Problem Of Simultaneous Estimation Research Articles

Two-parameter estimation with single squeezed-light interferometer via double homodyne detection

The simultaneous two-parameter estimation problem in a single squeezed-light Mach–Zehnder interferometer with the double-port homodyne detection is investigated in this work. The analytical form of the two-parameter quantum Cramér–Rao bound defined by the quantum Fisher information matrix is presented, which shows the ultimate limit of the phase sensitivity will be further approved by the squeezed vacuum state. It can not only surpass the standard quantum limit, but also can even surpass the Heisenberg limit when half of the input intensity of the interferometer is provided by the coherent state and half by the squeezed light. For the double-port homodyne detection, the classical Fisher information matrix is also obtained. Our results show that although the classical Cramér–Rao bound does not saturate the quantum one, it can still asymptotically approach the quantum Cramér–Rao bound when the intensity of the coherent state is large enough. Our results also indicate that the squeezed vacuum state indeed can further improve the phase sensitivity, similar to the single-parameter estimation. In addition, when half of the input intensity of the interferometer is provided by the coherent state and half by the squeezed light, the phase sensitivity obtained by the double-port homodyne detection can also surpass the Heisenberg limit for a small range of the estimated phases.

Estimating high-dimensional Hawkes process with time-dependent covariates

The Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike train data. Despite this popularity, existing methodological and theoretical work has mainly focused on models without assumption of time-varying covariates, such as stimulus drive. In this article, motivated by neuronal spike trains study in the presence of stimuli, we propose a new Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality to establish the consistency of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set.

Estimation of Thermal Properties of Solid–Liquid Phase Change Material Using Fuzzy Inference Methods

The accurate measurement of thermal properties in phase change materials holds significant importance for engineering applications. This research introduces fuzzy inference methods to estimate the thermal properties of phase change materials. The solution to the coupled heat transfer involving radiation and conduction in material is achieved through a hybrid approach, which combines the finite volume method with the discrete ordinate method. The estimation process is structured as an inverse problem, where the temperature on the material surface acts as the measurement signal for conducting the inverse analysis. Both the fuzzy inference method and the decentralized fuzzy inference method are utilized to address the inverse heat transfer problem. This enables the determination of latent heat and thermal conductivities for both solid and liquid regions within the phase change material. Retrieval results demonstrate that the thermal properties of phase change materials can be accurately estimated using fuzzy inference methods. While both two fuzzy inference methods perform similarly in estimating a single parameter, the fuzzy inference method has limitations in multiparameter estimation tasks. Conversely, the decentralized fuzzy inference method yields accurate results in simultaneous estimation problems. Furthermore, this method proves robust in estimating the thermal properties of phase change materials, even in the presence of noisy data.

Event-Triggered State and Disturbance Estimation for Lipschitz Nonlinear Systems With Unknown Time-Varying Delays.

We consider the event-triggered state and disturbance simultaneous estimation problem for Lipschitz nonlinear systems with an unknown time-varying delay in the state vector. For the first time, state and disturbance can be robustly estimated by using an event-triggered state observer. Our method uses only information of the output vector when an event-triggered condition is satisfied. This contrasts with previous methods of simultaneous state and disturbance estimation based on augmented state observers where the information of the output vector was assumed to be always continuously available. This salient feature, thus, lessens the stress on communication resources while can still maintain an acceptable estimation performance. First, to solve the new problem of event-triggered state and disturbance estimation, and to tackle unknown time-varying delays, we propose a novel event-triggered state observer and establish a sufficient condition for its existence. Then to overcome some technical difficulties in synthesizing observer parameters, we introduce some algebraic transformations and use inequalities, such as the Cauchy matrix inequality and the Schur complement lemma to establish a convex optimization problem in which observer parameters and optimal disturbance attenuation levels can be systematically derived. Finally, we demonstrate the applicability of the method by using two numerical examples.

Robust adaptive variable selection in ultra-high dimensional linear regression models

We consider the problem of simultaneous variable selection and parameter estimation in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property with simpler assumptions and lesser computational burden. Noting the non-robust nature of the usual adaptive procedures (e.g. adaptive LASSO) based on the squared error loss function against data contamination, quite frequent with modern large-scale data sets (e.g. noisy gene expression data, spectra and spectral data), in this paper, we present a new adaptive regularization procedure using a robust loss function based on the density power divergence (DPD) measure under a general class of error distributions. We theoretically prove that the proposed adaptive DPD-LASSO estimator of the regression coefficients is highly robust, consistent, asymptotically normal and leads to robust oracle-consistent variable selection under easily verifiable assumptions. Numerical illustrations are provided for the mostly used normal and heavy-tailed error densities. Finally, the proposal is applied to analyse an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries.

Event-triggered state and fault simultaneous estimation for nonlinear systems with time delays

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method.

Support recovery with Projected Stochastic Gates: Theory and application for linear models

Consider the problem of simultaneous estimation and support recovery of the coefficient vector in a linear data model with additive Gaussian noise. We study the problem of estimating the model coefficients based on a recently proposed non-convex regularizer, namely the stochastic gates (STG) (Yamada et al., 2020). We suggest a new projection-based algorithm for solving the STG regularized minimization problem, and prove convergence and support recovery guarantees of the STG-estimator for a range of random and non-random design matrix setups. Our new algorithm has been shown to outperform the existing STG algorithm and other classical estimators for support recovery in various real and synthetic data analyses.

Single 24-GHz FMCW Radar-Based Indoor Device-Free Human Localization and Posture Sensing With CNN

The position information and posture information of a device-free human in a confined indoor environment have multiple uses in health monitoring and other areas. In this study, we aim to use a single-input-single-output (SISO) frequency-modulated continuous-wave (FMCW) radar at 24-GHz band for simultaneous localization and posture estimation of one device-free human target. This device is easy to deploy in new setups. We use image formation to convert temporal measurements of the radar signal into image-like data and convert the problem of simultaneous position estimation and posture perception into an image classification problem. Leveraging the use of convolutional neural networks (CNNs) for image classification, we design a variety of tests to explore the most favorable parameters of the CNN model and then use the best practice model to accomplish the classification task involving a fusion of localization and pose recognition. To explain the primary causes of inaccuracies, we examine not only cases based on a fused position and posture dataset but also cases based on position-only and posture-only datasets. On both real-life datasets, our proposed scheme can achieve 98% classification accuracy and less than 1-m localization accuracy within 0.95 cumulative error probability within the area of interest, outperforming traditional classification methods.

Neural-Network-Based Set-Membership Fault Estimation for 2-D Systems Under Encoding-Decoding Mechanism.

In this article, the simultaneous state and fault estimation problem is investigated for a class of nonlinear 2-D shift-varying systems, where the sensors and the estimator are connected via a communication network of limited bandwidth. With the purpose of relieving the communication burden and enhancing the transmission security, a new encoding-decoding mechanism is put forward so as to encode the transmitted data with a finite number of bits. The aim of the addressed problem is to develop a neural-network (NN)-based set-membership estimator for jointly estimating the system states and the faults, where the estimation errors are guaranteed to reside within an optimized ellipsoidal set. With the aid of the mathematical induction technique and certain convex optimization approaches, sufficient conditions are derived for the existence of the desired set-membership estimator, and the estimator gains and the NN tuning scalars are then presented in terms of the solutions to a set of optimization problems subject to ellipsoidal constraints. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed estimator design method.

Minimax estimation in multi-task regression under low-rank structures

This study investigates the minimaxity of a multi-task nonparametric regression problem. We formulate a simultaneous function estimation problem based on information pooling across multiple experiments under a low-dimensional structure. A nonparametric reduced rank regression estimator based on the nuclear norm penalisation scheme is proposed to incorporate the low-dimensional structure in the estimation process. A rank of a set of functions is defined in terms of their Fourier coefficients to formally characterise the dependence structure among functions. Minimax upper and lower bounds are established under various asymptotic scenarios to examine the role of the low-rank structure in determining optimal rates of convergence. The results confirm that exploiting the low-rank structure can significantly improve the convergence rate for the simultaneous estimation of multiple functions. The results also imply that the proposed estimator is rate optimal in the minimax sense for the rank-constraint Sobolev class of vector-valued functions.

Regularization in dynamic random‐intercepts models for analysis of longitudinal data

AbstractThis paper addresses the problem of simultaneous variable selection and estimation in the random‐intercepts model with the first‐order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra‐class correlation, and the first lagged response to address the serial correlation, which are two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring correlation among random effects and initial responses can lead to biased regularized estimates. Furthermore, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of dynamic random‐intercepts models leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low‐ and high‐dimensional settings and evaluate regularized estimators' performances by conducting simulation studies and analyzing a real dataset. Supporting information is available online.

Multiparameter estimation for qubit states with collective measurements: a case study

Quantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically prepared qubit states that is confined to a plane, where in order to obtain the optimal estimation precision for both parameters, collective measurements on multiple qubits are necessary. Upon treating N qubits as an ensemble of spin-1/2 systems, we show that simultaneous optimal estimation for both parameters can be attained asymptotically with a simple collective measurement strategy—first, we estimate the length parameter by measuring the populations in spaces corresponding to different total angular momentum values j, then we estimate the direction parameter by performing a spin projection onto an optimal basis. Furthermore, we show that when the state is nearly pure, for sufficiently but not arbitrarily large N, most information will be captured in the largest three j-subspaces. Then, we study how the total angular-momentum measurement can be realized by observing output signatures from a Bell multiport setup, either exactly for N = 2, 3, or approximately when the qubits are nearly pure for other N values. We also obtain numerical results that suggest that using a Bell multiport setup, one can distinguish between projection onto the j = N/2 and j = N/2 − 1 subspaces from their respective interference signatures at the output.

Entity aware sequence to sequence learning using LSTMs for estimation of groundwater contamination release history and transport parameters

Groundwater contaminant sources identification and parameter estimation using the simulation–optimization (S/O) approach require numerous runs of the computationally expensive simulation model through the optimization algorithm. The computational cost can be effectively reduced by using a surrogate model which can accurately approximate the simulation model. With the advent of deep learning, Long Short-Term Memory (LSTM) networks, which are suitable to learn sequential data, are being increasingly applied to regression problems involving time dependencies. However, for the simultaneous contaminant source identification and parameter estimation problem, the surrogate model requires to establish a relationship between release histories at the source locations to concentration measurements at observation points subject to given values of aquifer parameters. In this study, a novel deep neural network framework Entity Aware Sequence to sequence learning using Long Short-Term Memory (EAS-LSTM) is proposed as a surrogate model which takes both sequential i.e., release histories at the source locations at different stress periods and static variables i.e., transport parameters as inputs to predict breakthrough curves (BTCs) at observation points. The proposed surrogate model is applied to a heterogeneous field scale aquifer with 4 zones. The Mean Squared Error (MSE) using EAS-LSTM is 0.0033 ppm2 which is significantly better than that of Kriging and Support Vector Regression (SVR) which are 0.048 ppm2 and 1.302 ppm2 respectively. Comparison of EAS-LSTM model performance with Kriging and SVR based models demonstrates its higher accuracy. Further, the optimization algorithms for inverse modelling, the performances of Multiverse Optimizer (MVO), Grey wolf optimization (GWO) and Particle swarm optimization (PSO) are investigated. It is observed that the combination of EAS-LSTM and MVO provides better results in comparison to other surrogate simulation optimization (SSO) models.

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

Simultaneous variable selection and estimation for longitudinal ordinal data with a diverging number of covariates

<abstract><p>In this paper, we study the problem of simultaneous variable selection and estimation for longitudinal ordinal data with high-dimensional covariates. Using the penalized generalized estimation equation (GEE) method, we obtain some asymptotic properties for these types of data in the case that the dimension of the covariates $ p_n $ tends to infinity as the number of cluster $ n $ approaches to infinity. More precisely, under appropriate regular conditions, all the covariates with zero coefficients can be examined simultaneously with probability tending to 1, and the estimator of the non-zero coefficients exhibits the asymptotic Oracle properties. Finally, we also perform some Monte Carlo studies to illustrate the theoretical analysis. The main result in this paper extends the elegant work of Wang et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> to the multinomial response variable case.</p></abstract>

Investigation of simultaneous estimation of state and unknown parameters using a modified Kalman filter incorporating with moment equations in the prediction step

The modified Kalman filter, incorporating stochastic dynamic analysis in the prediction step, was introduced in a previous paper to systematically deal with nonlinear and parameter uncertainty excitation systems. In addition, the KF-SDA filter was extended to parameter estimation problems. However, the problem of simultaneous estimation of state and unknown parameters has not been developed in previous research. The problem of simultaneous estimation of state and unknown parameters is of great engineering significance as a method of state estimation and system identification under the limitation of the number and types of sensors. This paper deals with a method to apply KF-SDA to the problem of simultaneous estimation of state and unknown parameters. As a basic verification of the proposed method, numerical simulations are performed for a single-degree-of-freedom system which is subject to random noise excitation of parameters. Furthermore, the cases that the estimated value and the true value agree and the cases that they do not agree are considered using the time required for convergence.

Estimation in multivariate linear mixed models for longitudinal data with multiple outputs: Application to PBCseq data analysis

In many biomedical studies or clinical trials, we have data with more than one response variable on the same subject repeatedly measured over time. In analyzing such data, we adopt a multivariate linear mixed-effects longitudinal model. On the other hand, in longitudinal data, we often find features that do not impact modeling the response variable and are eliminated from the study. In this paper, we consider the problem of simultaneous variable selection and estimation in a multivariate t linear mixed-effects model (MtLMM) for analyzing longitudinally measured multioutcome data. This work's motivation comes from a cohort study of patients with primary biliary cirrhosis. The interest is eliminating insignificant variables using the smoothly clipped and absolute deviation penalty function in the MtLMM. The proposed penalized model offers robustness and flexibility to accommodate fat tails. An expectation conditional maximization algorithm is employed for the computation of maximum likelihood estimates of parameters. The calculation of standard errors is affected by an information-based method. The methodology is illustrated by analyzing Mayo Clinic Primary Biliary Cirrhosis sequential (PBCseq) data and a simulation study. We found drugs and sex can be eliminated from the PBCseq analysis, and over time the diseaseprogresses.

Latent variable modeling and state estimation of non-stationary processes driven by monotonic trends

In certain non-stationary processes, the non-stationary dynamics is caused by degradation or wearing of certain process components. Such dynamics can be characterized by a latent monotonic signal. Meanwhile, there also exist stationary dynamics characterizing the regular process variables. It hence becomes pertinent to distinguish these two sets of latent variables for the monitoring of the process from both the stationary and non-stationary aspects. In this regard, we propose a methodology to achieve such a goal by modeling the latent monotonic trend as a closed skew-normal random walk model. The other stationary relations are characterized by a state-space model with Gaussian noises. The problem is solved as a simultaneous state and parameter estimation problem using the expectation–maximization algorithm. As a result of the closed skew-normal random walk model for the monotonic trend, the state estimation problem becomes a skew-normal filtering and smoothing problem. The effectiveness of the proposed method is verified through a numerical simulation, and the algorithm is applied to solve a Hot Lime Softener fouling predictive monitoring problem.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Limited‐information learning observer for simultaneous estimation of states and parameters

AbstractThe problem of simultaneous estimation of states and uncertainties by using limited information is investigated in this article. A sampled‐data learning observer (SLO) is presented for linear time‐invariant continuous systems, which can achieve successful estimation while only needs intermittent sampled‐data, saves computing resources, and does not require persistent excitation signals. The observer's demand for continuous measurement is reduced, that is, limited‐information is sufficient. Notably, the uncertainty estimation is performed by a learning equation with only simple addition operations, which is particularly suitable for actual digital system scenarios. Simulation results illustrate the effectiveness of the proposed SLO.