Mean Square Error Criterion Research Articles

Gaussian Data-Aided Sensing With Multichannel Random Access and Model Selection

In this article, we study data-aided sensing (DAS) for a system consisting of a base station (BS) and a number of nodes, where the BS becomes a receiver that collects measurements or data sets from the nodes that are distributed over a cell. DAS is an iterative data collection scheme that allows the BS to efficiently estimate a target signal (i.e., all nodes’ measurements) with a small number of measurements (compared to random polling). In DAS, a set of nodes are selected in each round based on the data sets that are already available at the BS from previous rounds for efficient data collection. We consider DAS for measurements that are correlated with Gaussian in this article. The resulting DAS is referred to as Gaussian DAS. Using the mean-squared error (MSE) criterion, in each round, the BS is able to choose a node that has a data set to minimize the MSE of the next round. Furthermore, we generalize Gaussian DAS in two different ways: 1) with multiple parallel channels to upload measurements from nodes using random access and 2) with a model selection, where a multiarmed bandit problem formulation is used to combine the model selection with DAS.

Resilient fault-tolerant anti-synchronization for stochastic delayed reaction–diffusion neural networks with semi-Markov jump parameters

This paper deals with the anti-synchronization issue for stochastic delayed reaction–diffusion neural networks subject to semi-Markov jump parameters. A resilient fault-tolerant controller is utilized to ensure the anti-synchronization in the presence of actuator failures as well as gain perturbations, simultaneously. Firstly, by means of the Lyapunov functional and stochastic analysis methods, a mean-square exponential stability criterion is derived for the resulting error system. It is shown the obtained criterion improves a previously reported result. Then, based on the present analysis result and using several decoupling techniques, a strategy for designing the desired resilient fault-tolerant controller is proposed. At last, two numerical examples are given to illustrate the superiority of the present stability analysis method and the applicability of the proposed resilient fault-tolerant anti-synchronization control strategy, respectively.

Multitask diffusion affine projection sign algorithm and its sparse variant for distributed estimation

Distributed adaptation over multitask networks has attracted particular attention due to its enhanced modeling capacity compared to that over conventional single-task networks. Most of the existing works derive their multitask adaptive algorithms using mean-square error (MSE) or least squares (LS) criterion, leading to multitask LMS- or LS-type algorithms. These algorithms, however, may suffer from deteriorated convergence rate or even divergence in impulsive noise environments. In order to address this problem, we propose a robust diffusion affine projection sign algorithm for multitask parameter estimation. The algorithm is derived by using the method of data reusing and minimizing the weighted sum of the l1-norms of some intermediate error vectors plus a similarity term subject to constraints on intermediate weight vectors at each agent. The multitask similarity relationship is characterized by the distance regularization among weight vectors. Furthermore, a variant of this algorithm, which is obtained by further regularizing the cost function by the l0-norm of the intermediate weight vector at each agent, is presented to promote convergence rate for jointly sparse parameter vectors estimation.

Dissipativity-Based Sampled-Data Control for Fuzzy Switched Markovian Jump Systems

In this article, the dissipativity-based sampled-data control problem is studied for the fuzzy switched Markovian jump systems (FSMJSs). By considering the problem of the asynchronous switching caused by the subsystems' switching occurred during the sampling intervals, constructing novel time-dependent Lyapunov functional, and using average dwell time (ADT) approach, sufficient mean-square exponential stability criteria, and strictly ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> )-γ- dissipativity criteria are proposed under the constraints that the maximum sampling period is no larger than the dwell-time between the transition rates switching instants. Meanwhile, a relationship between ADT and sampling period is revealed for FSMJSs. Based on the strictly ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> )-γ- dissipativity criteria, the sampled-data controller is designed for FSMJSs. A circuit simulation example is provided to illustrate the effectiveness of the proposed method.

Recursive Polynomial Minimum Mean-Square Error Estimation with Applications to Orbit Determination

This paper presents a systematic generalization of the linear update structure associated with the extended Kalman filter for high-order polynomial estimation of nonlinear dynamical systems. The minimum mean-square error criterion is used as the cost function to determine the optimal polynomial update during the estimation process. The high-order series representation is implemented effectively using differential algebra techniques. Numerical examples show that the proposed algorithm, named the high-order differential algebra Kalman filter, provides superior robustness and/or mean-square error performance as compared to linear estimators under the condition considered.

Extreme Learning Machine Under Minimum Information Divergence Criterion

In recent years, extreme learning machine (ELM) and its improved algorithms have been successfully applied to various classification and regression tasks. In these algorithms, MSE criterion is commonly used to control training error. However, MSE criterion is not suitable to deal with outliers, which can exist in general regression or classification tasks. In this paper, a novel extreme learning machine under minimum information divergence criterion (ELM-MinID) is proposed to deal with the training set with noises. In minimum information divergence criterion, the Gaussian kernel function and Euclidean information divergence are utilized to substitute the mean square error (MSE) criterion to enhance the anti-noise ability of ELM. Experimental results on two synthetic datasets and eleven benchmark datasets show that this method is superior to traditional ELMs.

Iterative Sequential Estimation for Multiple Structured Signals

In this paper, we address the signal estimation problem for a linear combination of multiple structured models, which is widely employed in the passive and/or active sensing systems to characterize the behaviors, for example, jamming and multipath propagation, in radar and communication societies. An iterative sequential estimation (ISE) algorithm is presented to obtain simultaneously the multiple structured signals. At each iteration, employing the estimated signals at the previous step, the optimal linear filters, based on mean-squared error criteria, are designed to minimize the output average power for every element of each signal. Finally, we evaluate the performance of the proposed ISE method compared with the least-square and compressed sensing algorithms via numerical simulations. The results highlight the presented algorithm shows a better signal estimation performance at low SNR and plays a trade-off between the computational complexity and the signal estimation performance.

An improved weighted centroid localisation algorithm for wireless sensor networks in coal mine underground

In view of the practical characteristics of coal mine underground working environment and the low positioning accuracy of existing algorithm, an improved weighted centroid localisation algorithm based on received signal strength indicator (RSSI) is proposed. Firstly, the environmental parameters of RSSI ranging are modified by the least square method to eliminate the influence of various interferences on the measured data. The exponential factor and the modified RSSI value are directly calculated to determine the coordinates of the unknown node. The exponential factor is optimised by an improved quantum particle swarm optimisation algorithm based on the criterion of minimum root mean square error. The simulation results show that the proposed algorithm can reduce the influence of complex environment factors in the positioning process and has the better positioning accuracy than the traditional method, which meets requirements of personnel location precision in underground long-distance roadway.

Estimation of Dew Point Temperature in Different Climates of Iran Using Support Vector Regression

The prediction of global climate change using the values recorded in a statistical period requires a precise method that can accurately identify the fluctuations of these changes. By patterning these changes, the parameter values for the years or future periods are predicted, or the statistical gap can be eliminated. In this research, meteorological data of six stations in different climates of Iran were used to model and estimate the values of the dew point temperature (DPT). The stations studied are Ahvaz, Urmia, Kerman, Gorgan, Rasht, and Babolsar. In order to estimate the DPT values, support vector regression was used, and to optimize the parameters of the support vector regression model, the ant colony algorithm was used. In this study, four different input patterns of meteorological data have been investigated as input of the support vector regression model. Pattern I with seven inputs (monthly minimum, maximum, and average air temperatures, monthly precipitation, saturation vapor pressure, actual vapor pressure and relative humidity), Pattern II with three inputs (monthly average air temperature, saturation vapor pressure, and actual vapor pressure), Pattern III with two inputs (monthly minimum and maximum air temperatures), and Pattern IV with an input (monthly average air temperature) were used. It is recommended that if the number of inputs in the model is small, the model will be more user-friendly. Based on the results of analyzing different patterns, it can be concluded, that Pattern III is the suitable pattern for estimating DPT values at the stations studied in different climates of Iran based on the three criteria of root mean square error (RMSE), Nash–Sutcliffe model efficiency coefficient (NSE), and coefficient of determination (R2). Overall, the results showed that the selected pattern increases the accuracy of the model by up to 24% compared to the conventional model.

A Class of Diffusion Zero Attracting Stochastic Gradient Algorithms With Exponentiated Error Cost Functions

In this paper, a class of diffusion zero-attracting stochastic gradient algorithms with exponentiated error cost functions is put forward due to its good performance for sparse system identification. Distributed estimation algorithms based on the popular mean-square error criterion have poor behavior for sparse system identification with color noise. To overcome this drawback, a class of stochastic gradient least exponentiated (LE) algorithms with exponentiated error cost functions were proposed, which achieved a low steady-state compared with the least mean square (LMS) algorithm. However, those LE algorithms may suffer from performance deterioration in the spare system. For sparse system identification in the adaptive network, a polynomial variable scaling factor improved diffusion least sum of exponentials (PZA-VSIDLSE) algorithm and an l p -norm constraint diffusion least exponentiated square (LP-DLE2) algorithm are proposed in this work. Instead of using the l 1 -norm penalty, an l p -norm penalty and a polynomial zero-attractor are employed as a substitution in the cost functions of the LE algorithms. Then, we perform mean behavior model and mean square behavior modal of the LP-DLE2 algorithm with several common assumptions. Moreover, simulations in the context of distributed network sparse system identification show that the proposed algorithms have a low steady-state compared with the existing algorithms.

New Parametric Estimation Methods based on Ranked Set Sampling

The problem of parameters estimation plays a significant role in various areas of academic researches. In this article, we propose three different methods of estimation for the parameters of location-scale family under ranked set sampling in the view of missing data mechanism. Through a series of Monte Carlo simulations, it is well investigated that the proposed methods are relatively robust from violating the perfect ranking condition and provide better performance over their competitors using bias and MSE (mean square error) criteria. An empirical data set is also used for illustrative purposes.

PCN423 MEASURING FATIGUE SYMPTOMS AND IMPACTS IN CHRONIC LYMPHOCYTIC LEUKEMIA (CLL): EVALUATING DIMENSIONALITY OF THE FACIT-FATIGUE

The Functional Assessment of Cancer Therapy–Fatigue (FACIT-Fatigue) is a well-validated instrument to assess fatigue in cancer or other chronic illnesses. It can be reported as a single global fatigue score (GFS) or as separate scores for symptoms (FSS) and impacts (FIS) (Cella, 2011). Confirmatory factor analysis (CFA) and bifactor analysis were conducted to evaluate if this dimensionality also holds in the CLL population. FACIT-Fatigue data from 263 CLL patients were analyzed. Single factor models were specified for GFS, FSS and FIS to determine the dimensionality of all 13 items of FACIT-Fatigue. A bifactor model was tested including a global factor (defined by loadings of all 13 items) and two subdomain factors: symptoms (5 items) and impacts (8 items). Criteria of a Root Mean Square Error of Approximation (RMSEA) <0.10 and a Comparative Fit Index (CFI) >0.90 were set to define acceptable model fit. Mean scores for the items ranged from 0.53 to 2.23 (item range 0-4). For the three single-factor models specified (GFS, FSS and FIS), CFI values were >0.90 and RMSEA <0.10. All item factor loadings were statistically significant and >0.3. Bifactor model fit was excellent (CFI>0.95; RMSEA<0.08). All items had higher loadings on GFS, ranging from 0.36 (“Able to do my usual activities”) to 0.92 (“Trouble starting things”), than on their sub-domain factors, supporting the essential unidimensionality of the FACIT-Fatigue. Conclusion: Results confirmed the findings of Cella (2011) in the CLL population. FACIT-Fatigue is unidimensional, and the GFS is a valid endpoint to report in clinical research. If preferred by researchers, it can also be supplemented with two definable components of fatigue, symptoms and impacts, as supported by the bifactor model and CFA results for each subdomain. Being able to distinguish between these components enhances understanding of patients’ experience in CLL.

Directional Active Noise Control with a Local Minimax Error Criterion

The traditional mean squared error (MSE) criterion can be formulated as a quadratic function of a vector of control filter coefficients, and it is easy to obtain optimal control filter coefficients. Although the MSE criterion can lead to noise reductions in the control area, an unpredictable directional residual sound field is generated. In this paper, we propose a method for multi-channel active harmonic noise control with a local minimax error criterion based on the Nelder–Mead algorithm, which leads to reductions at all error positions and greater reductions at controllable positions. Directional noise reduction experiments of two areas are presented for two different error criteria at discrete locations in an anechoic chamber. Compared with a system employing the traditional MSE criterion, the results show that an active noise control system with the proposed criterion can achieve extra reductions at specified locations and overall noise reductions at the same time. The present research offers some important insights into directional control.

Joint Iterative Channel Estimation and Frequency-Domain Turbo Equalization for Single-Carrier Spatial Modulation

Single-carrier frequency-domain turbo equalization (SC-FDTE) has gained widespread adoption in the emerging broadband spatial modulation (SM) systems operating in frequency-selective channels, where the channel model considered is a quasi-static Rayleigh fading channel. In this paper, a new class of robust FDTE designs based on the minimum mean-square error (MMSE) criterion is conceived for broadband single-carrier SM (SC-SM) systems relying on realistic imperfect channel knowledge. First, a robust time-domain soft-decision feedback (TDSDF)-aided FDTE is proposed to cope with channel estimation errors at the receiver. Furthermore, its robust frequency-domain soft-decision feedback (FDSDF)-aided counterpart is derived to offer a low-complexity approximate solution. Finally, by exploiting the carefully selected reliable soft-decision output of the channel decoder as pilots, we refine the resultant decision-directed channel estimation. As a benefit, the performance of the two robust FDTEs can be further improved. Both our simulation results and our extrinsic information transfer (EXIT) chart analysis demonstrate that the proposed robust FDTEs achieve significant performance improvements over the conventional FDTEs.

Reconstructing Gaussian Sources by Spatial Sampling

Consider a Gaussian memoryless multiple source (GMMS) with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components is sampled and compressed with the objective of reconstructing all the $m$ components within a specified level of distortion under a mean-squared error criterion. In Bayesian and nonBayesian settings, the notion of universal sampling rate-distortion function for Gaussian sources is introduced to capture the optimal tradeoffs among sampling, compression rate, and distortion level. Single-letter characterizations are provided for the universal sampling rate-distortion function. Our achievability proofs highlight the following structural property: it is optimal to compress and reconstruct first the sampled components of the GMMS alone, and then form estimates for the unsampled components based on the former.

Non-linear state recovery in power system under bad data and cyber attacks

The problems of recovering the state of power systems and detecting the instances of bad data have been widely studied in literature. Nevertheless, these two operations have been designed and optimized for the most part in isolation. Specifically, state estimators are optimized based on the minimum mean-square error criteria, which is only optimal when the source of distortions in the data is Gaussian random noise. Hence, the state estimators fail to perform optimality when the data is further contaminated by bad data, which cannot necessarily be modeled by additive Gaussian terms. The problem of power state estimation has been studied extensively. But the fundamental performance limits and the attendant decision rules are unknown when the data is potentially compromised by random bad data (due to sensor failures) or structured bad data (due to cyber attacks, which are also referred to false data injection attacks). This paper provides a general framework that formalizes the underlying connection between state estimation and bad data detection routines. We aim to carry out the combined tasks of detecting the presence of random and structured bad data, and form accurate estimations for the state of power grid. This paper characterizes the optimal detectors and estimators. Furthermore, the gains with respect to the existing state estimators and bad data detectors are established through numerical evaluations.

Comparison of four methods to estimate the scale parameter for Extended Poisson Exponential distribution

In this paper, it was obtained estimators of the scale parameter of Extended Poisson Exponential distribution by four methods using complete data, these methods are the Maximum Likelihood Estimator (MLE), the Least Squares Estimator (LSE), Plotting Position Estimator (PPE) and White Estimator (WE), these four methods have been compared by the criteria of Mean Square Error (MSE) using Monte Carlo simulation, and from the results on the samples in the simulation, the comparison in this study showed that Maximum Likelihood Estimator method is best from other methods followed by the White Estimator method then the Least Squares Estimator method.

Diffusive MIMO Molecular Communications: Channel Estimation, Equalization, and Detection

In diffusion-based communication, for molecular systems, the achievable data rate depends on the stochastic nature of diffusion, which exhibits a severe inter-symbol-interference (ISI). Multiple-input multiple-output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean square error (MSE). The numerical validations in terms of MSE are compared with Cramer–Rao bound derived herein. Equalization is based on decision feedback equalizer (DFE) structure as this is effective in mitigating diffusive ISI/ILI. Zero-forcing, minimum MSE, and least-squares criteria have been paired to DFE, and their performances are evaluated in terms of bit error probability. D-MIMO time interleaving is exploited as an additional countermeasure to mitigate the ILI with remarkable performance improvements. The configuration of nano-transceivers is not static but affected by a Brownian motion. A block-type communication is proposed for D-MIMO channel estimation and equalization, and the corresponding time-varying D-MIMO MC system is numerically evaluated.

Generalized Classes of Regression-Cum-Ratio Estimators of Population Mean in Stratified Random Sampling

In this paper, classes of separate and combined regression-cum-ratio estimators have been proposed for estimating the finite population mean in stratified random sampling. The expressions for biases and mean square errors (MSEs) of the proposed classes have been derived to the first order of approximation. It has also been verified that the proposed classes of estimators, at their optimum conditions, are equivalent to the separate regression estimator. The proposed classes of estimators have been compared with the other existing estimators using MSE criterion, and the conditions under which the proposed classes perform better have been obtained. Numerical illustrations are given in support of theoretical findings. Relevance of the work The estimation theory is relevant to various interdisciplinary areas of research including economics, clinical trials, population studies, engineering, agriculture, etc. Also, the problem of estimation of mean is of huge importance in research, for instance, the estimation of: average agricultural production, average life span of persons in a region, mean concentration of dissolved minerals in water, and much more. For the estimation of mean, several design-based approaches are being widely used, for instance, simple random sampling, stratified random sampling, two-phase sampling, etc. If the population under study is homogeneous, then the simple random sampling design is used at the estimation stage. However, in various practical situations, the research study is based on the heterogeneous population, and in that case the stratified random sampling procedure is preferable over the simple random sampling. Considering the above fact, an attempt has been made in this paper to develop the classes of generalized estimators for the mean of the variable under study using stratified random sampling.

Two‐stage BFGS‐based hybrid precoding for mmWave multiuser MIMO systems

Millimetre wave (mmWave) communications are the most promising candidate for the future fifth-generation mobile broadband networks, which offer greater available spectrum than current cellular. However, the huge path loss and rain attenuation due to the characteristic of the mmWave channel make it difficult to realise. Thanks to the small wavelength of mmWave signals, massive multi-input-multi-output (MIMO) systems can be leveraged to overcome the path loss. Unfortunately, in contrast to conventional MIMO systems, high-power consumption and hardware cost make fully digital precoding impractical. In this study, the authors study the hybrid precoding structure for multiuser mmWave systems, which compromises the cost and performance. First, an extension algorithm from single user systems, which directly decomposes the optimal fully digital precoder into a baseband precoder and an analogue radio-frequency (RF) precoder, is introduced according to the recent work. Then, the drawback of this kind of algorithm is analysed at high signal-to-noise ratios. Subsequently, a two-stage hybrid precoding algorithm, which is based on the minimum mean-squared error criterion is proposed, where the modified Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is presented to reduce the reconstruction error of computing the analogue RF precoder. Simulation results show that the proposed precoding algorithm can significantly improve the performance of the system sum-rate.