the density in phase-space into
small smooth units having compact support. We call these small units ``clouds''
and choose them to be Gaussians of elliptical support. Fortunately, the
evolution of these clouds in the local potential has an analytical solution,
that can be used to evolve the whole system during a significant fraction of
dynamical time. In the process, the clouds, initially round, change shape and
get elongated. At some point, the system needs to be remapped on round clouds
once again. This remapping can be performed optimally using a small number of
Lucy iterations. The remapped solution can be evolved again with the cloud
method, and the process can be iterated a large number of times without showing
significant diffusion. Our numerical experiments show that it is possible to
follow the 2 dimensional phase space distribution during a large number of
dynamical times with excellent accuracy. The main limitation to this accuracy
is the finite size of the clouds, which results in coarse graining the
structures smaller than the clouds and induces small aliasing effects at these
scales. However, it is shown in this paper that this method is consistent with
an adaptive refinement algorithm which allows one to track the evolution of the
finer structure in phase space. It is also shown that the generalization of the
cloud method to the 4 dimensional and the 6 dimensional phase space is quite
natural.Comment: 46 pages, 25 figures, submitted to MNRA
Adaptive Estimation and Heuristic Optimization of Nonlinear Spacecraft Attitude Dynamics
For spacecraft conducting on-orbit operations, changes to the structure of the spacecraft are not uncommon. These planned or unanticipated changes in inertia properties couple with the spacecraft\u27s attitude dynamics and typically require estimation. For systems with time-varying inertia parameters, multiple model adaptive estimation (MMAE) routines can be utilized for parameter and state estimates. MMAE algorithms involve constructing a bank of recursive estimators, each assuming a different hypothesis for the systems dynamics. This research has three distinct, but related, contributions to satellite attitude dynamics and estimation. In the first part of this research, MMAE routines employing parallel banks of unscented attitude filters are applied to analytical models of spacecraft with time-varying mass moments of inertia (MOI), with the objective of estimating the MOI and classifying the spacecraft\u27s behavior. New adaptive estimation techniques were either modified or developed that can detect discontinuities in MOI up to 98 of the time in the specific problem scenario.Second, heuristic optimization techniques and numerical methods are applied to Wahba\u27s single-frame attitude estimation problem,decreasing computation time by an average of nearly 67 . Finally, this research poses MOI estimation as an ODE parameter identification problem, achieving successful numerical estimates through shooting methods and exploiting the polhodes of rigid body motion with results, on average, to be within 1 to 5 of the true MOI values
Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying
We study the problem of channel pairing and power allocation in a
multichannel multihop relay network to enhance the end-to-end data rate. Both
amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are
considered. Given fixed power allocation to the channels, we show that channel
pairing over multiple hops can be decomposed into independent pairing problems
at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal,
where each relay pairs its incoming and outgoing channels by their SNR order.
For the joint optimization of channel pairing and power allocation under both
total and individual power constraints, we show that the problem can be
decoupled into two subproblems solved separately. This separation principle is
established by observing the equivalence between sorting SNRs and sorting
channel gains in the jointly optimal solution. It significantly reduces the
computational complexity in finding the jointly optimal solution. It follows
that the channel pairing problem in joint optimization can be again decomposed
into independent pairing problems at each relay based on sorted channel gains.
The solution for optimizing power allocation for DF relaying is also provided,
as well as an asymptotically optimal solution for AF relaying. Numerical
results are provided to demonstrate substantial performance gain of the jointly
optimal solution over some suboptimal alternatives. It is also observed that
more gain is obtained from optimal channel pairing than optimal power
allocation through judiciously exploiting the variation among multiple
channels. Impact of the variation of channel gain, the number of channels, and
the number of hops on the performance gain is also studied through numerical
examples.Comment: 15 pages. IEEE Transactions on Signal Processin
Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying
We study the problem of channel pairing and power allocation in a
multichannel multihop relay network to enhance the end-to-end data rate. Both
amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are
considered. Given fixed power allocation to the channels, we show that channel
pairing over multiple hops can be decomposed into independent pairing problems
at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal,
where each relay pairs its incoming and outgoing channels by their SNR order.
For the joint optimization of channel pairing and power allocation under both
total and individual power constraints, we show that the problem can be
decoupled into two subproblems solved separately. This separation principle is
established by observing the equivalence between sorting SNRs and sorting
channel gains in the jointly optimal solution. It significantly reduces the
computational complexity in finding the jointly optimal solution. It follows
that the channel pairing problem in joint optimization can be again decomposed
into independent pairing problems at each relay based on sorted channel gains.
The solution for optimizing power allocation for DF relaying is also provided,
as well as an asymptotically optimal solution for AF relaying. Numerical
results are provided to demonstrate substantial performance gain of the jointly
optimal solution over some suboptimal alternatives. It is also observed that
more gain is obtained from optimal channel pairing than optimal power
allocation through judiciously exploiting the variation among multiple
channels. Impact of the variation of channel gain, the number of channels, and
the number of hops on the performance gain is also studied through numerical
examples.Comment: 15 pages. IEEE Transactions on Signal Processin
Fast Selection of Spectral Variables with B-Spline Compression
The large number of spectral variables in most data sets encountered in
spectral chemometrics often renders the prediction of a dependent variable
uneasy. The number of variables hopefully can be reduced, by using either
projection techniques or selection methods; the latter allow for the
interpretation of the selected variables. Since the optimal approach of testing
all possible subsets of variables with the prediction model is intractable, an
incremental selection approach using a nonparametric statistics is a good
option, as it avoids the computationally intensive use of the model itself. It
has two drawbacks however: the number of groups of variables to test is still
huge, and colinearities can make the results unstable. To overcome these
limitations, this paper presents a method to select groups of spectral
variables. It consists in a forward-backward procedure applied to the
coefficients of a B-Spline representation of the spectra. The criterion used in
the forward-backward procedure is the mutual information, allowing to find
nonlinear dependencies between variables, on the contrary of the generally used
correlation. The spline representation is used to get interpretability of the
results, as groups of consecutive spectral variables will be selected. The
experiments conducted on NIR spectra from fescue grass and diesel fuels show
that the method provides clearly identified groups of selected variables,
making interpretation easy, while keeping a low computational load. The
prediction performances obtained using the selected coefficients are higher
than those obtained by the same method applied directly to the original
variables and similar to those obtained using traditional models, although
using significantly less spectral variables
Adaptive control of large space structures using recursive lattice filters
The use of recursive lattice filters for identification and adaptive control of large space structures is studied. Lattice filters were used to identify the structural dynamics model of the flexible structures. This identification model is then used for adaptive control. Before the identified model and control laws are integrated, the identified model is passed through a series of validation procedures and only when the model passes these validation procedures is control engaged. This type of validation scheme prevents instability when the overall loop is closed. Another important area of research, namely that of robust controller synthesis, was investigated using frequency domain multivariable controller synthesis methods. The method uses the Linear Quadratic Guassian/Loop Transfer Recovery (LQG/LTR) approach to ensure stability against unmodeled higher frequency modes and achieves the desired performance
Using Automatic Differentiation as a General Framework for Ptychographic Reconstruction
Coherent diffraction imaging methods enable imaging beyond lens-imposed
resolution limits. In these methods, the object can be recovered by minimizing
an error metric that quantifies the difference between diffraction patterns as
observed, and those calculated from a present guess of the object. Efficient
minimization methods require analytical calculation of the derivatives of the
error metric, which is not always straightforward. This limits our ability to
explore variations of basic imaging approaches. In this paper, we propose to
substitute analytical derivative expressions with the automatic differentiation
method, whereby we can achieve object reconstruction by specifying only the
physics-based experimental forward model. We demonstrate the generality of the
proposed method through straightforward object reconstruction for a variety of
complex ptychographic experimental models.Comment: 23 pages (including references and supplemental material), 19
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