Mean Square Estimation Research Articles

Experimental Analysis of Methods Used to Solve Linear Regression Models

Predicting the value of one or more variables using the values of other variables is a very important process in the various engineering experiments that include large data that are difficult to obtain using different measurement processes. Regression is one of the most important types of supervised machine learning, in which labeled data is used to build a prediction model, regression can be classified into three different categories: linear, polynomial, and logistic. In this research paper, different methods will be implemented to solve the linear regression problem, where there is a linear relationship between the target and the predicted output. Various methods for linear regression will be analyzed using the calculated Mean Square Error (MSE) between the target values and the predicted outputs. A huge set of regression samples will be used to construct the training dataset with selected sizes. A detailed comparison will be performed between three methods, including least-square fit; Feed-Forward Artificial Neural Network (FFANN), and Cascade Feed-Forward Artificial Neural Network (CFFANN), and recommendations will be raised. The proposed method has been tested in this research on random data samples, and the results were compared with the results of the most common method, which is the linear multiple regression method. It should be noted here that the procedures for building and testing the neural network will remain constant even if another sample of data is used.

Про задачу оцiнювання стацiонарних процесiв неперервного часу за спостереженнями у спецiальних множинах точок

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary process from observations of the process with missings is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functionals are derived under the condition of spectral certainty, where the spectral density of the process is exactly known. The minimax (robust) method of estimation is applied in the case where the spectral density of the process is not known exactly while some sets of admissible spectral densities are given. Formulas that determine the least favourable spectral densities and the minimax spectral characteristics are derived for some special sets of admissible densities.

Communication Over Quantum Channels With Parameter Estimation

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model can be viewed as a form of quantum metrology, and as the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly-causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2016, on classical-quantum channels. Bosonic dirty paper coding is introduced as a consequence, where we demonstrate that the optimal coefficient is not necessarily that of minimum mean-square error estimation as in the classical setting.

Deception attacks on Kalman filtering with interval estimation performance loss

This paper studies the problem of optimal deception attacks against remote state estimation, where the measurement data is transmitted through an unreliable wireless channel. A malicious agent is capable of intercepting and modifying raw data, with the goal to cause the maximum estimation quality degradation and deceive χ2 anomaly detectors. Contrary to existing studies that focused on greedy attack performance, we consider a more general scenario that the attacker aims to maximize the summation of estimation errors in a fixed interval. It is shown that the information-based optimal attack is a linear combination of the minimum mean-square error estimates of all historical prediction errors. The combination coefficients can be obtained by solving a convex optimization problem. Moreover, the proposed attack can be generalized to deceive interval χ2 detectors with different lengths by slightly modifying the stealthiness constraint. The effectiveness of the proposed method is verified with numerical examples and comparative studies.

Correcting for linkage errors in contingency tables—A cautionary tale

Record linkage aims to bring records together from two or more files that belong to the same statistical entity. Naïvely treating a linked file as if there are no linkage errors may lead to biased inference. We present two general approaches for compensating for linkage error when calculating and analysing a two-way contingency table for categorical data, and study the following question: under what conditions can a compensation approach improve on the naïve approach, where linkage error is not compensated for? To this end, we compare estimation errors, bias, variance and mean square error for the naïve approach and two compensation approaches by means of an analytical study as well as a simulation study.

A new class of efficient and debiased two-step shrinkage estimators: method and application

This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators’ mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators’ performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners.

Sparse, Group-Sparse, and Online Bayesian Learning Aided Channel Estimation for Doubly-Selective mmWave Hybrid MIMO OFDM Systems

Sparse, group-sparse and online channel estimation is conceived for millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We exploit the angular sparsity of the mmWave channel impulse response (CIR) to achieve improved estimation performance. First a sparse Bayesian learning (SBL)-based technique is developed for the estimation of each individual subcarrier's quasi-static channel, which leads to an improved performance versus complexity trade-off in comparison to conventional channel estimation. Then a novel group-sparse Bayesian learning (G-SBL) scheme is conceived for reducing the channel estimation mean square error (MSE). The salient aspect of our G-SBL technique is that it exploits the frequency-domain (FD) correlation of the channel's frequency response (CFR), while transmitting pilots on only a few subcarriers, thus it has a reduced pilot overhead. A low complexity (LC) version of G-SBL, termed LCG-SBL, is also developed that reduces the computational cost of the G-SBL significantly. Subsequently, an online G-SBL (O-SBL) variant is designed for the estimation of doubly-selective mmWave MIMO OFDM channels, which has low processing delay and exploits temporal correlation as well. This is followed by the design of a hybrid transmit precoder and receive combiner, which can operate directly on the estimated beamspace domain CFRs, together with a limited channel state information (CSI) feedback. Our simulation results confirms the accuracy of the analysis.

Cramer-Rao lower bounds of target positioning estimate in netted radar system

Netted radar system has received wide attention due to its higher target detection probability, better target localization and tracking performance than the monostatic/bistatic radar systems. According to the complexity and difficulty of practical application, netted radar system can be divided into simply netted radar system with decentralized processing, traditional netted radar system with centralized data and information fusion processing. Without taking account of the SLP among multiple nodes, the traditional netted radar system has the definite radar coverage and target localization performance after deployment, which means it is not flexible enough to configure on demand in the search phase and localization phase. To further improve performance and flexibility, a novel netted radar system, across which signal, data and information can be shared and integrated to, is considered. In the novel netted radar system, the topology architecture, transmit receiving node, transmitted signal form and other resources are selected and reconstructed according to the task to be needed. To analyze the localization performance of the novel netted radar system, the Cramer–Rao lower bounds (CRLBs) of the target positioning estimate mean square errors (MSEs) are deduced for the coherent-processing (CP), noncoherent-processing (NCP) and data-level processing (DLP) in this paper. Then, the target localization performances of the novel netted radar system with different topology architectures are compared and analyzed.

Scheduler-based state estimation over multiple channels networks

We investigate the remote state estimation problem for networked systems over parallel noise-free communication channels. Due to limited network capabilities in practical network environments, communication schedulers are implemented at the transmit side of each subchannel to promote resource efficiency. Specifically, the processed signals are transmitted only when it is necessary to provide the real-time measurements to the remote estimator. The recursive approximate minimum mean-square error estimator is established to restore the state vector of a target plant by utilizing the scheduled transmission signals. All the information coming from the individual subchannels, even if no measurement is sent, will contribute to improve the estimation performance in an analytical form. Finally, a numerical example is given to illustrate the effectiveness of the main results.

Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method

In this article, a class of nonlinear Volterra-Fredholm fractional integro-differential equations is considered, both theoretical and computational aspects. The respective theoretical results are devoted to the existence of a solution via fixed point approach. Further, for the computational aspect, the Proposed Methodology of Haar wavelet collocation. This method minimizes a system of nonlinear algebraic equations, which is developed by Broyden’s method. In literature, the proposed method is taken for checking the convergence with help of some numerical examples. Calculate mean square root and maximum absolute errors for various collocation point numbers. The final outcomes show that the applied Haar method is effective, and the convergence rate for different collocation point is roughly equal to 2.

Event-triggered optimal Kalman consensus filter with upper bound of error covariance

In this paper, we present an event-triggered optimal Kalman consensus filter (EOKCF) for state estimation in distributed wireless sensor networks. The local message is exchanged only when the local estimation violates a predetermined Send-on-Delta (SoD) data transmission condition in order to reduce the amount of data transfer. The neighboring measurement and estimation information are integrated into the consensus filter, and a recursive upper bound of the error covariance is derived for uncertainties of interval communication from the event-based systems. The optimal Kalman gain and consensus gain matrices are obtained by minimizing the upper bound of state error covariance. The Crameˇr−−Rao lower bound (CRLB) of the state estimates is also introduced to measure the mean-square estimation error performance. The effectiveness of event-triggered communication protocol and the advantages of filtering performance of EOKCF are demonstrated using Monte Carlo simulations on a target tracking application in a distributed sensor network.

Rank-1 Matrix Approximation-Based Channel Estimation for Intelligent Reflecting Surface-Aided Multi-User MISO Communications

The acquisition of channel state information is an essential step in enabling intelligent reflecting surfaces (IRSs) for wireless communications. In this letter, we introduce a novel procedure to estimate the cascaded channel between the base station (BS), IRS, and users in a multi-user multiple-input single-output system. The common BS-IRS channel, over which all users transmit, is leveraged to decompose the cascaded channel into a series of rank-1 matrices. Low-rank matrix recovery methods are utilized to improve upon the linear minimum mean-squared error estimate of the cascaded channel. A theoretical upper bound for the mean-square error (MSE) of the proposed estimator is derived. Numerical results reveal that the proposed techniques outperform the existing counterparts in terms of the MSE and scale with the number of BS antennas.

Artificial intelligence modeling to predict transmembrane pressure in anaerobic membrane bioreactor-sequencing batch reactor during biohydrogen production

The complex nature of wastewater treatment has led to search for alternative strategies such as different artificial intelligence (AI) techniques to model the various operational parameters. The present work is aimed at predicting the transmembrane pressure (TMP) as a key operational parameter in the case of anaerobic membrane bioreactor-sequencing batch reactor (AnMBR-SBR) during biohydrogen production using the adaptive neuro-fuzzy inference systems (ANFIS) and artificial neural network (ANN). In both the models, organic loading rates (OLR) ranging from 0.5 to 8.0 g COD/L/d, effluent pH (3.6–6.9), mixed liquor suspended solid (4.6–21.5 g/L) and mixed liquor volatile suspended solid (3.7–15.5 g/L) were used as the input parameters to test TMP as an output parameter. The ANFIS model was trained using the hybrid algorithms for TMP prediction. The higher prediction performance was obtained by using the Gauss membership function with four membership numbers. A back-propagation algorithm was also employed for the feed forward training of ANN model; the best structure was a Levenberg-Marquardt training algorithm with nine neurons in the hidden layer. By employing ANFIS and ANN models, relatively a good prediction of TMP was obtained with the R2 values of 0.93 and 0.88, respectively while the calculated mean square error for TMP in the ANFIS model (7.3 × 10−3) was lower than that of ANN model (8.02 × 10−3). The higher R2 and lower MSE values for the ANFIS model exhibited a better TMP prediction performance than the ANN model. Finally, it was observed that in the sensitivity analysis of ANN model, OLR was the most important input parameter on the variation of TMP.

A measurement error Rao\u2013Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates

The assessment of prevalence on regional levels is an important element of public health reporting. Since regional prevalence is rarely collected in registers, corresponding figures are often estimated via small area estimation using suitable health data. However, such data are frequently subject to uncertainty as values have been estimated from surveys. In that case, the method for prevalence estimation must explicitly account for data uncertainty to allow for reliable results. This can be achieved via measurement error models that introduce distribution assumptions on the noisy data. However, these methods usually require target and explanatory variable errors to be independent. This does not hold when data for both have been estimated from the same survey, which is sometimes the case in official statistics. If not accounted for, prevalence estimates can be severely biased. We propose a new measurement error model for regional prevalence estimation that is suitable for settings where target and explanatory variable errors are dependent. We derive empirical best predictors and demonstrate mean-squared error estimation. A maximum likelihood approach for model parameter estimation is presented. Simulation experiments are conducted to prove the effectiveness of the method. An application to regional hypertension prevalence estimation in Germany is provided.

Optimal Causal Rate-Constrained Sampling of the Wiener Process

An encoder causally observes the Wiener process and decides when and what to transmit about it. A decoder makes real-time estimation of the process using causally received codewords. We determine the causal encoding and decoding policies that minimize the mean-square estimation error, under the long-term communication rate constraint of R bits/s. We show that an optimal encoding policy can be implemented as a causal sampling policy followed by a causal compressing policy. We prove that the optimal encoding policy samples the Wiener process once the innovation passes some threshold, and compresses the sign of the innovation (SOI) using a 1-bit codeword. The SOI coding scheme achieves the operational distortion-rate function. This is better than the distortion-rate tradeoff achieved by the best non-causal code, because the SOI coding scheme uses the free timing information supplied by the zero-delay channel between the encoder and the decoder. The distortion-rate tradeoffs achieved with deterministic sampling policies are much worse. The optimal strategy is to sample the process as fast as possible and to transmit 1-bit codewords to the decoder without delay.

Structure and dynamical properties of two-dimensional dusty plasmas on one-dimensional periodic substrates

In the presence of the substrate, various structural and dynamical properties of two-dimensional dusty plasma (2DDP) were investigated using Langevin dynamical simulations. This paper reviews a series of results of the structural and dynamical properties of 2DDP modified by one-dimensional periodic substrates (1DPSs) as follows. First, when the depth of the 1DPS increases gradually, it is found that the static structural order of 2DDP along each potential well of the 1DPS increases first and then decreases gradually. When the width of the 1DPS increases gradually, the particle arrangement in each potential well of the 1DPS changes from one straight row gradually to two rows, including the stable zigzag structure. Second, when there are two rows in each potential well of the 1DPS, the phonon spectra are split into two branches, corresponding to the breathing and sloshing modes, respectively. In addition, due to the pure repulsion between dust particles, from the obtained phonon spectra, the sloshing wave propagates backward at small wave numbers. Third, the calculated mean square displacement shown that, at the intermediate timescale between the initial ballistic and final diffusive motions, the particle motion tends to be more subdiffusive while the depth of the 1DPS increases. While the width of the 1DPS increases gradually, the long-time diffusive motion first increases, then decreases, and finally increases again, exhibiting the oscillation-like diffusion, due to the stable zigzag structure. Finally, when an external direct-current driving force is applied on all particles of 2DDP, three different depinning phases are discovered, which are the pinned, disordered plastic flow, and moving ordered states, respectively, as the driving force increases from zero. In addition, the continuous/discontinuous property of the phase transition between these different depinning states is investigated, showing that the transition property is modulated by the depth of the applied 1DPS.

Discrete-time estimation of switched stochastic polynomial systems and its application to reconstruction of induction motor variables

This paper presents a solution to the filtering problem for a class of stochastic discrete-time nonlinear polynomial systems with switching in the state equation over linear observations and its application to a mechatronic system. The switching in the state equation is performed between two different nonlinear functions according to a sequence of independent Bernoulli random variables that take the quantities of zero and one. The mean-square filtering solution is obtained for a general nonlinear discrete-time polynomial system and a finite-dimensional system of filtering equations is then obtained for a second degree polynomial system as a particular case. The mean-square estimates of polynomial state terms are expressed as functions of the estimate and covariance matrix. Finally, some numerical simulations are carried out to reconstruct the variable states given a vector output measurement for a linear system, a second degree polynomial system, and an induction motor model to show effectiveness of the proposed algorithm. The proposed method is compared with an extended Kalman filter-based algorithm for discrete-time switched nonlinear systems.

Automatic Prediction of Road Angles using Deep Learning-Based Transfer Learning Models

The construction of robust and complex roads requires a considerable amount of resources, time, and effort. These efforts get manifold, especially when a road is to be constructed on rugged terrains. The use of Artificial Intelligence (AI) can be seen in almost all the research sectors. The efforts and the cost involved in road construction can be reduced by the induction of AI-based techniques for the estimation of road construction-related parameters that are required to predict the tentative cost incurred in the whole road construction project. In this article, the angle, which is one of the crucial parameters that aids in estimating the total cost and time required for the whole road construction project is predicted using the variation of three transfer learning-based deep learning models viz. VGG-16, DenseNet-121, and DenseNet-169. The proposed VGG16 based CNN model performance is computed and compared in terms of the evaluation metrics like Mean Square Estimation (MSE), Mean Absolute Error (MAE), and Correlation Coefficient (R2). Based upon the simulation results conducted, it was observed that VGG-16 has yielded road angles with less difference error.

An enhanced iterative receiver based on vector approximate message passing for deep-sea vertical underwater acoustic communications.

Vertical underwater acoustic (UWA) communications play a crucial role in deep-sea applications. A vertical UWA channel generally features a moderate multipath but with time-varying Doppler shifts as well as loud impulsive noise. To achieve a robust vertical single-carrier UWA communication, this paper proposes an enhanced iterative receiver. First, a spline interpolation-based timing estimation approach is proposed to compensate for the time-varying Doppler effects efficiently. Then, the residual timing errors and the multipath interference are tackled by a fractionally spaced self-iterative soft equalizer (SISE) based on the vector approximate message passing (VAMP) algorithm. The VAMP-SISE consists of four parts: an inner soft slicer and an inner soft equalizer for symbol detection as well as a denoiser and a minimum mean-squared error estimator for impulsive noise suppression. Different parts iteratively exchange extrinsic information to improve the equalization performance. Last, a channel-fitting irregular convolutional code and a unity-rate code are employed at the transmitter to lower the signal-to-noise ratio threshold for reliable communications. Deep-sea experiments verify the performance superiority of the proposed receiver over existing schemes.

Multi-Sensor Fusion for Underwater Vehicle Localization by Augmentation of RBF Neural Network and Error-State Kalman Filter.

The Kalman filter variants extended Kalman filter (EKF) and error-state Kalman filter (ESKF) are widely used in underwater multi-sensor fusion applications for localization and navigation. Since these filters are designed by employing first-order Taylor series approximation in the error covariance matrix, they result in a decrease in estimation accuracy under high nonlinearity. In order to address this problem, we proposed a novel multi-sensor fusion algorithm for underwater vehicle localization that improves state estimation by augmentation of the radial basis function (RBF) neural network with ESKF. In the proposed algorithm, the RBF neural network is utilized to compensate the lack of ESKF performance by improving the innovation error term. The weights and centers of the RBF neural network are designed by minimizing the estimation mean square error (MSE) using the steepest descent optimization approach. To test the performance, the proposed RBF-augmented ESKF multi-sensor fusion was compared with the conventional ESKF under three different realistic scenarios using Monte Carlo simulations. We found that our proposed method provides better navigation and localization results despite high nonlinearity, modeling uncertainty, and external disturbances.