Minimum Error Estimation Research Articles

Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

In this paper, we consider the application of the matching pursuit algorithm (MPA) for spectral analysis of non-stationary signals. First, we estimate the approximation error and the performance time for various MPA modifications and parameters using central processor unit and graphics processing unit (GPU) to identify possible ways to improve the algorithm. Next, we propose the modifications of discrete wavelet transform (DWT) and package wavelet decomposition (PWD) for further use in MPA. We explicitly show that the optimal decomposition level, defined as a level with minimum entropy, in DWT and PWD provides the minimum approximation error and the smallest execution time when applied in MPA as a rough estimate in the case of using wavelets as basis functions (atoms). We provide an example of entropy-based estimation for optimal decomposition level in spectral analysis of seismic signals. The proposed modification of the algorithm significantly reduces its computational costs. Results of spectral analysis obtained with MPA can be used for various signal processing applications, including denoising, clustering, classification, and parameter estimation.

Calibration and Optimization of the Ångström–Prescott Coefficients for Calculating ET0 within a Year in China: The Best Corrected Data Time Scale and Optimization Parameters

This study used meteorological data from official data sets to correct Ångström–Prescott formula parameters for China’s agricultural zones for which existing research encountered the problem of spatio-temporal scale disunity. The data, collected from 124 stations, were used to correct the as and bs coefficients of the Ångström–Prescott formula, by area, at 5–50 year-scales, the former taking into account China’s comprehensive agricultural zones. We focused on how the as and bs obtained from the different time scales corrected data affected the calculating solar radiation (Rs_c) precision, determined the optimal time scale for the corrected data, and compared and selected the as and bs with the minimum estimation error as the recommended values. The results show that our corrected as and bs coefficient values significantly reduce the range of the relative error of Rs_c, with 10 years being the best time scale for the corrected data. Further, the Rs_c precisions estimated by as and bs coefficients based on the Food and Agriculture Organization of the United Nations (FAO) and the regression result of the best time scale corrected data are inconsistent in different months by area. The best choice in practice is combining the two coefficients and optimizing their use. This study provides a research-based process for standardizing the correction of Ångström–Prescott formula parameters and selecting the corrected data time scale in China. It would be helpful in improving the calculation accuracy for reference crop evapotranspiration (ET0).

Bandwidth-Aware Traffic Sensing in Vehicular Networks with Mobile Edge Computing.

Traffic sensing is one of the promising applications to guarantee safe and efficient traffic systems in vehicular networks. However, due to the unique characteristics of vehicular networks, such as limited wireless bandwidth and dynamic mobility of vehicles, traffic sensing always faces high estimation error based on collected traffic data with missing elements and over-high communication cost between terminal users and central server. Hence, this paper investigates the traffic sensing system in vehicular networks with mobile edge computing (MEC), where each MEC server enables traffic data collection and recovery in its local server. On this basis, we formulate the bandwidth-constrained traffic sensing (BCTS) problem, aiming at minimizing the estimation error based on the collected traffic data. To tackle the BCTS problem, we first propose the bandwidth-aware data collection (BDC) algorithm to select the optimal uploaded traffic data by evaluating the priority of each road segment covered by the MEC server. Then, we propose the convex-based data recovery (CDR) algorithm to minimize estimation error by transforming the BCTS into an -norm minimization problem. Last but not the least, we implement the simulation model and conduct performance evaluation. The comprehensive simulation results verify the superiority of the proposed algorithm.

Nonlinear approximation via compositions

Given a function dictionary D and an approximation budget N∈N, nonlinear approximation seeks the linear combination of the best N terms {Tn}1≤n≤N⊆D to approximate a given function f with the minimum approximation error εL,f≔min{gn}⊆R,{Tn}⊆D‖f(x)−∑n=1NgnTn(x)‖.Motivated by recent success of deep learning, we propose dictionaries with functions in a form of compositions, i.e., T(x)=T(L)∘T(L−1)∘⋯∘T(1)(x)for all T∈D, and implement T using ReLU feed-forward neural networks (FNNs) with L hidden layers. We further quantify the improvement of the best N-term approximation rate in terms of N when L is increased from 1 to 2 or 3 to show the power of compositions. In the case when L>3, our analysis shows that increasing L cannot improve the approximation rate in terms of N.In particular, for any function f on [0,1], regardless of its smoothness and even the continuity, if f can be approximated using a dictionary when L=1 with the best N-term approximation rate εL,f=O(N−η), we show that dictionaries with L=2 can improve the best N-term approximation rate to εL,f=O(N−2η). We also show that for Hölder continuous functions of order α on [0,1]d, the application of a dictionary with L=3 in nonlinear approximation can achieve an essentially tight best N-term approximation rate εL,f=O(N−2α∕d). Finally, we show that dictionaries consisting of wide FNNs with a few hidden layers are more attractive in terms of computational efficiency than dictionaries with narrow and very deep FNNs for approximating Hölder continuous functions if the number of computer cores is larger than N in parallel computing.

Deep Reinforced Learning Tree for Spatiotemporal Monitoring With Mobile Robotic Wireless Sensor Networks

This paper concerns the deployment problem of wireless sensor networks (WSNs) with mobile robotic sensor nodes for spatiotemporal monitoring. The proposed approach, deep reinforced learning tree (DRLT), utilizes deep reinforcement learning (DRL) to improve the efficiency of searching the most informative sampling locations. The parameterized sampling locations in an infinite horizon space are modeled according to their spatiotemporal correlations and subject to various constraints, including field estimation error and information gain. And the model-based information gain can be calculated efficiently over an infinite horizon. In this manner, the effectiveness of the sampling locations is learned through DRLT during the exploration by the robotic sensors. Then DRLT can instruct the robotic sensors to avoid unnecessary sampling locations in future iterations. Also, it is proved in this paper that the proposed algorithm is capable of searching for the near-optimal sampling locations effectively and guaranteeing a minimum field estimation error. Simulation based on national oceanic and atmospheric administration (NOAA) datasets is presented, which demonstrates the significant enhancements made by the proposed algorithm. Compared with the traditional approaches, such as the information theory-based greedy approach or random sampling, the proposed method shows a superior performance with regard to both estimation error and planning efficiency.

Разностная схема с оптимальным весом для уравнения диффузии-конвекции

Исследована разностная схема с весами для однородного пространственно-одномерного уравнения диффузии-конвекции. Выполнено исследование погрешности аппроксимации разностной схемы в зависимости от шага по времени на основе разложения функции решения и погрешности аппроксимации по тригонометрическому базису. Разработан алгоритм нахождения оптимального значения веса, обеспечивающий минимум погрешности аппроксимации решения исходной начально-краевой задачи для заданных значений шагов временной сетки. Улучшенная точность построенной схемы с оптимальным весом по сравнению с явной схемой и эффективность алгоритма поиска оптимального значения весового параметра продемонстрированы на примере тестовой задачи. A difference scheme with weights for a homogeneous spatially one-dimensional diffusion-convection equation is studied. An analysis of the approximation error for the difference scheme as a time step function is performed on the basis of the expansion of the solution and approximation error in a trigonometric basis. An algorithm is proposed to find the optimal weight value that ensures the minimum approximation error of the solution to an initial boundary value problem for the given values of the time grid steps. A better accuracy of the constructed scheme with the optimal weight compared to the explicit scheme as well as the efficiency of the algorithm for finding the optimal weight value is shown using a test problem.

Novel Radar Waveform Optimization for a Cooperative Radar-Communications System

We develop and present a novel minimum estimation error variance waveform design method. The method optimizes the spectral shape of a unimodular radar waveform such that the performance of a joint radar-communications system that shares spectrum is maximized. We also develop the novel spectral water-filling successive interference cancelation data rate, which employs the continuous spectral water-filling algorithm to obtain the optimal communications power spectrum. We perform a numerical study to compare the performance of the new technique with the previously derived spectral mask shaping method. The global estimation rate and the data rate capture the radar and the communications performance, respectively.

Regression Analysis to Estimate Morphology Parameters of Pepper Plant in a Controlled Greenhouse System

Regression analysis to predict growth indices of plant is essential for understanding the relationship between the total leaf area, production of fresh weight and dry matter, and expansion of the plant growth. An experiment was conducted to develop regression models for estimating leaf area, fresh weight, and dry weight from measurements of plant height at the vegetative phase of hot pepper (Capsicum annuum Linnaeus) grown in biodegradable pots in a greenhouse. Five models were evaluated and compared: linear regression model, two-order polynomial regression model (P. order 2), three-order polynomial regression model (P. order 3), four-order polynomial regression model (P. order 4), and power regression model. The models were compared using the coefficient of determination (R2), Pearson’s correlation coefficient (r), root mean square error (RMSE), relative standard error (RSE), and mean absolute percentage error (MAPE). Power regression involving plant height demonstrated the highest R-square among the other models with minimum error estimate for the expected leaf area (R2 > 0.96, r > 0.98, RMSE 0.98, r > 0.99, RMSE 0.97, r > 0.98, RMSE < 0.03, RSE < 0.02, and MAPE < 11.7) of the plant considering both the fit and degree of adjustment, and the interpretation of the model. This study creates scope for further experimentation on various species of crops by changing management practices under different environmental conditions to enhance knowledge and understanding of the growing patterns of plants.

Optimal parameter identification of synthetic gene networks using harmony search algorithm.

Computational modeling of engineered gene circuits is an important while challenged task in systems biology. In order to describe and predict the response behaviors of genetic circuits using reliable model parameters, this paper applies an optimal experimental design(OED) method to obtain input signals. In order to obtain informative observations, this study focuses on maximizing Fisher information matrix(FIM)-based optimal criteria and to provide optimal inputs. Furthermore, this paper designs a two-stage optimization with the modified E-optimal criteria and applies harmony search(HS)-based OED algorithm to minimize estimation errors. The proposed optimal identification methodology involves estimation errors and the sample size to pursue a trade-off between estimation accuracy and measurement cost in modeling gene networks. The designed cost function takes two major factors into account, in which experimental costs are proportional to the number of time points. Experiments select two types of synthetic genetic networks to validate the effectiveness of the proposed HS-OED approach. Identification outcomes and analysis indicate the proposed HS-OED method outperforms two candidate OED approaches, with reduced computational effort.

Kernel Flows: From learning kernels from data into the abyss

Learning can be seen as approximating an unknown function by interpolating the training data. Although Kriging offers a solution to this problem, it requires the prior specification of a kernel and it is not scalable to large datasets. We explore a numerical approximation approach to kernel selection/construction based on the simple premise that a kernel must be good if the number of interpolation points can be halved without significant loss in accuracy (measured using the intrinsic RKHS norm ‖⋅‖ associated with the kernel). We first test and motivate this idea on a simple problem of recovering the Green's function of an elliptic PDE (with inhomogeneous coefficients) from the sparse observation of one of its solutions. Next we consider the problem of learning non-parametric families of deep kernels of the form K1(Fn(x),Fn(x′)) with Fn+1=(Id+ϵGn+1)∘Fn and Gn+1∈span{K1(Fn(xi),⋅)}. With the proposed approach constructing the kernel becomes equivalent to integrating a stochastic data driven dynamical system, which allows for the training of very deep (bottomless) networks and the exploration of their properties. These networks learn by constructing flow maps in the kernel and input spaces via incremental data-dependent deformations/perturbations (appearing as the cooperative counterpart of adversarial examples) and, at profound depths, they (1) can achieve accurate classification from only one data point per class (2) appear to learn archetypes of each class (3) expand distances between points that are in different classes and contract distances between points in the same class. For kernels parameterized by the weights of Convolutional Neural Networks, minimizing approximation errors incurred by halving random subsets of interpolation points, appears to outperform training (the same CNN architecture) with relative entropy and dropout.

Non-invasive Estimation of Right Atrial Pressure Using Inferior Vena Cava Echography

The pulsatility of the inferior vena cava (IVC) reflects the volume status and central venous pressure of patients. The standard clinical indicator of IVC pulsatility is the caval index (CI), measured from ultrasound recordings. However, its estimation is not standardized and is vulnerable to artifacts, mostly because of IVC movements during respiration. Thus, we used a (recently patented) semi-automated method that tracks IVC movements and averages the CI across an entire section of the vein, which provides a more stable indication of pulsatility. This algorithm was used to estimate the CI, pulsatility indicators reflecting either respiratory or cardiac stimulation and the mean diameter of the IVC. These IVC indices, together with anthropometric information, were used as potential features to build an innovative model for the estimation of the right atrial pressure (RAP) recorded from 49 catheterized patients. An exhaustive search was carried out for the best among all possible models that could be obtained by using combinations of these features. The model with minimum estimation error (tested with a leave-one-out approach) was selected. This model estimated RAP with an error of about 3.6 ± 2.6 mm Hg (mean ± standard deviation); the error when using only operator measured variables, without software, was about 4.0 ± 2.5 mm Hg. These promising results underline the need for further study of our RAP estimation method on a larger data set.

Partitional calorimetry.

For thermal physiologists, calorimetry is an important methodological tool to assess human heat balance during heat or cold exposures. A whole body direct calorimeter remains the gold standard instrument for assessing human heat balance; however, this equipment is rarely available to most researchers. A more widely accessible substitute is partitional calorimetry, a method by which all components of the conceptual heat balance equation-metabolic heat production, conduction, radiation, convection, and evaporation-are calculated separately based on fundamental properties of energy exchange. Since partitional calorimetry requires relatively inexpensive equipment (vs. direct calorimetry) and can be used over a wider range of experimental conditions (i.e., different physical activities, laboratory or field settings, clothed or seminude), it allows investigators to address a wide range of problems such as predicting human responses to thermal stress, developing climatic exposure limits and fluid replacement guidelines, estimating clothing properties, evaluating cooling/warming interventions, and identifying potential thermoregulatory dysfunction in unique populations. In this Cores of Reproducibility in Physiology (CORP) review, we summarize the fundamental principles underlying the use of partitional calorimetry, present the various methodological and arithmetic requirements, and provide typical examples of its use. Strategies to minimize estimation error of specific heat balance components, as well as the limitations of the method, are also discussed. The goal of this CORP paper is to present a standardized methodology and thus improve the accuracy and reproducibility of research employing partitional calorimetry.

Human Emotion Characterization by Heart Rate Variability Analysis Guided by Respiration.

Developing a tool that identifies emotions based on their effect on cardiac activity may have a potential impact on clinical practice, since it may help in the diagnosing of psycho-neural illnesses. In this study, a method based on the analysis of heart rate variability (HRV) guided by respiration is proposed. The method was based on redefining the high frequency (HF) band, not only to be centered at the respiratory frequency, but also to have a bandwidth dependent on the respiratory spectrum. The method was first tested using simulated HRV signals, yielding the minimum estimation errors as compared to classic and respiratory frequency centered at HF band based definitions, independently of the values of the sympathovagal ratio. Then, the proposed method was applied to discriminate emotions in a database of video-induced elicitation. Five emotional states, relax, joy, fear, sadness, and anger, were considered. The maximum correlation between HRV and respiration spectra discriminated joy versus relax, joy versus each negative valence emotion, and fear versus sadness with p-value ≤ 0.05 and AUC ≥ 0.70. Based on these results, human emotion characterization may be improved by adding respiratory information to HRV analysis.

Adaptive Neuro-Filtering Based Visual Servo Control of a Robotic Manipulator

This paper focuses on the solutions to flexibly regulate robotic by vision. A new visual servoing technique based on the Kalman filtering (KF) combined neural network (NN) is developed, which need not have any calibration parameters of robotic system. The statistic knowledge of the system noise and observation noise are first given by Gaussian white noise sequences, the nonlinear mapping between robotic vision and motor spaces are then on-line identified using standard Kalman recursive equations. In real robotic workshops, the perfect statistic knowledge of the noise is not easy to be derived, thus an adaptive neuro-filtering approach based on KF is also studied for mapping on-line estimation in this paper. The Kalman recursive equations are improved by a feedforward NN, in which the neural estimator dynamic adjusts its weights to minimize estimation error of robotic vision-motor mapping, without the knowledge of noise variances. Finally, the proposed visual servoing based on adaptive neuro-filtering has been successfully implemented in robotic pose regulation, and the experimental results demonstrate its validity and practicality for a six-degree-of-freedom (DOF) robotic system which the hand-eye without calibrated.

Assessment of Breathing Parameters Using an Inertial Measurement Unit (IMU)-Based System.

Breathing frequency (fB) is an important vital sign that—if appropriately monitored—may help to predict clinical adverse events. Inertial sensors open the door to the development of low-cost, wearable, and easy-to-use breathing-monitoring systems. The present paper proposes a new posture-independent processing algorithm for breath-by-breath extraction of breathing temporal parameters from chest-wall inclination change signals measured using inertial measurement units. An important step of the processing algorithm is dimension reduction (DR) that allows the extraction of a single respiratory signal starting from 4-component quaternion data. Three different DR methods are proposed and compared in terms of accuracy of breathing temporal parameter estimation, in a group of healthy subjects, considering different breathing patterns and different postures; optoelectronic plethysmography was used as reference system. In this study, we found that the method based on PCA-fusion of the four quaternion components provided the best fB estimation performance in terms of mean absolute errors (<2 breaths/min), correlation (r > 0.963) and Bland–Altman Analysis, outperforming the other two methods, based on the selection of a single quaternion component, identified on the basis of spectral analysis; particularly, in supine position, results provided by PCA-based method were even better than those obtained with the ideal quaternion component, determined a posteriori as the one providing the minimum estimation error. The proposed algorithm and system were able to successfully reconstruct the respiration-induced movement, and to accurately determine the respiratory rate in an automatic, position-independent manner.

Low Complexity Fan Filters Using Multiobjective Artificial Bee Colony Optimization Aided McClellan Transformation for Directional Filtering

This brief considers an effective design method for quadrantally symmetric and centrosymmetric fan-type 2-D filters with minimum contour approximation error, using McClellan transformation aided by multiobjective artificial bee colony (MOABC) optimization. The novelty of the proposed approach lies in the use of MOABC optimization with McClellan transformation to realize fan filters with the least contour deviation error compared to the existing transformation-based design techniques, and highly reduced implementation complexity with comparable magnitude errors with respect to the existing optimal design techniques. Pareto-dominance-based MOABC optimization is used to find the optimal design parameters for transformation. The feasibility of the proposed method is verified for fan filters with different passband angles. The effectiveness of the designed filter in texture identification of an image is also demonstrated.

Three autoregressive-neural network hybrid models for energy efficiency estimation of induction motors

PurposeImprovements on the energy efficiency of the induction motors bear on not only these motors but also on the whole industry as a result of preference of these types of motors. In recent projects, energy efficiency of the induction motors is approaching to 90 per cent. The first necessary condition of the efficiency improvements is an accurate estimation of energy efficiency. This study aims to estimate the energy efficiency of induction motors by using three innovative estimation methods.Design/methodology/approachData for 307 motors were taken from three different companies and their torque, power, power factor and speed data were used. Three hybrid models were created by estimating the error of three autoregressive (AR)-based efficiency estimation models with the back-propagation artificial neural network (ANN) structure. In these proposed hybrid models, the AR models were supported with artificial neural networks to obtain a minimum estimation error. These three hybrid models were called as AR1-ANN, AR4-ANN and residual-ANN.FindingsWithout hybridization of AR models by back-propagation ANNs, the best estimation result was obtained by residual model. On the other hand, for the proposed hybrid models, the best estimation was obtained by AR1-ANN, followed by AR4-ANN and finally the residual-ANN according to ME values.Practical implicationsProposed AR-ANN hybrid models relieve of longtime experiments for the energy efficiency measurement of induction motors. Furthermore, these AR-ANN models give more accurate results than the available methods in the literature. Engineering value of this research is three different issues in finding energy efficiency. The first one is minimizing of the test cost, the second one is no requirement the test equipment and the third one is not interrupting the motor. Every company that needs motors can use these estimation methods due to the advantages.Originality/valueNovel three AR-ANN hybrid models for energy efficiency estimation were studied. These novel methods give better response than the other methods which were used for estimation of induction motors in the literature.

A joint resource allocation method for multiple targets tracking in distributed MIMO radar systems

In order to simultaneously improve system performance and resource utilization of distributed multiple-input multiple-output (MIMO) radar systems, a joint resource allocation method is proposed to address the velocity estimation problem for multiple targets tracking in this paper. The paper focuses to improve the tracking performance for key targets using the remaining resources when the general targets have obtained resources to reach to tracking requirements. Firstly, a criterion minimizing the velocity estimation mean square error (MSE) for a key target is considered. Restricted by limited and relatively sufficient system resources and given velocity estimation requirements for general targets, a joint resource allocation optimization model with transmitters, receivers, transmitted power, and signal time is established. We propose a suboptimal method to approximately solve this problem. The method separates the optimization into three steps, where each step transforms the corresponding mixed-Boolean optimization problem into a second-order cone programming (SOCP) problem by convex relaxation. Finally, the approximately optimal solution can be obtained by cyclic minimization method. Extensive simulations indicate that compared with other methods, the proposed joint method can achieve the lowest velocity estimation MSE with the fewest transmitters. Meanwhile, limited by the given velocity estimation MSE, the proposed method can focus on the key target and achieve the whole velocity estimation error minimization while a greater flexibility for target tracking number can be obtained. Moreover, random experiments can further validate and evaluate the proposed method’s effectiveness and traceability with the given scenario.

Tamil and English speech database for heartbeat estimation

The aim of this research work is to provide an open source database containing speech signals and the corresponding heartbeat rates, so as to further widen the area of research in speech signal processing, especially estimation of heartbeat rate from speech. Tamil and English Speech Database for Heartbeat Estimation consists of 10,040 speech recordings. The speech signals were recorded from 109 persons, 52 females and 57 males with an average age of 25 years and 6 months. The informed consented volunteers were asked to perform three tasks; like answering and reading in rest state; answering and reading after physical exercise and answering after watching video clips. 24-th and 72-nd order Mel-Frequency Cepstral Coefficients and 14-th and 52-nd order Auto Regressive Reflection Coefficients are extracted from the speech signal. Prediction of heartbeat is done by linear regression using support vector machine. The statistical significance of the heartbeat prediction results are improved by 10-fold speaker-independent cross validation scheme. Experimental results show a minimum average estimation error of ± 13.

Spike-triggered averaging provides inaccurate estimates of motor unit twitch properties under optimal conditions

Spike-triggered averaging is a commonly used technique for the estimation of motor unit twitches during voluntary contractions, although the obtained twitch estimates are known to be inaccurate in several conditions. Nevertheless, it is commonly assumed that a careful selection of the triggers may reduce the inaccuracy. This study aimed to analyze the impact of trigger selection criteria and thereby to identify the minimum estimation errors using a computational neuromuscular model. Force signals of five-minute duration were simulated at 10 contraction levels between 1 and 30% of the maximal voluntary contraction level (MVC) for motor unit pools of varying size (100, 300, and 800 motor units). Triggers were selected based on the inter-spike intervals (minimal value: 90–175 ms) and the number of triggers (minimal value: 100–800). The simulation results indicated that a minimum of 400 triggers with inter-spike intervals >125 ms are needed to achieve the most accurate twitch estimates. Even under these conditions, however, a substantial estimation error remained (11.8–31.2% for different twitch parameters for simulations with 100 motor units). The error increased with the innervation number. The study demonstrates the fundamental inaccuracy of twitch estimates from spike-triggered averaging, which has important implications for our understanding of muscular adaptations.