Minimum Variance Criterion Research Articles

Robust fusion filter for networked uncertain descriptor systems with colored noise and cyber-attacks

The robust fusion filtering problem of multi-sensor networked uncertain descriptor systems (NUDSs) with colored noise, uncertain noise variances and cyber-attacks is investigated. During data transmission in unreliable communication networks, the data can be maliciously attacked by attackers. In other words, the local filters (LFs) may receive false data or may not receive data because of the cyber-attacks. By adopting the singular value decomposition (SVD) method, the original NUDSs can be converted into two reduced-order subsystems with uncertain correlated fictitious white noises, and the cyber-attacks are transformed into the fictitious noises. Cross-covariance matrices between local filtering errors are derived. The robust LFs are obtained according to the minimax robust estimation principle. Under the linear unbiased minimum variance criterion, three weighted fusion algorithms are applied to fuse the LFs. For all allowable uncertainties of noise variances and cyber-attacks, the minimal upper bounds of covariance matrices of the local and distributed fusion filters are guaranteed. The proof of their robustness is established through the minimax estimation principle and Lyapunov equation method. Finally, the correctness and effectiveness of the proposed algorithms are verified by a circuit system example.

Credit market conditions, expected return proxies, and bank stock returns

We evaluate the performance of expected return proxies during extreme credit market conditions and extreme phases of business cycles when realized returns on banks stocks are large in absolute value. We construct three sets of expected return proxies for individual bank stocks: (i) characteristic-based proxies; (ii) standard risk-factor-based proxies; and (iii) risk-factor-based proxies in which betas depend on firm characteristics. Based on the newly developed minimum error variance (MEV) criterion (Lee et al., 2020), the best performing expected return proxy is the risk-factor-based model that allows betas to vary with firm characteristics. We also examine whether these three expected return proxies can capture actual returns during either extreme credit market or extreme business-cycle conditions. We find that both risk-factor-based proxies explain returns better than characteristic-based proxies during these periods.

Identification and distributed fusion filter for multi-sensor networked systems with stochastic deception attacks

In the multi-sensor networked systems, each sensor produces its local state estimate based on its own observations, and then sends it to a fusion center (FC) for fusion estimation. During transmitting local state estimates to the fusion center, the data may suffer from stochastic deception attacks from malicious attackers, where the probabilities of attacks and the variances of attack noises are unknown. Using a correlation function method (CFM), the probabilities of attacks and the variances of attack noises in individual channels are identified in parallel. The possibly attacked local state estimate is filtered to reproduce local state estimate in the FC. Using the matrix-weighted fusion algorithm in the linear unbiased minimum variance (LUMV) criterion, a distributed fusion filter is performed based on the reproduced local state estimates. A simulation example illustrates the validity of the algorithms.

Federal Algorithm Design and Numerical Experiments of Ensemble Kalman Filter Data Assimilation Analysis Process

Based on the federated Kalman filter proposed by Carlson with linear systems, we propose a federated computing scheme for the ensemble Kalman filter (EnKF) assimilation analysis process for nonlinear systems, and give an optimal information fusion estimation algorithm weighted by diagonal matrix under the linear minimum variance criterion, that is, the assimilation analysis values of each variable in the global estimation are linear combinations of the assimilation analysis values of the corresponding variables in the local estimation of sub-filters, and the calculation of the combination coefficients is given. The federated algorithm of the EnKF assimilation analysis process for nonlinear systems is verified by the Lorenz (1963) system.

Variability of photosynthetic parameters of macroalgae and seagrasses based on laboratory experiments

The PE-curve describes dependence of the macroalgae and seagrasses photosynthesis rate on the irradiance. To determine the main parameters of the PE-curve (photosynthetic parameters) at various temperatures and light intensities, an archive of laboratory experiments data was collected from the available published sources, and systematized (a total of 125 species of macroalgae and 14 species of seagrasses). The available data on the ratio of plant surface area to volume (SA:V) were added to the database. All macroalgae species were assigned to functional-form groups according to Littler [15], and an additional group “seagrasses” was determined.The data on photosynthetic parameters of macrophytobenthos were clusterized using the Ward's minimum variance criterion, which made it possible to identify clusters that differ greatly in the rate of photosynthesis. The composition of each cluster was determined within the framework of the classification by functional-form groups. The variability of functional parameters was studied by calculating the coefficients of variation within a functional-form group, cluster, and taxonomic division in a narrow temperature range.Graphs of the oxygen daily production by plants were plotted for different water temperatures to determine the temperature dependence of the photosynthesis rate. Using the method of constructing a neural network, the regression equations for the photosynthetic parameters were found in the form of polynomial dependencies on the morphological characteristics of algae: the SA:V ratio and the Littler group. With limited prognostic value, they illustrate well the qualitative changes in photosynthetic parameters during the transition from thin sheet-like and filamentous structures of thalli to coarser and more resistant ones.

Dynamic displacement estimation and modal analysis of long-span bridges integrating multi-GNSS and acceleration measurements

Compared with acceleration-based modal analysis, displacement can provide a more reliable and robust identification result for output-only modal analysis of long-span bridges. However, the estimated displacements from acceleration records are frequently unavailable due to unrealistic drifts. Aiming at obtaining more accurate and stable results for determining the modal parameters, this study develops a multi-rate weighted data fusion approach for estimating displacement responses in dynamic monitoring of structures based on global navigation satellite system (GNSS) and acceleration measurements. The approach initially derives the local estimations from displacement and acceleration sensors via a Kalman filter algorithm with colored measurement noise, and later uses a weighted fusion criterion of scalar linear minimum variance to fuse the results of local estimations. Then, structural modal pamameters are identified by employing data-driven stochastic subspace identification (SSI) algorithm. The proposed approach is validated in a four degree-of-freedom numerical model and then applied to a long-span bridge in engineering practice. The results illustrate that the proposed approach can reduce the error of GNSS-obtained displacement and expand recognizable frequency range by introducing dynamic displacement component from acceleration measurement.

Distributed Matrix-Weighted Fusion Consensus Filtering With Two-Stage Filtering for Sensor Networks

This article is concerned with a distributed consensus filtering problem in a sensor network (SN). In the SN, each sensor node plays a local fusion center. By diffusion and fusion of information among sensor nodes, estimates of all nodes in the SN tend to consensus. At each sensor node, a distributed consensus filtering algorithm with a two-stage filtering structure is devised. At each time, the first stage filtering is that each sensor node produces its local filter estimate based on its own measurement and previous fused estimate, and then transmits it to its neighbor nodes; and the second stage filtering is that each sensor node produces a fused estimate by using a matrix-weighted optimal fusion algorithm in the linear unbiased minimum variance (LUMV) criterion to iteratively fuse estimates of sensor itself and neighbor nodes, where cross-covariance matrices (CCMs) between sensor nodes at different fusion times are derived. Its estimation accuracy is gradually improved with the increase of fusion times and approximates a centralized fusion filter (CFF). To avoid calculation of CCMs between sensor nodes, a suboptimal distributed consensus filtering algorithm is also presented by minimizing an upper bound of the fusion filtering error covariance at each fusion in the second stage. It has reduced computational cost at the expense of accuracy loss. The performance of the proposed distributed consensus filters is analyzed. A tracking system is used to verify the effectiveness of the algorithms.

Design of distributed recursive filters based on data compression for sensor networks

This paper is concerned with the distributed filtering problem based on data compression for linear discrete time-varying systems over sensor networks. Two kinds of sensors are considered: one kind only has a measuring capability and communicates measurements, while the other adds a calculating capability and communicates estimates. At each sensor node with calculating capability, a weighted measurement fusion algorithm is employed to compress the measurements of the sensor and its neighbor nodes with only measuring capability; and a weighted state fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. Using compressed data, an optimal distributed recursive filter with a Kalman consensus filter form is devised in the linear unbiased minimum variance (LUMV) criterion. Cross-covariance matrices (CCMs) of the filtering errors between sensor nodes are derived. To avoid calculating CCMs, a suboptimal distributed recursive filter is presented, where a covariance intersection fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. The filtering and consensus gains are solved to minimize an upper bound of covariance matrix (CM) of the filtering error. It is proved that the filtering error is exponentially bounded in the mean square. Simulations illuminate the effectiveness of proposed algorithms.

Adaptive Modified Unbiased Minimum-Variance Estimation for Highly Maneuvering Target Tracking With Model Mismatch

Due to the complexity, time variability, and mutability of the noncooperative maneuvering target, the dynamic tracking model of the target does not match with the actual state, which reduces the tracking accuracy or even completely tracking loss. In this article, an expectation maximization-based adaptive modified unbiased minimum-variance estimation (EM-AMUMVE) algorithm is proposed for highly maneuvering target tracking with model mismatch. First, the virtual maneuvering noise and the first-order Markov process model are integrated to quantitatively describe the maneuvering acceleration according to the boundness of the maneuvering acceleration. Then, the maneuvering acceleration and state estimation are derived based on the unbiased minimum-variance criterion, and the expectation maximization (EM) is introduced in the updating procedure of the quadratic Bayesian filter to adaptively estimate the mean and covariance of virtual maneuvering noise and thus to improve the accuracy of maneuvering acceleration estimation. Finally, the optimality of the adaptive modified maneuvering acceleration estimation is theoretically proved, and the tracking scenarios of time-varying maneuvering target with model mismatch and reentry gliding trajectory of typical hypersonic vehicle hypersonic technology vehicle 2 (HTV-2) are built to demonstrate the validness, convergence, sensitivity, and engineering practicability of the proposed algorithm.

The development of a management decision-making method based on the analysis of information from space observation systems

The object of this study is the process of making a management decision based on the analysis of information from space surveillance systems. Unlike the well-known ones, the method of making a management decision based on the analysis of information from space surveillance systems involves: – segmentation of an optoelectronic image; – determination and prediction of a priori probabilities of possible environmental states; – an application for making a management decision of a combination of Bayes criteria and a minimum of variance. Experimental studies have been carried out on making a management decision based on the analysis of information from space surveillance systems. To conduct experimental research on making a management decision based on the analysis of information from space surveillance systems, a model problem has been stated. As images from space surveillance systems, images obtained from the WorldView-2 spacecraft (USA) with a difference of four days were considered. The vegetation index was calculated, and the probabilities of degradation dynamics of plant segments were determined. It was established that the maximum value of the estimated functional is achieved when choosing a solution φ1, which is optimal according to the Bayesian criterion and the criterion of minimum variance. The quality of management decision-making was assessed by the well-known and developed methods. To assess the quality of management decision-making, the concepts of objectivity of the decision-making method and the selectivity of the decision-making method by known and developed method were introduced. It has been established that both methods are objective, and the improved method is more selective (the gain is 2.6 times). This becomes possible through the use of information from space surveillance systems.

Distributed Optimal and Self-Tuning Filters Based on Compressed Data for Networked Stochastic Uncertain Systems with Deception Attacks

In this study, distributed security estimation problems for networked stochastic uncertain systems subject to stochastic deception attacks are investigated. In sensor networks, the measurement data of sensor nodes may be attacked maliciously in the process of data exchange between sensors. When the attack rates and noise variances for the stochastic deception attack signals are known, many measurement data received from neighbour nodes are compressed by a weighted measurement fusion algorithm based on the least-squares method at each sensor node. A distributed optimal filter in the linear minimum variance criterion is presented based on compressed measurement data. It has the same estimation accuracy as and lower computational cost than that based on uncompressed measurement data. When the attack rates and noise variances of the stochastic deception attack signals are unknown, a correlation function method is employed to identify them. Then, a distributed self-tuning filter is obtained by substituting the identified results into the distributed optimal filtering algorithm. The convergence of the presented algorithms is analyzed. A simulation example verifies the effectiveness of the proposed algorithms.

Optimal sensor placement of triaxial accelerometers for modal expansion

Sensor placement is a vital factor affecting the quality and accuracy of virtual sensing. Modal expansion techniques are well-known methods to expand the measured displacements or accelerations to all unmeasured degrees of freedom. For this purpose, a two-phase sensor placement optimisation method is proposed for commonly used triaxial accelerometers. The method uses minimum variance criterion of an estimation error of structural responses. A measure of redundancy of information is introduced as an additional criterion for the placement of the triaxial sensors to minimise the redundancy between the sensors. This was addressed to avoid spatial correlation and clustering of the sensor locations. In addition, a proposal for modal displacement-based weighting is introduced to avoid potential selection of sensor locations with low vibration energy, which can be critical in noisy environments. The efficiency of the proposed method is verified with numerical models of different types of structures and finally with the laboratory scale experiments. The mean error of the reconstructed response in this particular experimental case study was 1.4% of the maximum measured response amplitude. This method is especially applicable to large finite element models of industrial-scale structures with fine meshes.

Technical note: Modified variance incorporating high-order moments in risk measure with Gram-Charlier returns

This paper introduces a new risk measure for portfolio choice and compares its performance with two related metrics, namely the behavioral variance and the modified variance by using a Taylor’s expansion. The methodology for our proposal naturally incorporates investor attitudes to risk related to skewness and kurtosis by assuming a Gram-Charlier return distribution. The so-obtained risk measures represent a more reliable description of portfolio risk and encompass the cases where high-order moments are not relevant characteristics (i.e. under normality). Our results show the outperformance of our proposal for different risk tolerance parameters considering the minimum variance and Sharpe ratio criteria by employing random portfolio optimization technique for 11 sets of stocks.

Sparse Covariance Matrix Reconstruction-Based Nulling Broadening for UAV 2D Antenna Arrays

Since the antennas on UAVs may have slight vibrations or the interference source is in the state of rapid movement in practice, the interference suppression performance and robustness of the traditional methods may suffer a decline. In this paper, we propose a flexible asymmetric null widening technique, which allows flexible adjustment of the null width to accommodate the variation of the interference source. This method has a good effect of spreading zero trap on the two-dimensional array and can effectively reduce the waste of degrees of freedom. Firstly, the flexible asymmetric null widening method is extended to two-dimensional arrays to accommodate 2D array antennas of UAVs. Secondly, when the SMI algorithm is applied in adaptive beamforming, the desired signal appears in sampling snapshots or using data samples, resulting in a model mismatch. To solve the model mismatch problem of UAV antenna arrays, this paper applies a sparsity-based interference plus noise covariance matrix reconstruction technique. Finally, for the application scenario that the UAV may receive signals from multiple directions, we apply the linear constrained minimum variance criterion (LCMV) to achieve the main beam gain formation in multiple directions. The simulation results show that we can generate a wide null and adjust the null width asymmetrically. The results also show that the model mismatch problem is avoided, and the performance of the adaptive beamforming is almost optimal. For the UAV antenna, we also implemented multiple beams to receive multiple signals .

Beamspace Scene Classification Algorithm for Low-Angle Estimation in MIMO Radar

This paper discusses the issue of low-angle estimation in multiple-input, multiple-output (MIMO) radar. Due to the low amount of data transmission, storage, and computation required for beamspace super-resolution algorithms in low-angle estimation, the method has gained considerable interest in recent years. This paper develops a beamspace scene classification (BSC) algorithm to enhance the performance of low-angle estimation in MIMO radar. The proposed BSC algorithm solves an initial angle estimate and the multipath coefficient estimate using the 3D beamspace data, and further constructs the beamspace data required for transmitting and receiving sides to reduce the data dimensions. It is additionally used to provide three estimation schemes with closed-form solutions for three multipath scenes (obtaining two estimations for transmitting and receiving sides). Finally, it fuses the estimates of the two sides by the minimum variance criterion. As a result, the proposed method achieves high estimation accuracy while requiring few processing resources. Moreover, the computational complexity of the proposed algorithm is examined in this study, with the results demonstrating that the proposed method is superior for engineering applications.

Prediction of Industrial Network Security Situation Based on Noise Reduction Using EMD

Industrial Internet security is a prerequisite to ensure the high-quality development of the Industrial Internet. The significant way to curb Industrial Internet security accidents and prevent cyber threats proactively is effectively controlling the changes in network situations. In this paper, we propose a new prediction model based on Long Short-Term Memory (LSTM), minimum mean square variance criterion (MMSVC), and empirical mode decomposition (EMD), with the aim of effective noise reduction and high prediction accuracy. To minimize the disturbance of random noise, we firstly deleted several outliers in high-frequency and noisy Intrinsic Mode Functions (IMFs) decomposed by EMD. MMSVC performs well in identifying noisy IMFs without using thresholds. For the blank places, we refilled them by a certain weight with relevant figures. After that, the LSTM model was applied to predict the denoised signal. The preliminary experimental analysis illustrated that noise reduction with the EMD method could provide a significant boost in forecasting performance.

A low complexity STPAP algorithm based on an alternating polarization-sensitive array

BackgroundSpace–time adaptive processing (STAP) has been widely used in the fields of communication, radar, and navigation anti-jamming. However, the traditional scalar arrays used with STAP have limitations because they can only obtain spatial information. To improve the performance, joint space–time filtering is proposed using an alternating polarization-sensitive array (APSA). Compared to a dual-polarization sensitive array (DPSA), this array can provide polarization information and reduce the computational complexity.MethodsAn alternating polarization-sensitive array space–time polarization adaptive processing (APSA-STPAP) algorithm is proposed based on the linear constraint minimum variance (LCMV) criterion. Different from the traditional LCMV criterion, the space–time polarization joint steering vector of the desired and interference signals is used as the constraint matrix, and the “set 1” and “set 0” conditions are used as the constraint conditions to effectively suppress the interference signals and enhance the desired signals.ResultsSimulation results are presented which show the following. (1) Filtering with the proposed APSA-STPAP algorithm is similar to that with the DPSA-STPAP algorithm. From the perspective of the spatial, time, and polarization domains, it can form nulls in the directions of the interference and realize space–time-polarization adaptive processing. (2) The APSA-STPAP algorithm has lower computational complexity than the DPSA-STPAP algorithm. Moreover, the dipole of the alternating polarization sensitive array is halved, which reduces the coupling effect between electric dipoles and makes implementation easier. (3) The APSA-STPAP algorithm maintains good anti-interference performance even when the electric dipole and anti-jamming degrees of freedom are reduced by half, and the anti-jamming performance is similar to that of a polarization-sensitive array. There is little difference between the anti-interference performance of the APSA-STPAP and DPSA-STPAP algorithms when SNR ≥ − 10 dB.

A S-transform Based Algorithm for Doppler Frequency Rate-of-Change Estimation from Coherent Pulse Train

The traditional Fourier correlation method has the problem of poor accumulation effect, which leads to the low estimation accuracy of Doppler frequency change rate coherent pulse signal under the condition of low signal-to-noise ratio or short pulse duration. To solve this problem, an estimation algorithm based on S-transform is proposed to estimate the Doppler frequency change rate. By means of higher time-frequency aggregation of S transform, the coherent accumulation of the coherent pulse signal is better realized; Then the high accuracy Doppler frequency change rate is obtained by using the minimum variance criterion in the phase domain. Theoretical derivation and simulation results show that the algorithm in this paper can improve the accuracy of about 1 times compared with the traditional algorithm. It lays a solid foundation for the estimation of the high-precision Doppler frequency change rate in the practical application of subsequent projects, and improves the accuracy of target positioning and tracking.

Multi-Satellite Cooperative Beamforming ALOHA for LEO Satellite IoT Networks

In this paper, we proposed a cooperative beamforming ALOHA (CBA) scheme based on linearly constrained minimum variance criterion for low Earth orbit satellite (LEO) IoT networks to solve the problem of ‘deadlock’ in multi-satellite scenario. In multi-satellite overlapping coverage areas, packets can be received by multiple satellite receivers by sending them only once, which forms the concept of spatial diversity. The cooperative beamforming collision resolution technique combined with successive interference cancellation scheme is design to efficiently resolve packet collision by iteration way at the gateway station. The performance of cooperative beamforming ALOHA scheme is evaluated via mathematical analysis and simulations. Simulation results show that the proposed CBA scheme can effectively solve the problem of ‘deadlock’ and improve the performances of random access compared with benchmark problems.

Adaptive Unscented Kalman Filter for Target Tacking with Time-Varying Noise Covariance Based on Multi-Sensor Information Fusion

In this paper, an innovative optimal information fusion methodology based on adaptive and robust unscented Kalman filter (UKF) for multi-sensor nonlinear stochastic systems is proposed. Based on the linear minimum variance criterion, this multi-sensor information fusion method has a two-layer architecture: at the first layer, a new adaptive UKF scheme for the time-varying noise covariance is developed and serves as a local filter to improve the adaptability together with the estimated measurement noise covariance by applying the redundant measurement noise covariance estimation, which is isolated from the state estimation; the second layer is the fusion structure to calculate the optimal matrix weights and gives the final optimal state estimations. Based on the hypothesis testing theory with the Mahalanobis distance, the new adaptive UKF scheme utilizes both the innovation and the residual sequences to adapt the process noise covariance timely. The results of the target tracking simulations indicate that the proposed method is effective under the condition of time-varying process-error and measurement noise covariance.