Noiseless Measurements Research Articles

Moving horizon estimation and control of a binary simulated moving bed chromatographic processes with Langmuir isotherms

Simulated moving bed chromatographic (SMB) chromatographic processes are widely used for separations in pharmaceutical and biotechnological industries. In the present work, the control of such processes is proposed based on a semi-centralized control scheme that utilizes a combination of model predictive control (MPC) and classical PID control. The necessary information from the process, i.e. the internal concentration profiles, for the MPC is obtained by a moving horizon estimator (MHE) in real-time from the available limited measurements (the cycle-averaged concentrations of the extract and raffinate product streams and the dimensionless retention times of the concentration waves in the regeneration zones). As a test case study, the separation of a hypothetical system governed by the Langmuir isotherms in the nonlinear concentration range of the isotherms is considered. First, the stand-alone MHE is validated in open loop mode with no plant-model mismatch under deterministic and stochastic conditions. In the latter case, the true measurements are subject to random normally distributed noise. To evaluate the performance of the proposed control strategy, a reference tracking (change of the requirements for both the purities and the retention times) scenario is simulated. The investigated scenarios are: (i) no plant-model mismatch, (ii) MHE with ideal noiseless measurements and finally (iii) MHE under the influence of measurement noise. Results show that the controller is able to follow the change of the references from reduced purity to complete separation and vice versa closely.

Two-stage estimator for the complete inertia tensor of uncooperative debris on CubeSat based Active Debris Removal missions

The threat of debris collisions in Low Earth Orbit (LEO) has driven many researchers to develop Active Debris Removal (ADR) missions to manage large debris in LEO. A modern method of capturing debris with a non-rigid tether has been a recent research focus because of difficult post capture dynamics associated with controlling an uncooperative debris through a tether. To facilitate these control schemes, this paper proposes a new two-stage inertia estimator that estimates all principal and products of inertia for an uncooperative space debris using LiDAR and tether force measurements made on-board a CubeSat sized chaser satellite. The method proposed in this work estimates the debris center of mass with a novel pseudo measurement Kalman Filter so that the full inertia tensor can be subsequently estimated using an additional iterative parameter identification algorithm. In addition, the paper achieves online inertia estimation without assuming the tether connection point on the debris by approximating its location using tether tension measurements. The proposed control and estimation scheme is shown in this paper to estimate the full debris inertia tensor even with frequent tether slackness. Two simulation scenarios are presented in this paper, one where the connection point of the tether on the debris is approximated using noiseless measurements of tether tension, and a second where the location of the tether connection point is approximated using noisy measurements of tether tension. For the simulation conditions used in this research, it is shown that the proposed two-stage estimator (TSE) is successful for both cases that the debris is inertially asymmetrical and tri-inertial with non-zero products of inertia.

Bias-Correction Errors-in-Variables Hammerstein Model Identification

In this paper, a Bias-Correction Least-Squares (BCLS) algorithm is proposed for identifying block-oriented Errors-In-Variables nonlinear Hammerstein (EIV-Hammerstein) systems. Due to both the input and output of the EIV-Hammerstein system are observed with additive white noises, the estimation bias of traditional LS algorithm is introduced. The estimation bias is derived from a consistency point of view, which is a function about noises variances and monomial of noiseless system input-output measurements. A bias-estimation scheme based only on the available noisy measurements is then proposed for consistent identification of the monomial of noiseless system input-output measurements in a recursive form. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the unknown noise variances for practical applications. Such that the noise effect can be eliminated and the consistent estimated parameters are obtained. The effectiveness of the proposed method is demonstrated by a simulation example and an experimental prototype of wireless power transfer system.

Mitigation of state of charge estimation error due to noisy current input measurement

The key indicator to assess the performance of a battery management system is the state of charge (SoC). Although various SoC estimation algorithms have been developed to increase the estimation accuracy, the effect of the current input measurement error on the SoC estimation has not been adequately considered in these algorithms. The majority of SoC estimation algorithms are based on noiseless current measurement models in the literature. More realistic battery models must include the current measurement modelled with the bias noise and the white noise. We present a novel method for mitigating noise in current input measurements to reduce the SoC estimation error. The proposed algorithm is validated by computer simulations and battery experiments. The results show that the proposed method reduces the maximum SoC estimation error from around 11.3% to 0.56% in computer simulations and it is reduced from 1.74% to 1.17% in the battery experiment.

Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Models

In order to make data-driven models of physical systems interpretable and reliable, it is essential to include prior physical knowledge in the modeling framework. Hamiltonian Neural Networks (HNNs) implement Hamiltonian theory in deep learning and form a comprehensive framework for modeling autonomous energy-conservative systems. Despite being suitable to estimate a wide range of physical system behavior from data, classical HNNs are restricted to systems without inputs and require noiseless state measurements and information on the derivative of the state to be available. To address these challenges, this paper introduces an Output Error Hamiltonian Neural Network (OE-HNN) modeling approach to address the modeling of physical systems with inputs and noisy state measurements. Furthermore, it does not require the state derivatives to be known. Instead, the OE-HNN utilizes an ODE-solver embedded in the training process, which enables the OE-HNN to learn the dynamics from noisy state measurements. In addition, extending HNNs based on the generalized Hamiltonian theory enables to include external inputs into the framework which are important for engineering applications. We demonstrate via simulation examples that the proposed OE-HNNs results in superior modeling performance compared to classical HNNs.

Heart rate estimation network from facial videos using spatiotemporal feature image

Remote health monitoring has become quite inevitable after SARS-CoV-2 pandemic and continues to be accepted as a measure of healthcare in future too. However, contact-less measurement of vital sign, like Heart Rate(HR) is quite difficult to measure because, the amplitude of physiological signal is very weak and can be easily degraded due to noise. The various sources of noise are head movements, variation in illumination or acquisition devices. In this paper, a video-based noise-less cardiopulmonary measurement is proposed. 3D videos are converted to 2D Spatio-Temporal Images (STI), which suppresses noise while preserving temporal information of Remote Photoplethysmography(rPPG) signal. The proposed model projects a new motion representation to CNN derived using wavelets, which enables estimation of HR under heterogeneous lighting condition and continuous motion.STI is formed by the concatenation of feature vectors obtained after wavelet decomposition of subsequent frames. STI is provided as input to CNN for mapping the corresponding HR values. The proposed approach utilizes the ability of CNN to visualize patterns.Proposed approach yields better results in terms of estimation of HR on four benchmark dataset such as MAHNOB-HCI, MMSE-HR, UBFC-rPPG and VIPL-HR.

On the Support Recovery of Jointly Sparse Gaussian Sources via Sparse Bayesian Learning

In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is formulated as the marginalized maximum likelihood (or type-II ML) estimation of the variance hyperparameters of a joint sparsity inducing Gaussian prior on the source signals. We derive conditions under which the resulting nonconvex constrained optimization perfectly recovers the nonzero support of a joint-sparse Gaussian source ensemble with arbitrarily high probability. The support error probability decays exponentially with the number of MMVs at a rate that depends on the smallest restricted singular value and the nonnegative null space property of the self Khatri-Rao product of the sensing matrix. Our analysis confirms that nonzero supports of size as high as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(m^{2})$ </tex-math></inline-formula> are recoverable from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> measurements per sparse vector. Our derived sufficient conditions for support consistency of the proposed constrained type-II ML solution also guarantee the support consistency of any global solution of the multiple sparse Bayesian learning (M-SBL) optimization whose nonzero coefficients lie inside a bounded interval. For the case of noiseless measurements, we further show that a single MMV is sufficient for perfect recovery of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -sparse support by M-SBL, provided all subsets of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k + 1$ </tex-math></inline-formula> columns of the sensing matrix are linearly independent.

Measuring nanoparticles in liquid with attogram resolution using a microfabricated glass suspended microchannel resonator

The use of nanoparticles has been growing in various industrial fields, and concerns about their effects on health and the environment have been increasing. Hence, characterization techniques for nanoparticles are essential. Here, we present a silicon dioxide microfabricated suspended microchannel resonator (SMR) to measure the mass and concentration of nanoparticles in a liquid as they flow. We measured the mass detection limits of the device using laser Doppler vibrometry. This limit reached a minimum of 377 ag that correspond to a 34 nm diameter gold nanoparticle or a 243 nm diameter polystyrene particle, when sampled every 30 ms. We compared the fundamental limits of the measured data with an ideal noiseless measurement of the SMR. Finally, we measured the buoyant mass of gold nanoparticles in real-time as they flowed through the SMR.

Effect of relativity and vacuum fluctuations on quantum measurement

Vacuum fluctuations can obscure the detection signal of the measurement of the smallest quantum objects like single particles seemingly implying a fundamental limit to measurement accuracy. However, as we show relativistic invariance implies the disappearance of fluctuations for the space-like spectrum of an observable at zero temperature. This complete absence of noise can be harnessed to perform noiseless measurement of single particles, as we illustrate for electrons or photons. We outline a general scheme to illustrate the noiseless measurement involving the space-like spectrum of observables based on the self-interference of counter-propagating paths of a single particle in a triangular Sagnac interferometer.

Identifying 3D Genome Organization in Diploid Organisms via Euclidean Distance Geometry

The spatial organization of the DNA in the cell nucleus plays an important role for gene regulation, DNA replication, and genomic integrity. Through the development of chromosome conformation capture experiments (such as 3C, 4C, Hi-C) it is now possible to obtain the contact frequencies of the DNA at the whole-genome level. In this paper, we study the problem of reconstructing the 3D organization of the genome from such whole-genome contact frequencies. A standard approach is to transform the contact frequencies into noisy distance measurements and then apply semidefinite programming (SDP) formulations to obtain the 3D configuration. However, neglected in such reconstructions is the fact that most eukaryotes including humans are diploid and therefore contain two copies of each genomic locus. We prove that the 3D organization of the DNA is not identifiable from distance measurements derived from contact frequencies in diploid organisms. In fact, there are infinitely many solutions even in the noise-free setting. We then discuss various additional biologically relevant and experimentally measurable constraints (including distances between neighboring genomic loci and higher-order interactions) and prove identifiability under these conditions. Furthermore, we provide SDP formulations for computing the 3D embedding of the DNA with these additional constraints and show that we can recover the true 3D embedding with high accuracy from both noiseless and noisy measurements. Finally, we apply our algorithm to real pairwise and higher-order contact frequency data and show that we can recover known genome organization patterns.

Less entanglement exhibiting more nonlocality with noisy measurements

The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.

Convergence and stability analysis of iteratively reweighted least squares for noisy block sparse recovery

This paper considers the theoretical properties of iteratively reweighted least squares algorithm for noisy block sparse recovery problem (BIRLS for short). Li et al. used numerical experiments to show the remarkable performance of BIRLS algorithm for recovering a block sparse signal in noiseless measurement case, but no convergence analysis was given. In this paper, we focus on providing convergence, convergence rate and stability analysis of BIRLS algorithm for block sparse recovery in the presence of noise. The convergence of BIRLS is proved strictly. Furthermore, when the linear measurement matrix A satisfies the block restricted isometry property (abbreviated as block RIP), we show that BIRLS algorithm is stable and give the error analysis of BIRLS algorithm. We also characterize the convergence rate of the BIRLS algorithm, which implies global linear convergence for p=1 and local super-linear convergence for 0<p<1. The simplicity of BIRLS algorithm, along with the theoretical guarantees provided in this paper, make a compelling case for its adoption as a standard tool for block sparse recovery.

A Bayesian Optimization Approach for Multi-Function Estimation for Environmental Monitoring Using an Autonomous Surface Vehicle: Ypacarai Lake Case Study

Bayesian optimization is a sequential method that can optimize a single and costly objective function based on a surrogate model. In this work, we propose a Bayesian optimization system dedicated to monitoring and estimating multiple water quality parameters simultaneously using a single autonomous surface vehicle. The proposed work combines different strategies and methods for this monitoring task, evaluating two approaches for acquisition function fusion: the coupled and the decoupled techniques. We also consider dynamic parametrization of the maximum measurement distance traveled by the ASV so that the monitoring system balances the total number of measurements and the total distance, which is related to the energy required. To evaluate the proposed approach, the Ypacarai Lake (Paraguay) serves as the test scenario, where multiple maps of water quality parameters, such as pH and dissolved oxygen, need to be obtained efficiently. The proposed system is compared with the predictive entropy search for multi-objective optimization with constraints (PESMOC) algorithm and the genetic algorithm (GA) path planning for the Ypacarai Lake scenario. The obtained results show that the proposed approach is 10.82% better than other optimization methods in terms of R2 score with noiseless measurements and up to 17.23% better when the data are noisy. Additionally, the proposed approach achieves a good average computational time for the whole mission when compared with other methods, 3% better than the GA technique and 46.5% better than the PESMOC approach.

Gridless Multidimensional Angle-of-Arrival Estimation for Arbitrary 3D Antenna Arrays

A full multi-dimensional characterization of the angle of arrival (AoA) has immediate applications to the efficient operation of modern wireless communication systems. In this work, we develop a compressed sensing based method to extract multi-dimensional AoA information exploiting the sparse nature of the signal received by a sensor array. The proposed solution, based on the atomic <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm, enables accurate gridless resolution of the AoA in systems with arbitrary 3D antenna arrays. Our approach allows characterizing the maximum number of distinct sources (or scatters) that can be identified for a given number of antennas and array geometry. Both noiseless and noisy measurement scenarios are addressed, deriving and evaluating the resolvability of the AoA propagation parameters through a multi-level Toeplitz matrix rank\nolimits-minimization problem. To facilitate the implementation of the proposed solution, we also present a least squares approach regularized by a convex relaxation of the rank\nolimits-minimization problem and characterize its conditions for resolvability.

Nonlocal Low-Rank Regularization Combined with Bilateral Total Variation for Compressive Sensing Image Reconstruction

The use of non-local self-similarity prior between image blocks can improve image reconstruction performance significantly. We propose a compressive sensing image reconstruction algorithm that combines bilateral total variation and nonlocal low-rank regularization to overcome over-smoothing and degradation of edge information which result from the prior reconstructed image. The proposed algorithm makes use of the preservation of image edge information by bilateral total variation operator to enhance the edge details of the reconstructed image. In addition, we use weighted nuclear norm regularization as a low-rank constraint for similar blocks of the image. To solve this convex optimization problem, the Alternating Direction Method of Multipliers (ADMM) is employed to optimize and iterate the algorithm model effectively. Experimental results show that the proposed algorithm can obtain better image reconstruction quality than conventional algorithms with using total variation regularization or considering the nonlocal structure of the image only. At 10% sampling rate, the peak signal-to-noise ratio gain is up to 2.39 dB in noiseless measurements compared with Nonlocal Low-rank Regularization (NLR-CS). Reconstructed image comparison shows that the proposed algorithm retains more high frequency components. In noisy measurements, the proposed algorithm is robust to noise and the reconstructed image retains more detail information.

Analyzing cross-validation in compressed sensing with Poisson noise

In many compressive sensing reconstruction algorithms, a good choice of important parameters such as the optimal number of measurements (which is dependent upon the unknown signal sparsity) or the regularization parameter, is critical for successful signal recovery. Cross-validation provides a principled method of doing so, by dividing the measurements into a ‘reconstruction set’ to recover the signal given each candidate parameter value, and a ‘cross-validation set’ to determine in a purely data-driven manner as to which candidate parameter value is optimal. In previous work, such a technique has been theoretically analyzed for the case of noiseless compressive measurements or for the case of additive i.i.d. Gaussian noise in the measurements. This paper presents the first theoretical analysis of this technique for compressed sensing when the measurements are corrupted by Poisson noise, the dominant noise distribution in optical systems. Using two different methods, we present different types of theoretical bounds in the form of confidence intervals on the actual (unobservable) recovery error in terms of the (observable) cross-validation error. We show in particular that these bounds become tighter with increase in the underlying signal intensity or number of cross-validation measurements (if other factors are held constant). We validate our theoretical bounds with simulations and experimental results for Poisson compressed sensing with the widely used Lasso estimator.

Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation.

We demonstrate the ability of statistical data assimilation (SDA) to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain estimates of undetected (that is, unmeasured) infectious populations, by measuring the detected cases together with the recovered and dead - and without assumed knowledge of the detection rates. Given a noiseless measurement of the recovered population, excellent estimates of all quantities are obtained using a temporal baseline of 101 days, with the exception of the time-varying transmission rate at times prior to the implementation of social distancing. With low noise added to the recovered population, accurate state estimates require a lengthening of the temporal baseline of measurements. Estimates of all parameters are sensitive to the contamination, highlighting the need for accurate and uniform methods of reporting. The aim of this paper is to exemplify the power of SDA to determine what properties of measurements will yield estimates of unknown parameters to a desired precision, in a model with the complexity required to capture important features of the COVID-19 pandemic.

Extension-Deformation Approach to Extended Object Tracking

This article presents a new approach, named extension-deformation approach (EDA), to extended object tracking (EOT). It models the extension of an object as being deformed from a simple reference extension by moving several control points. Then, a complex object extension can be characterized by these control points given the reference extension. This greatly simplifies the problem of shape description. Thus, modeling and estimation of the extension reduce to those of the control points, which are treated as state components of the extension. A noiseless measurement is a point on the deformed extension that corresponds to a source on the reference extension. Once the source is given, the corresponding measurement model is linear in the state, making state estimation simple and direct. However, the source is unknown and hard to estimate accurately. To handle this problem, a multiple-source approach to kinematic state and extension estimation is proposed. Overall the proposed approach is simple and it can effectively track an object with an extension that can be nonstar-convex. Simulation results are given to illustrate the effectiveness of the proposed approach.

Bayesian system ID: optimal management of parameter, model, and measurement uncertainty

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning problem to several commonly used least squares-based optimization objectives used in system ID. Our comparisons indicate that the log posterior has improved geometric properties compared with the objective function surfaces of traditional methods that include differentially constrained least squares and least squares reconstructions of discrete time steppers like dynamic mode decomposition (DMD). These properties allow it to be both more sensitive to new data and less affected by multiple minima --- overall yielding a more robust approach. Our theoretical results indicate that least squares and regularized least squares methods like dynamic mode decomposition and sparse identification of nonlinear dynamics (SINDy) can be derived from the probabilistic formulation by assuming noiseless measurements. We also analyze the computational complexity of a Gaussian filter-based approximate marginal Markov Chain Monte Carlo scheme that we use to obtain the Bayesian posterior for both linear and nonlinear problems. We then empirically demonstrate that obtaining the marginal posterior of the parameter dynamics and making predictions by extracting optimal estimators (e.g., mean, median, mode) yields orders of magnitude improvement over the aforementioned approaches. We attribute this performance to the fact that the Bayesian approach captures parameter, model, and measurement uncertainties, whereas the other methods typically neglect at least one type of uncertainty.

Solving Inverse Problems via Auto-Encoders

Compressed sensing (CS) is about recovering a structured signal from its under-determined linear measurements. Starting from sparsity, recovery methods have steadily moved towards more complex structures. Emerging machine learning tools such as generative functions that are based on neural networks are able to learn general complex structures from training data. This makes them potentially powerful tools for designing CS algorithms. Consider a desired class of signals $\cal Q$, ${\cal Q}\subset{R}^n$, and a corresponding generative function $g:{\cal U}^k\rightarrow {R}^n$, ${\cal U}\subset {R}$, such that $\sup_{{\bf x}\in {\cal Q}}\min_{{\bf u}\in{\cal U}^k}{1\over \sqrt{n}}\|g({\bf u})-{\bf x}\|\leq \delta$. A recovery method based on $g$ seeks $g({\bf u})$ with minimum measurement error. In this paper, the performance of such a recovery method is studied, under both noisy and noiseless measurements. In the noiseless case, roughly speaking, it is proven that, as $k$ and $n$ grow without bound and $\delta$ converges to zero, if the number of measurements ($m$) is larger than the input dimension of the generative model ($k$), then asymptotically, almost lossless recovery is possible. Furthermore, the performance of an efficient iterative algorithm based on projected gradient descent is studied. In this case, an auto-encoder is used to define and enforce the source structure at the projection step. The auto-encoder is defined by encoder and decoder (generative) functions $f:{R}^n\to{\cal U}^k$ and $g:{\cal U}^k\to{R}^n$, respectively. We theoretically prove that, roughly, given $m>40k\log{1\over \delta}$ measurements, such an algorithm converges to the vicinity of the desired result, even in the presence of additive white Gaussian noise. Numerical results exploring the effectiveness of the proposed method are presented.