Estimation Problem Research Articles

Bayesian 3D User Localization and Channel Reconstruction with Planar Extremely Large-Scale Antenna Array

An extremely large-scale antenna array (ELAA) can potentially provide significantly increased spatial multiplexing and beamforming gains, as well as enhanced localization capability. While presenting new potential, its near-field propagation and spatial non-stationary properties also impose a great challenge on the receiver design. This paper focuses on the receiver design in an uplink orthogonal frequency-division multiplexing system with a planar ELAA deployed at the base station. To solve the challenging problem of 3D user localization and channel estimation with the planar ELAA, a space-frequency user localization and channel reconstruction (SF-ULCR) receiver is proposed. Under the Bayesian framework, an extended probability model is first established, to capture the channel structural information comprehensively, based on which an iterative receiver consisting of three modules is derived: element-wise line spectrum estimation (ELSE), distance parameter estimation (DPE), and near-field localization (NFL). In particular, the ELSE module handles the line spectrum relationships among multiple subcarriers in the frequency domain, the DPE module extracts and integrates the distance information from the line spectrum parameters, and the NFL module utilizes the messages of distances for user localization based on near-field spatial characteristics. Our numerical results demonstrate that the proposed SF-ULCR algorithm outperforms existing baselines in terms of channel estimation and localization performance, and that it approaches the Cramèr–Rao bound.

Using Cognitive Models to Improve the Wisdom of the Crowd

The wisdom of the crowd is the finding that aggregating the judgments of many people can lead to surprisingly accurate group judgments. Usually statistical methods are used to aggregate people’s judgments, but there are advantages to using cognitive models instead. Crowd judgments based on cognitive modeling can (a) identify experts and amplify their judgments, (b) provide a representational structure for aggregating complicated multidimensional judgments, (c) debias judgments that are affected by heuristic cognitive processes or competitive social situations, and (d) diversify the crowd by incorporating predictions about judgments that have not been observed. Demonstrations of these advantages are provided in case studies involving ranking, probability estimation, and categorization problems.

Analysis of a Class of Minimization Problems Lacking Lower Semicontinuity

The minimization of nonlower semicontinuous functions is a difficult topic that has been minimally studied. Among such functions is a Heaviside composite function that is the composition of a Heaviside function with a possibly nonsmooth multivariate function. Unifying a statistical estimation problem with hierarchical selection of variables and a sample average approximation of composite chance constrained stochastic programs, a Heaviside composite optimization problem is one whose objective and constraints are defined by sums of possibly nonlinear multiples of such composite functions. Via a pulled-out formulation, a pseudostationarity concept for a feasible point was introduced in an earlier work as a necessary condition for a local minimizer of a Heaviside composite optimization problem. The present paper extends this previous study in several directions: (a) showing that pseudostationarity is implied by (and thus, weaker than) a sharper subdifferential-based stationarity condition that we term epistationarity; (b) introducing a set-theoretic sufficient condition, which we term a local convexity-like property, under which an epistationary point of a possibly nonlower semicontinuous optimization problem is a local minimizer; (c) providing several classes of Heaviside composite functions satisfying this local convexity-like property; (d) extending the epigraphical formulation of a nonnegative multiple of a Heaviside composite function to a lifted formulation for arbitrarily signed multiples of the Heaviside composite function, based on which we show that an epistationary solution of the given Heaviside composite program with broad classes of B-differentiable component functions can in principle be approximately computed by surrogation methods. Funding: The work of Y. Cui was based on research supported by the National Science Foundation [Grants CCF-2153352, DMS-2309729, and CCF-2416172] and the National Institutes of Health [Grant 1R01CA287413-01]. The work of J.-S. Pang was based on research supported by the Air Force Office of Scientific Research [Grant FA9550-22-1-0045].

Interval estimation of dynamic liquid level of sucker-rod pumping systems based on dynamometer card

This paper is concerned with the interval estimation problem of the dynamic liquid level for sucker-rod pumping systems via dynamometer cards. Firstly, a surface dynamometer card-based dynamic liquid level model is established in terms of the operational mechanism of the pump and the dynamics of the rod strings. Then, an underdamped oscillation method and a boxplot-based denoising method are developed respectively to determine the damping coefficient in the dynamics of the rod strings and deal with the uncertainties in the dynamometer card. Based on these, a finite difference-based interval estimation strategy is proposed to determine dynamic liquid level via the surface dynamometer card. Finally, simulation results with the field measurements demonstrate the validity of the proposed method.

A TDOA sequence estimation method of underwater sound source based on hidden Markov model

To address the time difference of arrival (TDOA) estimation problem in the passive positioning system with wideband underwater motion sound sources and distributed hydrophones, a hidden Markov model-based (HMM) TDOA sequence estimation method is proposed in this paper. The method estimates the TDOA with multi-frame output of cross-correlated signals received on hydrophones. The transfer equation of the TDOA is established as a first-order hidden Markov process by analyzing the motion characteristics of the moving sound source and delays obtained from different hydrophones. Dynamic assignment of the HMM parameters is proposed to address the inconsistent change rate of the TDOA. We then achieve an HMM expression of the TDOA sequence by fitting the transfer equation and dynamic assignment of parameters into the HMM. Then, the Viterbi algorithm (VA) is applied to distinguish the optimal sequence of the TDOA among ambiguous estimations. To deal with the problem of data loss or unreliable issues caused by interferences, a data prediction algorithm which could produce possible time delays is added to VA to avoid the impact of outliers on the estimation results. By utilizing multi-frame processing, the proposed method reduces the signal-to-noise ratio (SNR) requirement of single frames since it does not require accurate estimations of TDOA for each frame. Moreover, the method adapts to a lower SNR, which has significant advantages in terms of whole sequence estimation compared with common methods. The results from the simulations and lake experiments validated the proposed TDOA sequence estimation method.

Novel reachable set estimation results for delayed linear systems with bounded disturbance

Reachable set estimation is a prominent research topic in control theory and systems science. Reachable set estimation for time-delay systems has drawn a lot of interest. Until now, most approaches to the reachable set estimation problem of time-delay systems have involved building intricate Lyapunov functionals and utilizing LMI techniques. This has resulted in complicated LMI conditions and a proof procedure. The reachable set estimation issue for delayed linear systems with bounded disturbance will be reviewed in this paper. A novel reachable set estimation lemma with a time-delay term is proposed, and based on the acquired lemma, a sufficient condition is given to bound the reachable set estimation of the systems under discussion. In addition, an event-based sufficient criterion for reachable set estimation is also provided. The theoretical analysis in this paper is succinct when compared to previous findings, and the obtained conditions are simple to validate. Lastly, two examples are presented to confirm that the theoretical results hold true.

An improved nutcracker optimization algorithm for discrete and continuous optimization problems: Design, comprehensive analysis, and engineering applications

This study is presented to examine the performance of a newly proposed metaheuristic algorithm within discrete and continuous search spaces. Therefore, the multithresholding image segmentation problem and parameter estimation problem of both the proton exchange membrane fuel cell (PEMFC) and photovoltaic (PV) models, which have different search spaces, are used to test and verify this algorithm. The traditional techniques could not find approximate solutions for those problems in a reasonable amount of time, so researchers have used metaheuristic algorithms to overcome those shortcomings. However, the majority of metaheuristic algorithms still suffer from slow convergence speed and stagnation into local minima problems, which makes them unsuitable for tackling these optimization problems. Therefore, this study proposes an improved nutcracker optimization algorithm (INOA) for better solving those problems in an acceptable amount of time. INOA is based on improving the performance of the standard algorithm using a newly proposed convergence improvement strategy that aims to improve the convergence speed and prevent stagnation in local minima. This algorithm is first applied to estimating the unknown parameters of the single-diode, double-diode, and triple-diode models for a PV module and a solar cell. Second, four PEMFC modules are used to further observe INOA's performance for the continuous optimization challenge. Finally, the performance of INOA is investigated for solving the multi-thresholding image segmentation problem to test its effectiveness in a discrete search space. Several test images with different threshold levels were used to validate its effectiveness, stability, and scalability. Comparison to several rival optimizers using various performance indicators, such as convergence curve, standard deviation, average fitness value, and Wilcoxon rank-sum test, demonstrates that INOA is an effective alternative for solving both discrete and continuous optimization problems. Quantitively, INOA could solve those problems better than the other rival optimizers, with improvement rates for final results ranging between 0.8355 % and 3.34 % for discrete problems and 4.97 % and 99.9 % for continuous problems.

A kernel-type regression estimator for NMAR response variables with applications to classification

This work deals with the problem of nonparametric estimation of a regression function when the response variable may be missing according to a not-missing-at-random (NMAR) setup. To assess the theoretical performance of our estimators, we study their strong convergence properties in Lp norms where we also look into their rates of convergence. We also study applications of our results to the problem of statistical classification in semi-supervised learning.

Estimating optimal decision trees for treatment assignment: The case of K > 2 treatment alternatives.

For many problems in clinical practice, multiple treatment alternatives are available. Given data from a randomized controlled trial or an observational study, an important challenge is to estimate an optimal decision rule that specifies for each client the most effective treatment alternative, given his or her pattern of pretreatment characteristics. In the present paper we will look for such a rule within the insightful family of classification trees. Unfortunately, however, there is dearth of readily accessible software tools for optimal decision tree estimation in the case of more than two treatment alternatives. Moreover, this primary tree estimation problem is also cursed with two secondary problems: a structural missingness in typical studies on treatment evaluation (because every individual is assigned to a single treatment alternative only), and a major issue of replicability. In this paper we propose solutions for both the primary and the secondary problems at stake. We evaluate the proposed solution in a simulation study, and illustrate with an application on the search for an optimal tree-based treatment regime in a randomized controlled trial on K = 3 different types of aftercare for younger women with early-stage breast cancer. We conclude by arguing that the proposed solutions may have relevance for several other classification problems inside and outside the domain of optimal treatment assignment.

A Novel Two-Step Channel Estimation Method for RIS-Assisted mmWave Systems.

In this work, we resolve the cascaded channel estimation problem and the reflected channel estimation problem for the reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) systems. The novel two-step method contains modified multiple population genetic algorithm (MMPGA), least squares (LS), residual network (ResNet), and multi-task regression model. In the first step, the proposed MMPGA-LS optimizes the crossover strategy and mutation strategy. Besides, the ResNet achieves cascaded channel estimation by learning the relationship between the cascaded channel obtained by the MMPGA-LS and the channel of the user (UE)-RIS-base station (BS). Then, the proposed multi-task-ResNet (MTRnet) is introduced for the reflected channel estimation. Relying on the output of ResNet, the MTRnet with multiple output layers estimates the coefficients of reflected channels and reconstructs the channel of UE-RIS and RIS-BS. Remarkably, the proposed MTRnet is capable of using a lower optimization model to estimate multiple reflected channels compared with the classical neural network with the single output layer. A series of experimental results validate the superiority of the proposed method in terms of a lower norm mean square error (NMSE). Besides, the proposed method also obtains a low NMSE in the RIS with the formulation of the uniform planar array.

Frequency-domain diffusion adaptation over networks with missing input data

Recently, a modified adapt-then-combine diffusion (mATC) strategy has been developed to handle distributed estimation problem with missing regressions (inputs). However, the mATC algorithm only considers the white input scenario and suffers from high complexity for long model filter lengths. To overcome these shortcomings, this paper proposes novel regularization-based frequency-domain diffusion algorithms for networks with missing input data. First, bias-eliminating cost function based on regularization is established by using the frequency-domain diagonal approximation. Then, with stochastic gradient descent, periodic update, and power normalization schemes, we design the regularization-based frequency-domain least mean square (R-FDLMS) algorithm as well as its normalized variant (R-FDNLMS). The latter converges faster than the former under colored inputs. The stability and steady-state behavior of the R-FDNLMS algorithm are also analyzed. Moreover, two effective power estimation methods are presented for both situations without and with the power ratio between the input signal and perturbation noise, along with a reset mechanism in the first case to enhance tracking performance. Finally, simulations are conducted to illustrate the superiority of the proposed algorithms and the validity of theoretical findings.

Determining the Suction Capacity of Compacted Clays with Fuzzy-Set Theory

Water suction capacity is an important parameter affecting the swelling properties and volumetric change of soil. Determination of the water suction capacity is made by the experiments which are needed long time in laboratory. However, this has random errors due to the heterogeneous and anisotropic structure of soil sample together with the error caused by the operator made the experiment. Such an estimation problem, included the errors, may be easily solved with the fuzzy-set theory. In this study, the suction capacity of compacted clayey soils is predicted with the fuzzy-set theory. For this reason, the engineering properties of clayey soil (plasticity index, dry density, initial water content and suction capacity) are partitioned into fuzzy subsets, and fuzzy rules are formed. Later, a computer program in the Fortran language is written to estimate the suction capacity of compacted clayey soil from these properties. It is shown that there is a good similarity between the results of the tests and proposed fuzzy logic model.

Set‐membership state estimation for delayed switched systems with interval uncertainty: A zonotopic approach

SummaryConsidering the existence of time delay and interval uncertainty, a set‐membership state estimation problem based on zonotopes is studied for discrete‐time switched systems subject to unknown but bounded noises. To conform the actual situation, a state observer asynchronous with the subsystem is designed. The performance is introduced to attenuate the effect of noises in the observer design. By dealing with the interval uncertainty, the design approach of observer is given and transformed into a convex optimization problem which can be solved off‐line. The zonotope and the estimation interval containing state are provided based on the observer. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.

One-stage estimation of cyclic arrival rates using license plate recognition data

Traffic arrival on urban roads usually reveals time-varying rates due to the effects of signal control, motivating us to investigate the distribution of arrival rates within the signal cycle. However, such information is not readily available as only a portion of arrival traffic can be observed in the field. Previous studies have utilized different data sources and proposed probability-based models to solve the estimation problem. However, these studies rely heavily on the assumption that the observed vehicles are evenly distributed in the arrival traffic flow and exact signal timings are known. This study uses license plate recognition (LPR) data collected at adjacent signalized intersections to estimate cyclic arrival rates in a historical period. A probability-based model is formulated by parameterizing the vehicle arrival distribution as a mixture of circular distributions. This facilitates us to describe similar traffic arrival patterns over different signal cycles and capture multiple arrival platoons from different signal phases within the signal cycle. The proposed model is validated in a field experiment with different arrival patterns and traffic conditions. Model performance under both full and partial monitoring of LPR sensors at the upstream intersection is analyzed. The robustness of the proposed model with unevenly sampled observations in arrival traffic flow is also investigated.

Estimating Exposure to Information on Social Networks

Estimating exposure to information on a social network is a problem with important consequences for our society. The exposure estimation problem involves finding the fraction of people on the network who have been exposed to a piece of information (e.g., a URL of a news article on Facebook, a hashtag on Twitter). The exact value of exposure to a piece of information is determined by two features: the structure of the underlying social network and the set of people who shared the piece of information. Often, both features are not publicly available (i.e., access to the two features is limited only to the internal administrators of the platform) and are difficult to estimate from data. As a solution, we propose two methods to estimate the exposure to a piece of information in an unbiased manner: a vanilla method which is based on sampling the network uniformly and a method which non-uniformly samples the network motivated by the Friendship Paradox. We provide theoretical results which characterize the conditions (in terms of properties of the network and the piece of information) under which one method outperforms the other. Further, we outline extensions of the proposed methods to dynamic information cascades (where the exposure needs to be tracked in real-time). We demonstrate the practical feasibility of the proposed methods via experiments on multiple synthetic and real-world datasets.

Two-Dimensional Inverse Method to Estimate the Heat Flux Function in a Phase Change Material Heat-Exchanger

A two-dimensional inverse method is presented for estimating the boundary heat flux imposed on phase change materials in the melting/solidification process. The inverse problem is handled by the conjugate gradient method with the adjoint problem for function estimation. The method is verified using unsynthetic data, and the effect of the number of sensors, sensor placement, and measurement errors on the accuracy is investigated. In all cases, it is found that the method remains stable and accurate with a root mean square relative error less than 10%. Also, the number of sensors depends on the desired accuracy, computing time, and frequency of spatial changes in heat flux. Using field measurement is the best option for high accuracy and time-efficient estimation of spatial changes in the heat flux function. The accuracy of the estimated heat flux strongly depends on the sensor distance from the boundary. Therefore, it is desirable to place the sensor as close to the boundary as possible. With the addition of measurement errors, the presented method remains stable even with high measurement errors. This shows that this method can be used for real conditions.

Identification of fractional Hammerstein systems with the conformable fractional derivative

SummaryIn this article, we study parameter estimation problems for fractional commensurate Hammerstein systems utilizing the conformable fractional derivative. Two algorithms are investigated: first, the Poisson moment functions (PMF) method, aiming to transfer the fractional derivative of the measurement signal into PMF using the fractional Laplace transform and convolution; second, a proposed new instrumental variable algorithm, which is based on the conformable fractional derivative. Both algorithms have been analyzed and shown to be consistent. A comprehensive complexity analysis is provided for each algorithm. Furthermore, a kind of special time‐varying systems are discussed under the conformable fractional derivative. Finally, an example is given to illustrate the effectiveness of the proposed algorithms.

Angle-of-attack and angle-of-sideslip estimation and complementary filter design for civil aircraft

Angle-of-Attack (AOA) and angle-of-sideslip (AOS) are critical flight parameters affecting the flight safety, and their accuracy and reliability directly impact the operating status and performance of some significant airborne systems. To enhance the redundancy and accuracy of AOA and AOS, this article investigates the problem of the airflow angles estimation and complementary filter design for civil aircraft. Specifically, an extended Kalman filter based AOA and AOS estimation method considering acceleration correction is developed to increase the redundancy. Subsequently, a novel inertial AOA and inertial AOS calculation method using attitude angles, azimuth angle, and flight path angle is introduced, and two schemes for designing the discrete complementary filter based on Tustin transform are presented to improve the accuracy. Through simulations, the developed algorithms are verified, and the results illustrate that the AOA estimation error is within ± 0.6°, and the AOS estimation error is within ± 0.3°.

Parameter Estimation of Chikungunya in the Case of Incomplete Information about Its Model

This paper presents solutions to the problem of parameter estimation of mathematical model of Chikungunya with incomplete information about the model parameters. The process involves finding a set of unknown parameters from the given model such that the behavior of the predicted system reflects the original behavior (measurement) using the same scientific assumptions. To achieve this, we solve the differential equations which describe the relation between unknown functions and their derivatives using the fundamental theorem of ordinary differential equation (ODE) (i.e., the theorem of existence) to obtain solutions for the initial value problems. The solutions to the ODE give unknown parameters which functionally depend on the original unknown parameters. And these parameters have two constraints between them. We further find solutions to the constraints minimization problem to obtain estimations of a-parameters. But, the method of constraint minimization problem stipulates the ill-conditioned problem and makes it impossible to accurately identify a-parameters. It is necessary therefore to formulate the goal function using the Least squares method to determine the unknown parameters. This method works reliably well and converges at a large interval of initial guess values of parameters.

A Bertalanffy–Richards growth model perturbed by a time-dependent pattern, statistical analysis and applications

We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the Richards growth curve through a given constant boundary. The relevant features of the modified growth model are studied and compared with those of the original one. A sensitivity analysis on the switching time is also performed. Then, we define two different stochastic processes, i.e. a non-homogeneous linear birth–death process and a lognormal diffusion process, such that their means identify to the growth curve under investigation. For the diffusion process, we address the problem of parameters estimation through the maximum likelihood method. The estimates are obtained via meta-heuristic algorithms (namely, Simulated Annealing and Ant Lion Optimizer). A simulation study to validate the estimation procedure is also presented, together with a real application to oil production in France. Special attention is devoted to the approximation of switching time density, viewed as the first-passage-time density for the lognormal process.