Mean Square Error Sense Research Articles

Atomic physics-inspired atom search optimization heuristics integrated with chaotic maps for identification of electro-hydraulic actuator systems

Electro-hydraulic actuator system (EHAS) has imposed a challenge in the research community for accurate mathematical modeling and identification due to non-linearities. In this paper, autoregressive exogenous (ARX) structure is used for EHAS modeling and identification is performed by exploiting the competency of atomic physics-based chaotic atom search optimization (CASO) that adapts ten chaotic maps (Chebyshev, Circle, Gauss, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal and Tent) in position update of atom search optimization (ASO). The fitness/merit function of the EHAS model is developed in mean-square error (MSE) sense between desired and approximated values. Simulations and analysis show that ASO with a chaotic logistic map (CASO5) performs better than the ASO and its other chaotic variants, as well as other recently introduced metaheuristics for diverse variations in the system model. Statistics based on MSE, learning plots, results of autonomous trials and average fitness analyses verify the consistency and reliability of the CASO5 for the identification of the EHAS model.

Blood Pressure Estimation from Photoplythmography Using Hybrid Scattering–LSTM Networks

One of the most significant indicators of heart and cardiovascular health is blood pressure (BP). Blood pressure (BP) has gained great attention in the last decade. Uncontrolled high blood pressure increases the risk of serious health problems, including heart attack and stroke. Recently, machine/deep learning has been leveraged for learning a BP from photoplethysmography (PPG) signals. Hence, continuous BP monitoring can be introduced, based on simple wearable contact sensors or even remotely sensed from a proper camera away from the clinical setup. However, the available training dataset imposes many limitations besides the other difficulties related to the PPG time series as high-dimensional data. This work presents beat-by-beat continuous PPG-based BP monitoring while accounting for the aforementioned limitations. For a better exploration of beats’ features, we propose to use wavelet scattering transform as a better descriptive domain to cope with the limitation of the training dataset and to help the deep learning network accurately learn the relationship between the morphological shapes of PPG beats and the BP. A long short-term memory (LSTM) network is utilized to demonstrate the superiority of the wavelet scattering transform over other domains. The learning scenarios are carried out on a beat basis where the input corresponding PPG beat is used for predicting BP in two scenarios; (1) Beat-by-beat arterial blood pressure (ABP) estimation, and (2) Beat-by-beat estimation of the systolic and diastolic blood pressure values. Different transformations are used to extract the features of the PPG beats in different domains including time, discrete cosine transform (DCT), discrete wavelet transform (DWT), and wavelet scattering transform (WST) domains. The simulation results show that using the WST domain outperforms the other domains in the sense of root mean square error (RMSE) and mean absolute error (MAE) for both of the suggested two scenarios.

Video coding using closed-loop texture analysis and synthesis

The compression of video content containing high-frequency textures using the Mean Squared Error (MSE) criterion or other similar distortion measures typically leads to very large bit rate assignments to these areas. However, we assume that the exact reproduction (in an MSE sense) is subjectively not required and that other measures and coding methods can be used leading to substantially lower bit rate assignments. One such measure is a global similarity measure and we demonstrate its suitability for assessing the distortion of such textures in the context of video coding. The above-mentioned concept is adapted to a new, generic, and fully automated video coding scheme that provides a texture analyzer at the encoder and a texture synthesizer at the decoder. The texture analyzer thereby identifies the target textures, where it is assumed that the viewer perceives the semantic meaning of the displayed texture rather than the specific details therein. The texture synthesizer regenerates an approximate version of the original texture based on corresponding meta data transmitted by the encoder. The texture itself is not coded in the sense of minimizing MSE or other similar distortion measures. The new approacch is integrated into an H.264/AVC video codec and yields bit rate reductions of up to 41% when compared at the same visual quality to a reference H.264/AVC codec.

Gaussian Particle Filtering for Nonlinear Systems With Heavy-Tailed Noises: A Progressive Transform-Based Approach.

The Gaussian particle filter (GPF) is a type of particle filter that employs the Gaussian filter approximation as the proposal distribution. However, the linearization errors are introduced during the calculation of the proposal distribution. In this article, a progressive transform-based GPF (PT-GPF) is proposed to solve this problem. First, a progressive transformation is applied to the measurement model to circumvent the necessity of linearization in the calculation of the proposal distribution, thereby ensuring the generation of optimal Gaussian proposal distributions in sense of linear minimum mean-square error (LMMSE). Second, to mitigate the potential impact of outliers, a supplementary screening process is employed to enhance the Monte Carlo approximation of the posterior probability density function. Finally, simulations of a target tracking example demonstrate the effectiveness and superiority of the proposed method.

Shrinkage estimators of BLUE for time series regression models

The least squares estimator (LSE) seems a natural estimator of linear regression models. Whereas, if the dimension of the vector of regression coefficients is greater than 1 and the residuals are dependent, the best linear unbiased estimator (BLUE), which includes the information of the covariance matrix Γ of residual process has a better performance than LSE in the sense of mean square error. As we know the unbiased estimators are generally inadmissible, Senda and Taniguchi (2006) introduced a James–Stein type shrinkage estimator for the regression coefficients based on LSE, where the residual process is a Gaussian stationary process, and provides sufficient conditions such that the James–Stein type shrinkage estimator improves LSE. In this paper, we propose a shrinkage estimator based on BLUE. Sufficient conditions for this shrinkage estimator to improve BLUE are also given. Furthermore, since Γ is infeasible, assuming that Γ has a form of Γ=Γ(θ), we introduce a feasible version of that shrinkage estimator with replacing Γ(θ) by Γ(θˆ) which is introduced in Toyooka (1986). Additionally, we give the sufficient conditions where the feasible version improves BLUE. Besides, the results of a numerical studies confirm our approach.

Designing a heuristic computing structure to solve the human balancing model

The current study provides numerical solutions to the human balancing system using novel framework-based artificial neural networks and the hybrid competency of global heuristic genetic algorithm and local search sequential quadratic programming. These networks tend to handle complicated tasks and perform contemporary performance in different areas. The neural networks performances based on the hybridization schemes are presented using the discretization of the model to express the fitness function in the sense of mean square error. The numerical representations are presented for three cases of the delay terms-based human balancing model in order to validate the consistency and efficacy of the proposed stochastic scheme. The acceptability of the proposed solver is oppressed through the overlapping of obtained and reference results. The negligible values of absolute error also provide the accuracy of the scheme. Additionally, the graphs based on the statistical interpretations provide the precision, and convergence of stochastic computing solver.

A Light-Weighted Machine Learning Approach to Channel Estimation for New-Radio Systems

In this paper, we provide a light-weighted Machine Learning (ML) approach to channel estimation for New-Radio (NR) systems. Specifically, based on the equivalence between the Channel Impulse Response (CIR) in the time domain and its corresponding Channel Frequency Response (CFR) in the frequency domain, the light-weighted ML model for the channel estimation is shown to be established in comparison to the existing ML-based channel estimator. Furthermore, for practical use, the quantized weights for the light-weighted ML-based estimator are shown to be feasible without significant performance degradation in the sense of mean square error (MSE), which shows the effectiveness of the proposed approach from the perspective of memory overhead. Consequently, we show that there exists Signal to Noise Ratio (SNR) gain in comparison with the existing ML-based estimator, which is validated by numerical results considering the Sounding Reference Signal (SRS) for NR in the 3rd Generation Partnership Project (3GPP).

Approximate Kalman filtering by both M-robustified dynamic stochastic approximation and statistical linearization methods

The problem of designing a robustified Kalman filtering technique, insensitive to spiky observations, or outliers, contaminating the Gaussian observations has been presented in the paper. Firstly, a class of M-robustified dynamic stochastic approximation algorithms is derived by minimizing at each stage a specific time-varying M-robust performance index, that is, general for a family of algorithms to be considered. The gain matrix of a particular algorithm is calculated at each stage by minimizing an additional criterion of the approximate minimum variance type, with the aid of the statistical linearization method. By combining the proposed M-robust estimator with the one-stage optimal prediction, in the minimum mean-square error sense, a new statistically linearized M-robustified Kalman filtering technique has been derived. Two simple practical versions of the proposed M-robustified state estimator are derived by approximating the mean-square optimal statistical linearization coefficient with the fixed and the time-varying factors. The feasibility of the approaches has been analysed by the simulations, using a manoeuvring target radar tracking example, and the real data, related to an object video tracking using short-wave infrared camera.

Low-Resolution MMSE Equalization for Massive MU-MIMO Systems

Finite-alphabet equalization that represents a spatial equalization matrix with low-resolution coefficients is a promising technique to reduce the power consumption, processing delay, and circuit area of baseband processing in the context of all-digital massive multiuser multiple-input multiple-output uplink systems. However, to minimize the performance loss caused by a coarse-resolution spatial equalization matrix, its coefficients must be carefully designed in the minimum mean-square error sense to achieve the desired bit error rate (BER) performance, which unfortunately constitutes an NP-hard optimization problem. To tackle this problem, we first reformulate the finite-alphabet equalization design problem as an unconstrained optimization on a smooth Riemannian manifold. Then we propose an algorithm based on Riemannian manifold optimization (RMO) to solve the reformulated problem. Based on simulation results, the proposed 2-bit RMO-assisted equalizer outperforms its state-of-the-art counterparts while maintaining the same asymptotic complexity. In addition, the proposed 2-bit RMOassisted equalizer exhibits a loss of only 1.47 dB at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> compared to an unquantized linear minimum mean squared error equalizer.

Longitudinal Data Analysis Based on Bayesian Semiparametric Method

A Bayesian semiparametric model framework is proposed to analyze multivariate longitudinal data. The new framework leads to simple explicit posterior distributions of model parameters. It results in easy implementation of the MCMC algorithm for estimation of model parameters and demonstrates fast convergence. The proposed model framework associated with the MCMC algorithm is validated by four covariance structures and a real-life dataset. A simple Monte Carlo study of the model under four covariance structures and an analysis of the real dataset show that the new model framework and its associated Bayesian posterior inferential method through the MCMC algorithm perform fairly well in the sense of easy implementation, fast convergence, and smaller root mean square errors compared with the same model without the specified autoregression structure.

Lossy State Communication over Fading Multiple Access Channels.

Joint communications and sensing functionalities integrated into the same communication network have become increasingly relevant due to the large bandwidth requirements of next-generation wireless communication systems and the impending spectral shortage. While there exist system-level guidelines and waveform design specifications for such systems, an information-theoretic analysis of the absolute performance capabilities of joint sensing and communication systems that take into account practical limitations such as fading has not been addressed in the literature. Motivated by this, we undertake a network information-theoretic analysis of a typical joint communications and sensing system in this paper. Towards this end, we consider a state-dependent fading Gaussian multiple access channel (GMAC) setup with an additive state. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and non-causally available to all the transmitting nodes. The fading gains on the respective links are assumed to be stationary and ergodic and available only at the receiver. In this setting, with no knowledge of fading gains at the transmitters, we are interested in joint message communication and estimation of the state at the receiver to meet a target distortion in the mean-squared error sense. Our main contribution here is a complete characterization of the distortion-rate trade-off region between the communication rates and the state estimation distortion for a two-sender GMAC. Our results show that the optimal strategy is based on static power allocation and involves uncoded transmissions to amplify the state, along with the superposition of the digital message streams using appropriate Gaussian codebooks and dirty paper coding (DPC). This acts as a design directive for realistic systems using joint sensing and transmission in next-generation wireless standards and points to the relative benefits of uncoded communications and joint source-channel coding in such systems.

대응비교를 통한 가우시안 프로세스 회귀모형의 공분산 모수 선택법

With the development of computer technology, experiments of computer are being performed with a simulator, and the tuning parameters are optimized with metamodel. As a metamodel, the Gaussian process regression model (GPRM) has been used in many studies.&#x0D; GPRM consists of regression coefficient 's and covariance parameter 's. In order to make a better GPRM, many studies have been dealt with the selection of , but only Welch's algorithm (1992) for has been proposed. We propose a selection method using all possible pairwise combinations. The combinations of are classified using the Bayes information criterion(BIC) and Bonferroni correction. Welch's algorithm estimates only a few important ’s individually and estimates the remaining as a single common . In the proposed algorithm, several common ’s may appear depending on the characteristics of , and the calculation time is cheaper because only two-dimensional data are considered. The prediction performance was compared to the Welch's algorithm in the sense of root mean square error (RMSE) through three test functions.

Estimation of Consistent Cross-Covariance Matrices in a Multisensor Data Fusion

The article investigates the problems relevant to the fusion of data provided by sensors used for detection and tracking. One of the most burdensome problems on any data fusion in these fields of application is the search for the appropriate correlation function between the estimation errors of the tracks from the various sensors. The absence of such a function can lead to excessively optimistic cross-covariance matrices between tracks with consequent inconsistencies and missed associations. The article has the aim to provide an effective solution to this problem. The proposed technique resides to build consistent cross-covariance matrices by means of a tracking system which uses as input the simultaneous associations of the tracks of the involved sensors. Furthermore, a fusion equation, that provides an unbiased and optimal global estimate in the sense of the minimum mean square error, is proposed. The method results simple and fast as well as precise. Finally, the robustness of the algorithms is proved through dedicated simulations.

New Method Determines Optimized Reference SDM for MIMO Testing

Abstract The paper presents a new method for vibration testing of articles such as satellites, aerospace subsystems, transportation subsystems, civil structures, or articles whose reliability in operation may be evaluated using either mechanical or acoustic vibration testing. The method can be used for direct field or reverberant acoustic test facility testing (acoustic) systems or multiple-exciter (mechanical) testing systems to perform vibration testing. The method improves the ability of Multiple-Input-Multiple-Output (MIMO) acoustic testing systems to create diffuse or other types of acoustic fields and MIMO mechanical testing systems to produce vibration responses conforming to an initial reference Spectral Density Matrix (SDM) specification in the least mean-square error (LMSE) sense. It provides an updated positive definite or semi-definite reference SDM that enables such tests to run with less error, using minimum required drive power, as a function of the initial definition of the reference SDM, by modifying its coherence and phase off-diagonal terms, to approximate initially defined off-diagonal terms in the LMSE sense, but maintaining its initially defined diagonal terms exactly, while accounting for physical limitations existing in the overall MIMO testing system.

On the accuracy limits of misspecified delay-Doppler estimation

This work derives compact closed-form expressions of the misspecified Cramér–Rao bound and pseudo-true parameters of time-delay and Doppler for a high dynamics signal model. Those expressions are validated by analyzing the mean square error (MSE) of the misspecified maximum likelihood estimator. A noteworthy outcome of these MSE results is that, for some magnitudes of acceleration and signal-to-noise ratios, neglecting the acceleration is beneficial in the MSE sense. The variance performance improvement is obtained at the cost of a systematic error in the true parameter estimation. This can be seen as a specific case of the trade-off between bias and variance. Neglecting the acceleration can improve the Doppler estimation when the error induced on the misspecified model is less than the variance increase due to including an extra parameter to estimate. Then, for some non-zero acceleration magnitudes and short integration times, the Doppler estimation using a misspecified model outperforms a correctly specified model in the MSE sense.

Distributed Kalman Filtering for Interconnected Dynamic Systems.

This article is concerned with the distributed Kalman filtering problem for interconnected dynamic systems, where the local estimator of each subsystem is designed only by its own information and neighboring information. A decoupling strategy is developed to minimize the impact of interconnected terms on the estimation performance, and then the recursive and distributed Kalman filter is derived in the minimum mean-squared error sense. Moreover, by using Lyapunov criterion for linear time-varying systems, stability conditions are presented such that the designed estimator is bounded. Finally, a heavy duty vehicle platoon system is employed to show the effectiveness and advantages of the proposed methods.

Consensus-Based Cooperative Algorithms for Training Over Distributed Data Sets Using Stochastic Gradients.

In this article, distributed algorithms are proposed for training a group of neural networks with private data sets. Stochastic gradients are utilized in order to eliminate the requirement for true gradients. To obtain a universal model of the distributed neural networks trained using local data sets only, consensus tools are introduced to derive the model toward the optimum. Most of the existing works employ diminishing learning rates, which are often slow and impracticable for online learning, while constant learning rates are studied in some recent works, but the principle for choosing the rates is not well established. In this article, constant learning rates are adopted to empower the proposed algorithms with tracking ability. Under mild conditions, the convergence of the proposed algorithms is established by exploring the error dynamics of the connected agents, which provides an upper bound for selecting the constant learning rates. Performances of the proposed algorithms are analyzed with and without gradient noises, in the sense of mean square error (MSE). It is proved that the MSE converges with bounded errors determined by the gradient noises, and the MSE converges to zero if the gradient noises are absent. Simulation results are provided to validate the effectiveness of the proposed algorithms.

Regularizing ill-posed problem of single-epoch precise GNSS positioning using an iterative procedure

Abstract This paper analyses the regularization of an ill-conditioned mathematical model in a single-epoch precise GNSS positioning. The regularization parameter (RP) is selected as a parameter that minimizes the criterion of the Mean Squared Error (MSE) function. The crucial for RP estimation is to ensure stable initial least-squares (LS) estimates to replace the unknown quadratic matrix of actual values with the LS covariance matrix. For this purpose, two different data models are proposed, and two research scenarios are formed. Two regularized LS estimations are tested against the non-regularized LS approach. The first one is the classic regularization of LS estimation. In turn, the second one is its iterative counterpart. For the LS estimator of iterative regularization, regularized bias is significantly lower while the overall accuracy is improved in the sense of MSE. The regularized variance-covariance matrix of better precision can mitigate the impact of regularized bias on integer least-squares (ILS) estimation up to some extent. Therefore, iterative LS regularization is well-designed for single-epoch integer ambiguity resolution (AR). Nevertheless, the performance of the ILS estimator is studied in the context of the probability of correct integer AR in the presence of regularized bias.

Optimal subsampling for large‐sample quantile regression with massive data

AbstractTo balance the explosive growth of data volume and limited budgets for computational resources, one of the popular methods is downscaling the data volume by subsampling a subdataset that inherits the relevant property of the full data. As an alternative to the mean regression model, the quantile regression model has been studied extensively when the data are independent and the data scale is medium. This article focuses on quantile regression with massive data where the sample size n (greater than in general) is extraordinarily large but the dimension d (smaller than 20 in general) is small. We first formulate the general subsampling procedure and establish the asymptotic property of the resultant estimator. Then, with the help of optimality criteria in experimental design, we derive two subsampling probabilities that are optimal in the sense of smallest asymptotic mean square error. Since the optimal subsampling probabilities depend on the full data estimator, we develop a two‐step optimal subsampling algorithm and study the consistency and asymptotic normality of the resultant estimator. The empirical performance of the optimal subsampling algorithm is evaluated with synthetic and real datasets.

Estimation of Tempered Stable Lévy Models of Infinite Variation

Truncated realized quadratic variations (TRQV) are among the most widely used high-frequency-based nonparametric methods to estimate the volatility of a process in the presence of jumps. Nevertheless, the truncation level is known to critically affect its performance, especially in the presence of infinite variation jumps. In this paper, we study the optimal truncation level, in the mean-square error sense, for a semiparametric tempered stable Lévy model. We obtain a novel closed-form 2nd-order approximation of the optimal threshold in a high-frequency setting. As an application, we propose a new estimation method, which combines iteratively an approximate semiparametric method of moment estimator and TRQVs with the newly found small-time approximation for the optimal threshold. The method is tested via simulations to estimate the volatility and the Blumenthal-Getoor index of a generalized CGMY model and, via a localization technique, to estimate the integrated volatility of a Heston type model with CGMY jumps. Our method is found to outperform other alternatives proposed in the literature when working with a Lévy process (i.e., the volatility is constant), or when the index of jump intensity Y is larger than 3/2 in the presence of stochastic volatility.