Case Of Noisy Measurements Research Articles

Parallel matching pursuit algorithm and analysis

For the existing compressed sensing greedy reconstruction algorithm, it is easy to fall into local optimum and overfitting problems. In this paper, we propose a new sparse recovery algorithm, called Parallel Matching pursuit (PMP), which searches the signal support set in both depth and breadth dimensions. PMP simultaneously examines multiple estimates of candidate support set in each iteration, and finally chooses the estimate that minimizes the reconstruction residual. Based on the restricted isometry property (RIP), sufficient conditions for PMP to reconstruct the signal are given to ensure that we can accurately recover any K-sparse signal from the measured value. Moreover, the recovery guarantee of the PMP algorithm is also provided for the case of noisy measurements. The performance of the PMP algorithm is evaluated by the signal reconstruction ability. Finally, numerical experiments verify the effectiveness of the algorithm.

A three-player Nash game for point-wise source identification in Cauchy–Stokes problems

We consider linear steady Stokes flow under the action of a finite number of particles located inside the flow domain. The particles exert point-wise forces on the fluid, and are unknown in number, location and magnitude. We are interested in the determination of these point-wise forces, using only a single pair of partially available Cauchy boundary measurements. The inverse problem then couples two harsh problems : identification of point-wise sources and recovery of missing boundary data. We reformulate it as a three-player Nash game. The first two players aim at recovering the Dirichlet and Neumann missing data, while the third one aims at the point-forces reconstruction of the number, location and magnitude of the point-forces. To illustrate the efficiency and robustness of the proposed algorithm, we finally present several numerical experiments for different geometries and source distribution, including the case of noisy measurements.

Multipath least squares algorithm and analysis

One important task in signal processing is to construct effective algorithms to reconstruct sparse signals from an underdetermined system of linear equations. In this paper, we propose a new sparse recovery algorithm called multipath least squares (MLS), which investigates multiple promising candidates per step and parallels the multipath matching pursuit (MMP) algorithm in this aspect. The performance of the MLS algorithm is evaluated through the ability of signal recovery. Specifically, a recovery guarantee based on the restricted isometry property (RIP) is established for MLS that ensures its exact recovery of any K-sparse signal x from the measurements y=Ax. It is also shown that this sufficient condition is nearly sharp by providing a counterexample such that the algorithm may fail to recover some K-sparse signal. Moreover, the recovery guarantee of the MLS algorithm is also provided for the case of noisy measurements. Finally, numerical experiments are conducted to demonstrate the validity and priority of the proposed algorithm.

A new bound on the block restricted isometry constant in compressed sensing

This paper focuses on the sufficient condition of block sparse recovery with the l_{2}/l_{1}-minimization. We show that if the measurement matrix satisfies the block restricted isometry property with delta_{2s|mathcal{I}}< 0.6246, then every block s-sparse signal can be exactly recovered via the l_{2}/l_{1}-minimization approach in the noiseless case and is stably recovered in the noisy measurement case. The result improves the bound on the block restricted isometry constant delta_{2s|mathcal {I}} of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, 2013).

Precoding for Robust Decentralized Estimation in Coherent-MAC-Based Wireless Sensor Networks

This letter proposes novel precoding techniques for robust decentralized parameter estimation with only imperfect channel state information (CSI) in a coherent multiple access channel based wireless sensor network. For scalar parameter estimation, the proposed technique minimizes the worst case estimation error arising due to the channel uncertainties while ensuring the maximum gain at each receive antenna. For vector parameter estimation, since the general noisy measurement case is intractable, a robust precoder is developed for noiseless sensor measurements that eliminates the need for postprocessing at the fusion center while simultaneously minimizing the worst case estimation error. Simulation results show that the proposed techniques have a superior performance in comparison to imperfect CSI agnostic estimation techniques.

Consensus of double-integrator multi-agent systems without relative state derivatives under communication noises and directed topologies

This paper presents a consensus algorithm for continuous-time double-integrator multi-agent systems with measurement/communication noises under directed fixed and switching topologies. The paper employs the algebraic graph theory and the stochastic tools to develop a consensus protocol in which a time-varying consensus gain is introduced to attenuate the additive white noises corrupting the information exchange between agents. Each agent׳s control input relies on its own information state and its neighbors׳ inaccurate information states and does not need the neighbors׳ information state derivatives. Conditions to guarantee mean square asymptotic convergence under noisy measurement for both fixed and switching topologies are derived. The consensus protocols developed in the noisy measurement case are proved to be still valid in the noise-free case, and they can ensure asymptotic mean square convergence. Finally, to illustrate the approach presented, some numerical simulations are carried out.

Nonlinear speed estimation of a GPS-free UAV

In this article, the problem of robust state observer design for a class of unmanned aerial vehicles (UAVs) is addressed. A prototype four-rotors helicopter robot for indoors and outdoors applications is considered: the drone is not equipped with GPS related devices, so we describe a strategy to estimate its translational velocity vector based on acceleration, angles and angular speeds measurements only. Since the linearised system is non-observable at the equilibrium point, a nonlinear observability verification is performed for persistently exciting trajectories. A global exponential solution to this open problem is provided in the framework of adaptive observation theory when exact measurements are available. A modified observer is presented to enhance velocity estimation robustness in the realistic case of noisy measurements. The results are compared with a classical estimation strategy based on the extended Kalman filter to test the algorithm's performance.

ADMiRA: Atomic Decomposition for Minimum Rank Approximation

In this paper, we address compressed sensing of a low-rank matrix posing the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target rank then provides the minimum rank solution satisfying a prescribed data approximation bound. We propose an atomic decomposition providing an analogy between parsimonious representations of a sparse vector and a low-rank matrix and extending efficient greedy algorithms from the vector to the matrix case. In particular, we propose an efficient and guaranteed algorithm named atomic decomposition for minimum rank approximation (ADMiRA) that extends Needell and Tropp's compressive sampling matching pursuit (CoSaMP) algorithm from the sparse vector to the low-rank matrix case. The performance guarantee is given in terms of the rank-restricted isometry property (R-RIP) and bounds both the number of iterations and the error in the approximate solution for the general case of noisy measurements and approximately low-rank solution. With a sparse measurement operator as in the matrix completion problem, the computation in ADMiRA is linear in the number of measurements. Numerical experiments for the matrix completion problem show that, although the R-RIP is not satisfied in this case, ADMiRA is a competitive algorithm for matrix completion.

Multichannel Sampling of Signals With Finite Rate of Innovation

In this letter, we present a possible extension of the theory of sampling signals with finite rate of innovation (FRI) to the case of multichannel acquisition systems. The essential issue of a multichannel system is that each channel introduces different unknown delays and gains that need to be estimated for the calibration of the channels. We pose both the synchronization stage and the signal reconstruction stage as a parametric estimation problem and demonstrate that a simultaneous exact synchronization of the channels and reconstruction of the FRI signal is possible. We also consider the case of noisy measurements and evaluate the Cramer-Rao bounds (CRB) of the proposed system. Numerical results as well as the CRB show clearly that multichannel systems are more resilient to noise than the single-channel ones.

Robust and Adaptive Observer-Based Partial Stabilization for a Class of Nonlinear Systems

The problem of adaptive stabilization with respect to a set for a class of nonlinear systems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case of noisy measurements is proposed. The efficiency of proposed solution is demonstrated via example of swinging a pendulum with unknown parameters.

Nonlinear attitude estimation based on fusion of inertial and magnetic sensors: Bio-logging application

AbstractThe aim of this paper concerns the 3D motion estimation problem using low-cost sensors fusion. This work will be applied in Bio-logging which is an interdisciplinary research area at the intersection of animal behavior and bioengineering. It refers to the use of miniaturized adapted-animal systems for logging and/or relaying of data about an animal's movements, physiology and/or environment. Generally, accurate attitude measurements are obtained using accelerometer and magnetometer, but at low frequencies movements. Then, to improve the performance and precision of the attitude estimation at high frequencies, we propose to add gyroscope and to develop an approach relaying on a quaternion-based nonlinear filter for the tracking of rigid body attitude (orientation) and heading. The algorithm fuses data from low-pass sensors such as 3-axis accelerometer, 3-axis magnetometer and high-pass sensor such as 3-axis gyroscope. Then, we exploit the sensor readings directly in the designed filter which lead to increase the computational requirements. Finally, the proposed approach is illustrated by an attitude estimation example in an experimental case of noisy measurements which shows the efficiency of the proposed algorithm.

Asymptotically Unbiased Average Consensus Under Measurement Noises and Fixed Topologies

This paper is concerned with average-consensus control under directed topologies and random measurement noises. To attenuate the measurement noises, time-varying consensus gains are introduced in the protocol. It is shown that under the protocol designed, all agents’ states converge to a common Gaussian random variable, whose mathematical expectation is just the average of the initial states, and the mean square static error vanishes as the number of agents increases to infinity under certain topologies. In addition, for the noise-free case, necessary and sufficient conditions are given on the network topology and consensus gains to achieve average-consensus; and for the noisy measurement case, by combining algebraic graph theory and stochastic analysis, necessary and sufficient conditions are given on the consensus gains to achieve asymptotically unbiased mean square average-consensus.

Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix

Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, nonuniform splines or piecewise polynomials, and call the number of degrees of freedom per unit of time the rate of innovation. Classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited. Recently, it was shown that, by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation, it is possible to reconstruct such signals uniquely . These sampling schemes, however, use kernels with infinite support, and this leads to complex and potentially unstable reconstruction algorithms. In this paper, we show that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm. The class of kernels that we can use is very rich and includes functions satisfying Strang-Fix conditions, exponential splines and functions with rational Fourier transform. This last class of kernels is quite general and includes, for instance, any linear electric circuit. We, thus, show with an example how to estimate a signal of finite rate of innovation at the output of an RC circuit. The case of noisy measurements is also analyzed, and we present a novel algorithm that reduces the effect of noise by oversampling

Theory of Aiming Control for Linear Stochastic Systems

The problem of aiming control is formulated and solved for linear time-invariant systems perturbed by small additive white noise. Both state feedback and dynamic output feedback laws are considered. In the case of dynamic output feedback, noiseless and noisy measurements are analyzed. In the noiseless measurement case it is shown that the fundamental bounds on the achievable precision of aiming may or may not be finite depending on the nonminimum phase zeros and the invertibility of the system. In the noisy measurement case the achievable precision of aiming is shown to be always bounded. Aiming controller design techniques that result in controllers compatible with the bounds are developed. The approach is based on the asymptotic large deviations theory.

A unified solution to the singular and nonsingular linear minimum-variance estimation problem

A unified solution is derived for the transfer function matrix of the minimum-variance estimator of the state of a linear continuous-time system with noisy or noise-free measurements. For the noisy measurement case, the Kalman-Bucy filter standard equations are used to give the general format of the transfer function. The Kalman-Bucy gain, using the spectral factorization on the algebraic in the S plane, is derived and substituted in the transfer-function expression. The singular case is then shown to be a special case of the noisy measurement estimator.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of noisy distributed parameter systems using stochastic approximation†

The parameter identification problem in systems governed by partial differential equations is investigated. Stochastic approximation algorithms are applied for identifying a class of distributed systems driven by random inputs and observed through noisy measurements. No restrictions about the probability distributions are imposed. These algorithms converge with probability one, and are suitable for on-line applications. The proposed identification method assumes that a previous system classification has been performed, such that the model to be identified is known up to a set of space-varying parameters, where extraneous terms may be included. The very real case of noisy measurements taken at a limited number of discrete points Located in the spatial domain is considered.

On the observability of non-linear systems with applications to non-linear regression analysis

Global inverse function theorems, applicable to the observability question, are presented. Comparisons are made to fixed point theorems and contraction mappings are shown to exist under general conditions. Extensions to the noisy measurement case are made.