1,235 research outputs found
Sampling from a system-theoretic viewpoint
This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. \ud
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The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the -norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is -causal for a given i.e., that its impulse response is zero in the time interval where is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function
Colored noise effects on batch attitude accuracy estimates
The effects of colored noise on the accuracy of batch least squares parameter estimates with applications to attitude determination cases are investigated. The standard approaches used for estimating the accuracy of a computed attitude commonly assume uncorrelated (white) measurement noise, while in actual flight experience measurement noise often contains significant time correlations and thus is colored. For example, horizon scanner measurements from low Earth orbit were observed to show correlations over many minutes in response to large scale atmospheric phenomena. A general approach to the analysis of the effects of colored noise is investigated, and interpretation of the resulting equations provides insight into the effects of any particular noise color and the worst case noise coloring for any particular parameter estimate. It is shown that for certain cases, the effects of relatively short term correlations can be accommodated by a simple correction factor. The errors in the predicted accuracy assuming white noise and the reduced accuracy due to the suboptimal nature of estimators that do not take into account the noise color characteristics are discussed. The appearance of a variety of sample noise color characteristics are demonstrated through simulation, and their effects are discussed for sample estimation cases. Based on the analysis, options for dealing with the effects of colored noise are discussed
Cram\'er-Rao bounds for synchronization of rotations
Synchronization of rotations is the problem of estimating a set of rotations
R_i in SO(n), i = 1, ..., N, based on noisy measurements of relative rotations
R_i R_j^T. This fundamental problem has found many recent applications, most
importantly in structural biology. We provide a framework to study
synchronization as estimation on Riemannian manifolds for arbitrary n under a
large family of noise models. The noise models we address encompass zero-mean
isotropic noise, and we develop tools for Gaussian-like as well as heavy-tail
types of noise in particular. As a main contribution, we derive the
Cram\'er-Rao bounds of synchronization, that is, lower-bounds on the variance
of unbiased estimators. We find that these bounds are structured by the
pseudoinverse of the measurement graph Laplacian, where edge weights are
proportional to measurement quality. We leverage this to provide interpretation
in terms of random walks and visualization tools for these bounds in both the
anchored and anchor-free scenarios. Similar bounds previously established were
limited to rotations in the plane and Gaussian-like noise
Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
The paper addresses the problem of learning a regression model parameterized
by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear
nature of the search space and on scalability to high-dimensional problems. The
mathematical developments rely on the theory of gradient descent algorithms
adapted to the Riemannian geometry that underlies the set of fixed-rank
positive semidefinite matrices. In contrast with previous contributions in the
literature, no restrictions are imposed on the range space of the learned
matrix. The resulting algorithms maintain a linear complexity in the problem
size and enjoy important invariance properties. We apply the proposed
algorithms to the problem of learning a distance function parameterized by a
positive semidefinite matrix. Good performance is observed on classical
benchmarks
Resource-aware motion control:feedforward, learning, and feedback
Controllers with new sampling schemes improve motion systems’ performanc
Finite worldlength effects in fixed-point implementations of linear systems
Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 173-194).by Vinay Mohta.M.Eng
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