Set Of Noisy Measurements Research Articles

Space–Time Sampling for Network Observability

Designing sparse sampling strategies are crucial in having resilient estimation and control in networked systems as they make sampling less expensive and networks more resilient w.r.t where and when samples are collected. It is shown under what conditions taking coarse samples from a network will contain the same amount of information as a finer set of samples. Our goal is to estimate the initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.

A probabilistic deep learning approach for thermal and exergy forecasting in organic Rankine cycles

Energy recovery from waste-energies sources is one of the main approaches for reducing carbon footprint and enhance sustainability indicators. One of the main challenges faced when dealing with complex processing systems refers to the development of reliable process models. Such a models are required for simulation, optimization, design and control tasks. When those models are time consuming to develop, or the basic underlying behaviour is not well understood, the leverage of surrogate models is a feasible alternative for addressing the past tasks. For surrogate modelling aims, we deploy feedforward fully connected deep learning nonlinear mappings, to learn process behaviour to forecast thermal and exergy efficiencies from a set of noisy measurements. We also show that common feedforward deep learning models are not reliable for extrapolation aims, and make some proposals to deal with this issue. Overall, this work aims to boost process intensification tasks in the energy recovery from exhaust or waste-energy sources commonly available in processing plants.

Refined least squares for support recovery

Sparse linear regression is a key step in many applications such as communication, image denoising or speech recognition. In these applications, the unknown signal of interest is often modeled using linear set of noisy equations. If the vector of regression coefficients (the signal) is sparse, then its values can be identified even if the system of equations is undetermined: recovery becomes possible with fewer observations than variables. In this work, we study the problem of exact support recovery based on noisy observations and present Refined Least Squares (ReLS). Given a set of noisy measurements, our goal is to recover the support of the (unknown) sparse signal. To recover the support of the unknown signal we use an average of multiple least squares solutions, each computed based on a subset of the full set of equations. The support is estimated by identifying the most significant coefficients of the average least squares solution. We demonstrate that in a wide variety of settings our method outperforms state-of-the-art support recovery algorithms.

Prescribed performance control for MIMO stochastic discrete-time nonlinear systems in a strict-feedback form using a set of noisy measurements

This paper presents a prescribed performance control for MIMO stochastic discrete-time nonlinear systems in a strict-feedback form using a set of noisy measurements. The prescribed performance control is proposed as follows. Transforming the un-constrained states into the constrained states, the proposed prescribed performance control with state constraints is designed based on the approach of backstepping control and the Lyapunov function without using approximate approaches. The nonlinear uncertainty is approximated as the fuzzy logic system based on the simplified extended single input rule modules to reduce the number of the fuzzy IF–THEN rules. The estimator to take the estimates for the unmeasurable states and the adjustable parameters is in a simplified structure designed. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Robust parameter estimation for constrained time-delay systems with inexact measurements

<p style='text-indent:20px;'>In this paper, we consider estimation problems involving constrained nonlinear systems with the unknown time-delays and unknown system parameters. These unknown quantities are to be estimated such that a least-squares error function between the system output and a set of noisy measurements is minimized subject to the characteristic time constraints specifying the restrictions. We first present the classical estimation formulation, where the expectation of the error function is regarded as the cost function. Then, in order to obtain robust estimates against the noises in measurements, we propose a robust estimation formulation, in which the cost function is the variance of the error function and an additional constraint indicates an allowable sacrifice from the optimal expectation value of the classical estimation problem. For these two estimation problems, we derive the gradients of the corresponding cost and constraint functions with respect to time-delays and system parameters by solving some auxiliary time-delay systems backward in time. On this basis, we develop gradient-based optimization algorithms to determine the optimal time-delays and system parameters. Finally, we consider two example problems, including a parameter estimation problem in microbial batch fermentation process, to illustrate the effectiveness and applicability of our proposed algorithms.

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems in pure-feedback form with input and state constraints using noisy measurements

ABSTRACTThis paper is concerned with the design of an adaptive fuzzy dynamic surface control for uncertain nonlinear pure-feedback systems with input and state constraints using a set of noisy measurements. The design approach is described as follows. The nonlinear uncertainties are approximated by using the fuzzy logic systems at the first stage, secondly the adaptive fuzzy dynamic surface control is introduced to remove the problem of the explosion of complexity for the derivation of the adaptive fuzzy backstepping control, thirdly a new saturation function for state constraints is proposed to design the controllers based on the Lyapunov function, fourthly the number of the adjustable parameters is reduced by using the simplified extended single input rule modules, and finally the weighted least squares estimator to take the estimates for the un-measurable states and the adjustable parameters is in a simplified structure designed. The proposed approach provides effective system performance in the simulation experiment.

Adaptive fuzzy dynamic surface control for a class of stochastic MIMO discrete-time nonlinear pure-feedback systems with full state constraints

ABSTRACTThis paper presents the design of an adaptive fuzzy dynamic surface control for a class of stochastic MIMO discrete-time nonlinear pure-feedback systems with full state constraints using a set of noisy measurements. The design approach is described as follows. The nonlinear uncertainty is approximated by using the fuzzy logic system at the first stage, secondly the proposed adaptive fuzzy dynamic surface control is designed based on a new saturation function for full state constraints, thirdly the number of the adjustable parameters is reduced by using the simplified extended single input rule modules, and finally the simplified weighted least squares estimator is in a simplified structure designed to take the estimates for the un-measurable states and the adjustable parameters. The simulation provides that the proposed approach is effective for the improvement of the system performance.

Conic Relaxations for Power System State Estimation With Line Measurements

This paper deals with the nonconvex power system state estimation (PSSE) problem, which plays a central role in the monitoring and operation of electric power networks. Given a set of noisy measurements, PSSE aims at estimating the vector of complex voltages at all buses of the network. This is a challenging task due to the inherent nonlinearity of power flows (PFs), for which the existing methods lack guaranteed convergence and theoretical analysis. Motivated by these limitations, we propose a novel convexification framework for the PSSE problem using semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations. We first study a related PF problem as the noiseless counterpart, which is cast as a constrained minimization program by adding a suitably designed objective function. We study the performance of the proposed framework in the case where the set of measurements includes: 1) nodal voltage magnitudes and 2) branch active PFs over at least a spanning tree of the network. It is shown that the SDP and SOCP relaxations both recover the true PF solution as long as the voltage angle difference across each line of the network is not too large (e.g., less than $90^{\circ }$ for lossless networks). By capitalizing on this result, penalized SDP and SOCP problems are designed to solve the PSSE, where a penalty based on the weighted least absolute value is incorporated for fitting noisy measurements with possible bad data. Strong theoretical results are derived to quantify the optimal solution of the penalized SDP problem, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector. An upper bound on the estimation error is also derived as a function of the noise power, which decreases exponentially fast as the number of measurements increases. Numerical results on benchmark systems, including a 9241-bus European system, are reported to corroborate the merits of the proposed convexification framework.

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.

Adaptive fuzzy dynamic surface control for uncertain discrete-time nonlinear systems in pure-feedback form using a set of noisy measurements

This paper is concerned with the design of an adaptive fuzzy dynamic surface control for multi-input multi-output uncertain discrete-time nonlinear systems in pure-feedback form. The states of the systems are observed with independent measurement noises. The design approach of the proposed adaptive fuzzy dynamic surface control is described as follows. By applying the theory of the adaptive fuzzy dynamic surface control, the problem of the explosion of complexity due to the repeated differentials of nonlinear functions is removed so that the controller is simplified in a structure at the first stage; second, the number of the adjustable parameters is reduced by using the simplified extended single-input rule modules; and, finally, the simplified weighted least squares estimator is designed to take the estimates for the unmeasurable states and the adjustable parameters. The simulation experiment for a simple numerical system provides the effectiveness of the proposed approach.

Simplified algorithm of an adaptive fuzzy backstepping control for MIMO uncertain discrete-time nonlinear systems using a set of noisy measurements

This paper presents a simplified algorithm of an adaptive fuzzy backstepping control (AFBC) for multi-input multi-output uncertain discrete-time nonlinear systems with uncertainties viewed as the modelling errors and the unknown external disturbances, and the observation of the states is taken with measurement noises. The simplified algorithm of the proposed AFBC is designed as follows. The explosion of complexity problem due to repeated computation of nonlinear functions is removed to derive the simplified algorithm at the first stage, secondly the number of the adjustable parameters is reduced by using the fuzzy inference approach based on the proposed simplified extended single input rule modules, and finally the simplified weighted least squares estimator is constructed by reducing the computational burden of the estimation for the un-measurable states and the adjustable parameters. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

A Topological Low-Pass Filter for Quasi-Periodic Signals

This article presents a two-stage topological algorithm for recovering an estimate of a quasiperiodic function from a set of noisy measurements. The first stage of the algorithm is a topological phase estimator, which detects the quasiperiodic structure of the function without placing additional restrictions on the function. By respecting this phase estimate, the algorithm avoids creating distortion even when it uses a large number of samples for the estimate of the function.

Techniques for Generating Analytic Covariance Expressions for Eigenvalues and Eigenvectors

One of the key problems in data fusion is the estimation of a parameter vector from a set of noisy measurements. In many cases, the optimal estimate of such a parameter vector can be solved through the least squares problem. There are, however, a number of important problems whose solution instead takes the form of an eigenvalue-eigenvector problem. Furthermore, knowledge of the uncertainty of the optimal estimate is as important as the estimate itself for many practical applications—and this uncertainty is typically captured in the form of a covariance matrix. While the covariance matrix for a least squares estimate has been well studied, there has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this paper, we develop general expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue–eigenvector problem given the uncertainty of the matrix. This includes developing expressions for the analytic derivatives of the eigenvalues and eigenvectors with respect to the matrix from which they come. Finally, the techniques developed are numerically validated with forward finite differencing and a Monte Carlo analysis and then used to determine covariance expressions for an ellipse fitting technique and the estimation of attitude quaternions.

Adaptive fuzzy backstepping control for MIMO uncertain discrete-time nonlinear systems using a set of noisy measurements

This paper presents an adaptive fuzzy backstepping control (AFBC) for multi-input and multi-output uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time state equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. The proposed AFBC is simplified in a structure by removing the explosion of complexity problem due to repeated time-differences of nonlinear functions. The modelling errors are approximated by using the fuzzy inference approach based on the extended single input rule modules, and the unknown external disturbances are denoted as unknown time-invariant parameters, and these estimates are derived by using the proposed simplified weighted least squares estimator. It is proved that the errors between the states and the virtual controls, and the estimation errors, are ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Adaptive fuzzy sliding mode control for uncertain multi-input multi-output discrete-time systems using a set of noisy measurements

This paper is concerned with the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain nonlinear multi-input multi-output (MIMO) dynamic systems using a set of noisy measurements. The dynamic systems to be considered here are described by a discrete-time nonlinear state equation with mismatched uncertainties, and the states are measured by the restriction of measurement sensors and the contamination of independent random noises. The estimates for the unmeasurable states and the uncertainties are obtained by using the weighted extended Kalman filter. In the design of the proposed AFSMC, the adaptive switching factor characterising the switching control is designed using the fuzzy inference approach where the unknown gain of the switching control is assumed to be a positive definite matrix. It is proved that under some conditions the estimation errors will converge to zero as the time tends to infinity, and the states are ultimately bounded under the action of the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of an active suspension system for a half-car model.

Discrete-time adaptive sliding mode controller for vehicle steering systems with preview

This paper presents the design of a vehicle steering system with preview for a vehicle model subject to an uncertain side aerodynamic force by the crosswind disturbance. The steering control with preview is automatically implemented by steering the angles of the front/rear wheels based on the discrete-time adaptive sliding mode controller (SMC). It is assumed that the measurement of the states is taken by the measurement constraint and the contamination with independent random noises. The estimates for the unmeasurable states and the uncertainty characterizing the side aerodynamic force are respectively obtained by the weighted least squares estimator using a set of noisy measurements, and the proposed discrete-time adaptive SMC is designed on the basis of the information of the estimates. The simulation result indicates that the proposed vehicle steering system with preview is very effective in the system performance and the practical implementation.

Clustering time-course microarray data using functional Bayesian infinite mixture model

This paper presents a new Bayesian, infinite mixture model based, clustering approach, specifically designed for time-course microarray data. The problem is to group together genes which have “similar” expression profiles, given the set of noisy measurements of their expression levels over a specific time interval. In order to capture temporal variations of each curve, a non-parametric regression approach is used. Each expression profile is expanded over a set of basis functions and the sets of coefficients of each curve are subsequently modeled through a Bayesian infinite mixture of Gaussian distributions. Therefore, the task of finding clusters of genes with similar expression profiles is then reduced to the problem of grouping together genes whose coefficients are sampled from the same distribution in the mixture. Dirichlet processes prior is naturally employed in such kinds of models, since it allows one to deal automatically with the uncertainty about the number of clusters. The posterior inference is carried out by a split and merge MCMC sampling scheme which integrates out parameters of the component distributions and updates only the latent vector of the cluster membership. The final configuration is obtained via the maximum a posteriori estimator. The performance of the method is studied using synthetic and real microarray data and is compared with the performances of competitive techniques.

Finite element method based Monte Carlo filters for structural system identification

The paper proposes a strategy for combining two powerful computational procedures, namely, the finite element method (FEM) for structural analysis and particle filtering for dynamic state estimation, to tackle the problem of structural system parameter identification based on a set of noisy measurements on static and (or) dynamic structural responses. The proposed identification method automatically inherits the wide ranging capabilities of both FEM and particle filtering procedures thereby enabling the treatment of many complicated features of system identification problems, namely, imperfections in mathematical models for structural behavior, noisy and spatially incomplete measurements, nonlinear models for process and measurement equations, possible non-Gaussian nature of system and measurement noises, and dynamic and (or) static behaviors of the structure. Additionally, the authors propose a method that permits assimilation of measurements from multiple static and (or) dynamic tests and from multiple sensors in the system identification procedure in a unified manner. The paper describes how finite element models residing in commercially available softwares can be made to communicate with a database of measurements via a particle filtering algorithm developed on the Matlab platform. This leads to a probabilistic description of system parameters to be identified. Illustrative examples consider measurements from computational models, laboratory and field tests. These illustrations include studies on a rubber sheet with a hole undergoing large deformations, laboratory investigations on a single span beam and field investigations on an existing multi-span masonry arch bridge subjected to diagnostic moving loads.

Circular inference in neuroscience: The dangers of double dipping

A neuroscientific experiment typically generates a large amount of data, of which only a small fraction is subjected to detailed analysis and presentation in a publication. This inevitable selection is a major determinant of the final conclusion, and selection among a set of noisy measurements can render circular an otherwise appropriate analysis, invalidating statistical tests. The issue of circularity is particularly important in both electrophysiological and neuroimaging experiments. Here we focus on neuroimaging and argue that the field needs to adjust some widespread practices to avoid the circularity that can arise from selection. Faced with even more parallel sites than electrophysiology (typically on the order of 100 000 voxels), neuroimaging has developed rigorous methods for statistical mapping. This powerful approach avoids selection altogether: by analyzing all locations equally, while accounting for the fact that multiple tests are performed. However, selective analysis is still commonly used to focus on a particular brain region and, in fact, statistical mapping can form the basis for defining a region of interest (ROI). Further analysis of such functionally defined regions must take the selection bias into account. This problem is well understood in theory and one solution is to use independent experimental data to analyze the ROI. In practice, however, the selection bias is often ignored and important claims rely on questionable circular analyses. In order to demonstrate the problem, we apply analyses widespread in the neuroimaging literature to data known not to contain any experimental effects: functional magnetic resonance imaging (fMRI) data acquired from a resting human subject performing no explicit task. This exercise shows that widespread analysis procedures can produce spurious effects in the context of both univariate activation analysis and multivariate pattern-information analysis. We conclude by suggesting some simple guidelines for better practice in research and reviewing.

Camera Motion Estimation Using a Novel Online Vector Field Model in Particle Filters

In this paper, a novel algorithm for parametric camera motion estimation is introduced. More particularly, a novel stochastic vector field model is proposed, which can handle smooth motion patterns derived from long periods of stable camera motion and can also cope with rapid camera motion changes and periods when the camera remains still. The stochastic vector field model is established from a set of noisy measurements, such as motion vectors derived, e.g., from block matching techniques, in order to provide an estimation of the subsequent camera motion in the form of a motion vector field. A set of rules for a robust and online update of the camera motion model parameters is also proposed, based on the expectation maximization algorithm. The proposed model is embedded in a particle filters framework in order to predict the future camera motion based on current and prior observations. We estimate the subsequent camera motion by finding the optimum affine transform parameters so that, when applied to the current video frame, the resulting motion vector field to approximate the one estimated by the stochastic model. Extensive experimental results verify the usefulness of the proposed scheme in camera motion pattern classification and in the accurate estimation of the 2D affine camera transform motion parameters. Moreover, the camera motion estimation has been incorporated into an object tracker in order to investigate if the new schema improves its tracking efficiency, when camera motion and tracked object motion are combined.