Mean Square Estimation Research Articles

Multi-headed deep learning-based estimator for correlated-SIRV Pareto type II distributed clutter

This paper deals with the problem of estimating the parameters of heavy-tailed sea clutter in high-resolution radar, when the clutter is modeled by the correlated Pareto type II distribution. Existing estimators based on the maximum likelihood (ML) approach, integer-order moments (IOM) approach, fractional-order moments (FOM), and log-moments (log-MoM) have shown to be sensitive to changes in data correlation. In this work, we resort to a deep learning (DL) approach based on a multi-headed architecture to overcome this problem. Offline training of the artificial neural networks (ANN) is carried out by using several combinations of the clutter parameters, with different correlation degrees. To assess the performance of the proposed estimator, we resort to Monte Carlo simulation, and we observed that it has superior performance over existing approaches in terms of estimation mean square error (MSE) and robustness to changes of the clutter correlation coefficient.

Integral mean-square estimation of error terms of Fourier coefficients attached to cusp forms

Integral mean-square estimation of error terms of Fourier coefficients attached to cusp forms

A Four-cell Division Method for Pilot Sequence Design to Reduce Pilot Pollution in Massive MIMO systems

A method for pilot sequence design with the Zadoff-Chu (ZC) sequence as a base sequence is proposed to address the problem of pilot pollution in massive multi-input multi-output (MIMO) systems. Instead of the odd-length ZC sequence currently in use, the ZC sequence of even length serves as the basis of the pilot. It has the advantage of a very small cross-correlation coefficient under the premise that the sum of cyclic displacement is odd. The results of the four-cell division method are compared between the even-length and odd-length ZC pilot sequences. The MATLAB simulation shows that the signal-to-noise ratio and the channel estimation mean square error of the designed even-length ZC pilot sequence are better than those of the existing odd-length ZC pilot sequence in the case of four-cell division.

Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems

<p><span lang="EN-US">Index modulation (IM) techniques have been employed in different communication systems to improve bandwidth efficiency by carrying additional information bits. In high-mobility communication systems and under both time-selective and frequency-selective fading channels with Doppler spread, channel variations can be tracked by employing pilot-aided channel estimation with minimum mean-squared error estimation. However, inserting pilot symbols among information symbols reduces the system's spectral efficiency in pilot-aided channel estimation schemes. We propose pilot-aided channel estimation with zero-pilot symbols and an energy detection scheme to tackle this issue. Part of the information bit-stream is conveyed by the indices of zero-pilot symbols leading to an increase in the system's spectral efficiency. We used an energy detector at the receiver to detect the transmitted zero-pilot symbols. This paper examines the impacts of diversity order on the zero-pilot symbol detection error probability and the mean-squared of error estimation. The impacts of pilot symbols number and the zero-pilot symbol number on the mean-squared error of the minimum mean-squared error (MMSE) estimator and the system error performance are also investigated in this paper.</span></p>

Optimal Design of Eigenvalues for the Full-Spectrum Modulated Nonlinear Frequency Division Multiplexing Transmission System

Nonlinear frequency division multiplexing (NFDM) system is an optional candidate to overcome the fiber nonlinearity limit. A full-spectrum modulated NFDM system, modulating data on combined continuous spectrum (CS) and discrete spectrum (DS) together, was proposed in recent years to improve the data rates and spectral efficiency (SE) by exploiting all the degrees of freedom offered in the nonlinear spectrum. However, the selection of discrete eigenvalues greatly affects the performance of both CS and DS. Designing appropriate eigenvalues of DS is an important issue to ensure the high SE and excellent performance of the system. In this paper, we discussed the selcection principle of eigenvalues and analyzed it from multiple perspectives, 11 eigenvalues with 64-quadrature amplitude modulation (64QAM) are selected for DS. Besides optimizing the eigenvalues at the transmitter, the linear minimum mean-square estimate (LMMSE) method was used at the receiver to furtherly improve the performance of DS. Through the numerical simulation, a 113 Gb/s (SE of 2.8 bits/s/Hz) full-spectrum modulated NFDM system was set up and transmitted 1120 km distance, where the Q-factors of both CS and DS are above the hard-decision forward error correction (HD-FEC) threshold. The results provide a way to design an efficiently full-spectrum modulated NFDM system.

Distributed Optimal Frequency Control under communication packet loss in multi-agent electric energy systems

This paper investigates the impact of communication packet loss on Distributed Optimal Frequency Control (DOFC) in Alternating Current (AC) electric energy systems, populated with multiple clusters of hybrid producer–consumer (prosumer) agents. The paper first establishes rigorous relationships between the communication packet delivery ratio and the convergence rate of the proposed DOFC algorithm. This provides a foundation for resource allocation on communication systems to enhance the convergence speed of distributed optimization and control algorithms, such as DOFC, under noisy and disrupted communication systems. The paper develops a systematic approach to identify the best possible convergence rate over all possible algorithms, by introducing an algorithm that can achieve asymptotically the Cramér-Rao (CR) lower bound. This fundamental result links the information contents of data to the best possible mean-square estimation error. Simulation studies on an electric energy system validate the theoretical results.

Multi-sensor fusion particle filtering for Boolean networks with multi-step randomly-delayed measurements

This paper is concerned with developing particle filters for Boolean networks with multi-step randomly-delayed measurements. Based on the semi-tensor product of matrices and dummy selection matrices, a generalized measurement model including multi-step randomly-delayed measurements is introduced. Besides, multi-sensor fusion particle filtering is proposed and two recursive algorithms are designed to minimize the mean-square estimation errors by fusing multi-sensor measurements. Simulation results show the effectiveness of the proposed multi-sensor fusion particle filters. It can be seen from the simulation results that the estimation performance of multi-sensor fusion has been improved compared to that of one sensor.

Optimal networked state estimation in the presence of multi-channel correlated packet losses

This paper studies the optimal estimation problem for linear time-invariant systems over lossy communication networks subject to multi-channel packet losses. In its full generality, we assume that the random packet losses are spatially correlated across different channels. The problem is addressed by employing a modified Kalman filter to estimate the system’s states, and the primary issue under study is the convergence of the state estimate under a mean-square criterion. This convergence is shown to be equivalent to the existence of a stabilizing solution to a modified algebraic Riccati equation. We provide a necessary and sufficient condition to characterize the existence of the stabilizing solution, and show that the solution can be computed by solving a set of linear matrix inequalities. Additionally, from a robust convergence perspective, we consider further packet losses whose probabilities are unknown and uncertain. We develop a matrix measure referred to as the critical matrix to characterize the maximal tolerance for the modified Kalman filter to converge. Specifically, we show that the mean-square estimation error is bounded if and only if the critical matrix satisfies a positive semi-definiteness condition.

A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

Covariance matrix estimation plays a significant role in both in the theory and practice of portfolio analysis and risk management. This paper deals with the available data prior to developing a factor model to enhance covariance matrix estimation. Our work has two main outcomes. First, for a general linear model with unknown prior parameters, a class of best linear empirical Bayes estimators is established through two kinds of architectures to improve the estimation accuracy by utilizing additional data prior. The theoretical results indicate two key points: the proposed estimators are equivalent to the linear minimum mean-square error estimator when complete or sufficient partial data prior are provided; and the proposed estimators perform better than the optimal weighted least squares method, which ignores the data prior in each situation. Second, the proposed estimators are used for calculating a high-dimensional covariance matrix through factor models. The numerical example and the simulation results verify the effectiveness of our methods.

The New Sub-regression Type Estimator in Ranked Set Sampling.

In this study, a new sub-regression type estimator for ranked set sampling (RSS) is proposed based on the idea of a sub-ratio estimator given in Koçyiğit and Kadılar (Commun Stat Theory Methods 1-23, 2022). The proposed unbiased estimator's mean square error is obtained and compared theoretically with other estimators. The theoretical results have been supported by the different simulations and real-life data sets studies and have shown that the proposed estimator is more effective than the estimators in the literature. It is also seen that the number of repetitions in the RSS affected the effectiveness of the sub-estimators.

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors (FMSE) and the true mean square errors (TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters. Obviously, it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models. Aiming at this, the concept of credibility is adopted to discuss the inconsistency problem in this paper. In order to formulate the degree of the credibility, a trust factor is constructed based on the FMSE and the TMSE. However, the trust factor can not be directly computed since the TMSE cannot be found for practical applications. Based on the definition of trust factor, the estimation of the trust factor is successfully modifled to online estimation of the TMSE. More importantly, a necessary and sufficient condition is found, which turns out to be the basis for better design of Kalman filters with high performance. Accordingly, beyond trust factor estimation with Sage-Husa technique (TFE-SHT), three novel trust factor estimation methods, which are directly numerical solving method (TFE-DNS), the particle swarm optimization method (PSO) and expectation max-imization-particle swarm optimization method (EM-PSO) are proposed. The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance. Meanwhile, the proposed EM-PSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.

Regularized Linear Regression via Covariance Fitting

The linear minimum mean-square error estimator (LMMSE) can be viewed as a solution to a certain regularized least-squares problem formulated using model covariance matrices. However, the appropriate parameters of the model covariance matrices are unknown in many applications. This raises the question: how should we choose them using only the data? Using data-adaptive matrices obtained via the covariance fitting SPICE-methodology, we show that the empirical LMMSE is equivalent to tuned versions of various known regularized estimators – such as ridge regression, LASSO, and regularized least absolute deviation – depending on the chosen covariance structures. These theoretical results unify several important estimators under a common umbrella. Furthermore, through a number of numerical examples we show that the regularization parameters obtained via covariance fitting are close to optimal for a range of different signal conditions.

Filtering problem for periodically correlated stochastic sequences with missing observations

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence from observations of the sequence with missings is considered. Formulas for calculation the mean-square error and the spectral characteristic of the optimal estimate of the functionals are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, when spectral densities of sequences are not exactly known but the class of admissible spectral densities is given.

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizations of sparse stochastic processes, which makes them ideally matched to variational sparsity-promoting techniques. We derive Gibbs sampling schemes to compute the minimum mean-square error estimators for processes with Laplace, Student's t, and Bernoulli-Laplace innovations. These allow our framework to provide quantitative measures of the degree of optimality (in the mean-square-error sense) for any given reconstruction method. We showcase our framework by benchmarking the performance of some well-known variational methods and convolutional neural network architectures that perform direct nonlinear reconstructions in the context of deconvolution and Fourier sampling. Our experimental results support the understanding that, while these neural networks outperform the variational methods and achieve near-optimal results in many settings, their performance deteriorates severely for signals associated with heavy-tailed distributions.

Optimal deception attacks on remote state estimators equipped with interval anomaly detectors

This paper studies the problem of optimal deception attacks on remote state estimation, where an interval χ2 detector is deployed to reveal anomalies. The information-based attack policy that can bypass the anomaly detector and cause the maximum estimation quality degradation is derived. For both attacks with strict and relaxed stealthiness, the optimal compromised measurements can be designed with three steps: obtain the minimum mean-square error estimation of the prediction error, de-correlate the estimate with historical compromised innovations, and design the compromised innovation as an optimal linear transformation. All available information for attackers is fully utilized for performance maximization while the stealthiness constraint is satisfied precisely to deceive the anomaly detector. The attack effect depends on both the amount of online information and the duration of detection interval. Contrary to well-studied innovation-based attacks using static linear combinations, the information-based deception policy is shown to be generated by a linear time-varying system, whose coefficients can be completely determined offline. The optimality of the proposed attack is verified with numerical examples and comparative studies.

Robust 3D imaging based on regularization by denoising.

Reconstructing a 3D image from the photon echo is a challenging task due to spurious detections associated with large amounts of background counts. Here, we propose a robust method for estimating the depth and reflectivity by using regularization by the denoising method, where the block matching and the 3D filtering are adopted as denoisers, and in the meantime, the steepest-descent method is implemented to solve the optimization problem. Experimental data with different signal-to-background ratios and different numbers of photons verify that our method is able to accurately recover 3D images. Compared with other existing methods, such as the maximum likelihood estimation algorithm, the photon efficient algorithm by Shin et al. [IEEE Trans. Comput. Imaging1, 112 (2015)2333-940310.1109/TCI.2015.2453093], and the ManiPoP algorithm, our method can effectively remove noise while preserving the edge information of depth images, with better depth image estimation and smaller root mean square error, especially at low signal-to-noise ratios. The superiority of this method over other methods is verified on simulated data sets under different conditions.

Fast hyperparameter-free spectral approach for 2D seismic data reconstruction

Reconstruction of missing seismic data is a critical procedure for subsequent applications like multiple wave suppression, wave-equation migration imaging and so on. In this paper, a fast, hyperparameter-free and sparse iterative spectral estimation approach is proposed for the reconstruction of two-dimensional seismic data of randomly missing traces. The proposed approach is based on the harmonic structure of the frequency slice of seismic data and the weighted covariance fitting criterion. Specifically, the method first iteratively estimates the spectrum of the frequency slice by solving a weighted covariance fitting problem. Then, the missing data is reconstructed by using the estimated spectrum and a linear minimum mean-squared error estimator. However, the spectral estimation depends on matrix-vector multiplications for each iteration, which has a high computational cost when the data increase to a large size. To solve this problem, a fast iterative technology is proposed by using an inverse fast Fourier transform, which fully exploits the Hermitian–Toeplitz structure of the covariance matrix and the exponential form of the steering vector and it significantly reduces the computational complexity. The proposed algorithm is hyperparameter-free, can provide super spectral resolution, and thus obtain better reconstruction performance. The experimental results of synthetic and real seismic data show that the proposed algorithm has higher reconstruction accuracy and lower computational complexity compared to other commonly used reconstruction algorithms.

Polarimetric Direction of Arrival Estimations Based on Adaptive Linear Time-Frequency Transforms

A spatially polarized time-frequency distribution (SPTFD) based on dual-polarized double-fed antenna arrays is adapted to deal with polarization-unstable signals. A linear time-frequency (TF) representation was used for an instantaneous frequency (IF) estimate, primarily due to its simplicity and immunity to cross-interference. Using a set of linear TF transformations using Gaussian windows and Fourier oscillation kernels, the IF estimated window widths of multiple unstable signals are obtained. This paper introduces a new method for estimating the direction of arrival (DOA) of polarized waves using adaptive linear time-frequency transforms. In this paper, a narrowband far-field point source on the receiving array is analyzed. The source signal is split into two orthogonally polarized components. The optimal window is determined by the first derivative of the IF; for this purpose, we take a simple algorithm for solving the derivative and optimize it. In developing TF-adaptive and fully automatic TF display technology, the first method is to use the time-adaptive window for minimizing the IF estimate mean square error (MSE) sum at each moment, while the second procedure is to adjust according to time and frequency and minimize estimate MSE sum at each position in the TF region. Due to its combination with signal polarization, the spatial time-frequency distribution (STFD) gains more freedom and thus perfects the phonon space estimation of noise and signal. On the SPTFD platform, polarized time-frequency multiple signal classification (PTF-MUSIC) is used for the estimation of signal direction of arrival, which outperforms conventional time-frequency MUSIC. Using the example of a synthesized signal, this method outperforms conventional techniques in DOA estimation.

Quality assessment of liquorice combined with quantum fingerprint profiles and electrochemical activity

Liquorice, as a nutritional plant with a long histroy, is used in food and medical fields. In this study, we explored the quality consistent of liquorice from different locations by using multiple fingerprint profiles, including High Performance Liquid Chromatography (HPLC) and Fourier Transform Infrared Spectroscopy (FTIR). In addition, the average method of systematic quantified fingerprint method (AMSQFM) was presented to combine the chemical information of chromatography and spectral fingerprint. Macro qualitative similarity (Sm) and macro quantitative similarity (Pm) were used to assess the quality of 55 samples in terms of both qualitative and quantitative aspects. As a result, all the samples were well differentiated and classified into 6 grades. Additionally, partial least squares (PLS) model was used to evaluate the feasibility of quantizing glycyrrhizic acid (GLA) and liquiritin (LQT) by FT-IR spectral quantized fingerprint. The explanatory ability (R2Y) and prediction ability (Q2) of model were all greater than 0.9 and 0.5 respectively, the root mean square error of estimation (RMSEE) and root mean square error of prediction (RMSEP) were both less than 2.0. In the end, two characteristic parameters of electrochemistry (EC), oscillation life (tosc) and maximum amplitude (ΔEmax), were used to predict the reducibility of liquorice. Models were accurate and had good predictive abilities with the appropriate parameters, five active components in liquorice all exhibited certain reducing ability. In conclusion, this study provides a new idea for evaluating the quality and reduction ability of liquorice.

Target Sensing With Intelligent Reflecting Surface: Architecture and Performance

Intelligent reflecting surface (IRS) has emerged as a promising technology to reconfigure the radio propagation environment by dynamically controlling wireless signal’s amplitude and/or phase via a large number of reflecting elements. In contrast to the vast literature on studying IRS’s performance gains in wireless communications, we study in this paper a new application of IRS for sensing/localizing targets in wireless networks. Specifically, we propose a new <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self-sensing IRS</i> architecture where the IRS controller is capable of transmitting probing signals that are not only directly reflected by the target (referred to as the direct echo link), but also consecutively reflected by the IRS and then the target (referred to as the IRS-reflected echo link). Moreover, dedicated sensors are installed at the IRS for receiving both the direct and IRS-reflected echo signals from the target, such that the IRS can sense the direction of its nearby target by applying a customized multiple signal classification (MUSIC) algorithm. However, since the angle estimation mean square error (MSE) by the MUSIC algorithm is intractable, we propose to optimize the IRS passive reflection for maximizing the average echo signals’ total power at the IRS sensors and derive the resultant Cramer-Rao bound (CRB) of the angle estimation MSE. Last, numerical results are presented to show the effectiveness of the proposed new IRS sensing architecture and algorithm, as compared to other benchmark sensing systems/algorithms.