Minimum Variance Criterion Research Articles

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.

Optimal sensor placement for uncertain inverse problem of structural parameter estimation

This paper presents an optimal sensor placement approach for the uncertain inverse problem of structural parameter estimation, aiming to mitigate the ill-posedness problem that often exists in inverse procedures. The key idea is to select the sensor positions with the most sensitive measured responses to the structural parameters and the least correlated measured responses at the selected positions. Our optimization strategy is to convert the traditional minimum variance criterion of structural parameters to be identified into a new maximum independent mean-variance criterion of structural responses, so that the complex optimal sensor placement problem is transformed into a forward uncertainty propagation problem. Then, two orthogonal matching pursuit (OMP) methods based on Monte Carlo simulation (MCS) and dimension reduction integration (DRI) method are presented in this work, in which the MCS and the much more efficient DRI method are employed to solve the forward uncertainty propagation problem, and the OMP methods in sample form and moment form are developed to determine the optimal sensor placement for the identification procedure by considering the uncertainties in the measured responses. A Markov Chain Monte Carlo algorithm is adopted to identify the distributions of structural parameters eventually. Numerical and experimental examples are presented to verify the practicability and effectiveness of the proposed methods.

Event-triggered optimal and suboptimal distributed Kalman consensus filters for sensor networks

This paper studies the distributed Kalman consensus filtering problem based on the event-triggered (ET) protocol for linear discrete time-varying systems with multiple sensors. The ET strategy of the send-on-delta rule is employed to adjust the communication rate during data transmission. Two series of Bernoulli random variables are introduced to represent the ET schedules between a sensor and an estimator, and between an estimator and its neighbor estimators. An optimal distributed filter with a given recursive structure in the linear unbiased minimum variance criterion is derived, where solution of cross-covariance matrix (CCM) between any two estimators increases the complexity of the algorithm. In order to avert CCM, a suboptimal ET Kalman consensus filter is also presented, where the filter gain and the consensus gain are solved by minimizing an upper bound of filtering error covariance. Boundedness of the proposed suboptimal filter is analyzed based on a Lyapunov function. A numerical simulation verifies the effectiveness of the proposed algorithms.

Event-triggered sequential fusion filters based on estimators of observation noises for multi-sensor systems with correlated noises

This paper studies event-triggered sequential fusion filtering problems for multi-sensor systems where observation noises are mutually correlated at the same moment and correlated with the process noise at the previous moment. To save energy consumption of sensors, an event-triggered mechanism is employed to reduce communication rates from a sensor to the fusion center. Event-triggered estimators of observation noises under the linear minimum variance criterion are derived for the first time. Based on estimators of observation noises, an event-triggered optimal sequential fusion filter under the linear minimum variance criterion is presented by taking the information of the event-triggered condition into account which brings some integral calculations. To reduce computational burden, an event-triggered suboptimal sequential fusion filter is also presented by ignoring the information of the event-triggered condition. Boundedness of variance of the proposed suboptimal sequential fusion filter is analyzed. Two simulation examples verify the effectiveness of our algorithms.

Time-Frequency-Bin-Wise Linear Combination of Beamformers for Distortionless Signal Enhancement

In this paper, we address signal enhancement in underdetermined situations and propose new beamforming algorithms. Beamforming in (over)determined situations can successfully reduce noise signals without distortion of a desired signal, which is known to be a desirable property, especially for automatic speech recognition systems. Even in underdetermined situations, time-frequency (TF) masking attains outstanding performance in noise reduction, although it tends to generate artifacts. Integrating these two approaches to benefit from both their advantages, we here propose time-frequency-bin-wise switching (TFS) and time-frequency-bin-wise linear combination (TFLC) beamforming. In the proposed methods, we utilize the best combination of beamformers among multiple beamformers at each TF bin, each of which suppresses a particular combination of interferers. First, we propose a general formulation of signal enhancement employing multiple spatial filters. Then a joint optimization problem of designing the spatial filters and estimating the suitable weights to combine them is considered under a unified minimum variance criterion. Finally, we present efficient algorithms to solve the problem. In experiments, we used an objective criterion that quantifies the amount of signal distortion caused by the enhancement function and confirmed that the proposed methods effectively suppress interferers without distortion of the target signal.

Bayesian analysis of restricted penalized empirical likelihood

In this paper, we introduce restricted empirical likelihood and restricted penalized empirical likelihood estimators. These estimators are obtained under both unbiasedness and minimum variance criteria for estimating equations. These scopes produce estimators which have appealing properties and particularly are more robust against outliers than some currently existing estimators. Assuming some prior densities, we develop the Bayesian analysis of the restricted empirical likelihood and the restricted penalized empirical likelihood. Moreover, we provide an EM algorithm to approximate hyper-parameters. Finally, we carry out a simulation study and illustrate the theoretical results for a real data set.

Data-driven performance assessment of multivariable control loops using a modified Hurst exponent–based index

Control system performance assessment is significant, especially in practical applications. One of the most important indices for the performance assessment of control systems is minimum variance. Calculating the minimum variance index in multivariate systems requires prior knowledge of system parameters and models, and is therefore an obstacle in practical applications. In this article, an index is proposed for the performance assessment of multivariate control loops, evaluating the system performance with the minimum variance criterion and using only the system’s routine operation data. This index can quantify the performance using neither any prior knowledge of system parameters nor the system’s optimal operation data. The proposed index is based on the Hurst exponent, a parameter for measuring correlations in time series data. In this article, detrended fluctuation analysis and rescaled range analysis are used to estimate the Hurst exponents of system outputs. Using a combination of these Hurst exponents, an index is defined for the performance assessment of multivariate systems. The results of simulation examples illustrate that the proposed index can assess the performance efficiently.

Off-grid DOA estimation of correlated sources for nonuniform linear array through hierarchical sparse recovery in a Bayesian framework and asymptotic minimum variance criterion

This paper provides a method to solve off-grid direction-of-arrival (DOA) estimation for nonuniform linear array (NLA) correlated source condition through hierarchical sparse recovery and asymptotic minimum variance (AMV) criterion. In this method, space is firstly divided into a discretized grid. Most rows and columns of the signal covariance matrix modeled on this grid are zero vectors because the number of sources is considerably smaller than that of grid points. Hence, the vectorized signal covariance matrix is regarded as a block-sparse vector, and active blocks are sparse vectors. Based on this, a hierarchical sparse prior is then assigned on the vectorized signal covariance matrix to encourage the sparsity between and within blocks. Finally, the variational Bayesian inference is applied to estimate the vectorized signal covariance matrix. Furthermore, first-order Taylor series expansion is applied to approximate the steering vector as a function of the grid error between the true DOA and the closest grid point. Grid error is estimated under the AMV criterion and applied to modify the grid iteratively, thus alleviating the basis mismatch. Simulation results show that the proposed method achieves high estimation accuracy for the NLA correlated source condition.

시변 이산 선형 시스템에 대한 지수가중 유한 임펄스 응답 필터

In this paper, an exponentially weighted Finite Impulse Response (FIR) filter is proposed for discrete-time linear time-varying systems. The weighting method of measurements was first introduced for the FIR structured estimators, then an optimal design of the exponentially weighted FIR filter was developed with respect to a minimum variance criterion for discrete-time linear time-varying systems. The proposed filter is designed to be unbiased and independent of initial state information. Due to the inclusion of the weighting factor, it is expected to be less prone to model uncertainty and numerical errors than the conventional optimal FIR filter. Moreover, the proposed FIR filter is reduced to the optimal time-varying FIR filter with an equal weight, and can thereby provide a more general solution than the conventional optimal FIR filter. Through a numerical study, the performance of the proposed FIR filter was shown by comparing it with the exponentially weighted Kalman filter and the conventional optimal FIR filter when the modeling uncertainties exist.

Optimal linear recursive estimators for stochastic uncertain systems with time-correlated additive noises and packet dropout compensations

This paper is concerned with the state estimation problem over a packet-dropping network for stochastic uncertain systems with time-correlated additive noises. Additive process and measurement noises are both depicted by first-order Gauss-Markov processes. Stochastic parameter uncertainties are described by correlated white multiplicative noises. When a sensor measurement transmitted over networks is lost, its predictor is used for compensation. The optimal linear recursive full-order state filter, predictor and smoother are proposed under the linear minimum variance (LMV) criterion by an innovation analysis approach. They are calculated in terms of the filter of the product of the multiplicative noise and state, estimators of the process and measurement noises, and cross-covariance matrices for the state and/or noises. The steady-state estimators are also studied. A sufficient condition for convergence of optimal linear estimators is given. The simulation results verify the effectiveness of the proposed algorithms.

Novel estimation method of utility harmonic impedance based on short‐term impedance minimum variance criterion

For harmonic control of a power grid, it is prerequisite to accurately estimate and follow the utility harmonic impedance at the point of common coupling (PCC). The existing estimation methods generally consider that the utility harmonic impedance is constant, which causes the estimation error and fail in tracking of impedance fluctuations, since the utility harmonic impedance is fluctuant in practice. Actually, the harmonic impedance fluctuations will lead to the transient variation of the harmonic voltage and current which is bad for harmonic control. In this study, to follow the harmonic impedance fluctuations, a longer observation period is divided into a series of shorter period, and the fluctuations of the utility harmonic impedance over a short period are regarded as a stationary random process. Then, for each short period, the utility harmonic impedance is estimated by minimizing the fluctuation variance of the utility harmonic impedance. Besides the high estimation precision and good tracking performance of impedance fluctuations, other advantages of the proposed method are not limited by the traditional assumptions, such as the background harmonics are stable and small, the customer harmonic impedance is much larger than the utility, and the harmonic sources of both sides are independent, and so on.

Distributed optimal linear fusion estimators

This paper is concerned with the distributed information fusion estimation problem in multi-sensor environments. A universal distributed optimal linear fusion estimation (DOLFE) algorithm, which has a Kalman-type structure with matrix gains, is presented under the linear unbiased minimum variance criterion. To reduce the computational burden, two suboptimal linear fusion estimation algorithms with diagonal-matrix gains and scalar gains are also presented. Based on the proposed DOLFE algorithm, a distributed optimal linear fusion filter (DOLFF) is presented for multi-sensor linear discrete-time stochastic systems. It has better accuracy than that based on the matrix-weighted fusion of local estimators but worse accuracy than the centralized fusion filter (CFF). The stability and steady-state property of the proposed DOLFF are analyzed. Then, the corresponding multi-step predictor and smoother are also developed based on DOLFF. To obtain the distributed fusion estimators, some estimation error cross-covariance matrices that are used to compute the gains are derived. At last, distributed optimal linear fusion estimators with feedback are also presented. Furthermore, it is strictly proved that the proposed distributed optimal linear fusion filter with feedback (DOLFFWF) has the same accuracy as the CFF. Two simulation examples show the effectiveness of the proposed algorithms.

Optimized Basis Functions Under Gaussian Color Noise for Magnetic Target Signal Detection

The orthogonal basis functions (OBFs) method is a viable approach for magnetic target signal detection under the Gaussian white noise. However, its performance would degrade overtly under the Gaussian color noise with the power spectral density of 1/f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> , which is the common environmental magnetic noise. In this letter, based on the linear constrained minimum variance criterion and the generalized likelihood ratio test, respectively, an alternative detection scheme is proposed through the optimization of the basis functions by considering both the signal and noise information. Experiment results using both the simulated data and the measured data show that the present approach can significantly improve the detection performance when compared to the original OBFs method.

Indoor multi-sensor fusion positioning based on federated filtering

In order to meet the requirements of high-precision indoor navigation, a fast point cloud registration method based on Voxel-SIFT (Scale-Invariant Feature Transform) is proposed to improve the registration efficiency of LiDAR (Light Detection and Ranging). Due to the influence of information distribution factors, the dynamic adaptive system cannot be realized in the traditional federated filter. In this case, a hybrid federated filter based on weighted least square method is designed. It is proposed that the main filter in the hybrid federated filter adopts the minimum variance criterion and the optimal estimate of the sub-filter are fused according to the optimal coefficient weighted algorithm. The information distribution factor can be dynamically updated in real time to obtain a global optimal estimate. Finally, the experimental results show that the method can significantly improve the indoor positioning accuracy of mobile robots. The average positioning error is 0.22 m, which is more accurate than the visual odometer method or the LiDAR odometer method alone.

Phase-Only Robust Minimum Dispersion Beamforming

A phase-only robust minimum dispersion (PO-RMD) beamformer is devised for non-Gaussian signals. Unlike conventional beamformers that adjust the complex-valued weights, including both amplitude and phase, of each antenna to fulfill spatial filtering, the proposed PO-RMD employs a unit-modulus constraint on the weights, which is equivalent to simply phase shifting at each antenna. Instead of the widely used minimum variance criterion, the PO-RMD adopts the minimum dispersion criterion, which minimizes the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm of the array output to utilize the non-Gaussianity of the signals. To achieve robustness against model uncertainty, the magnitude response of any steering vector within an uncertainty region is forced to exceed the threshold. A gradient projection (GP) algorithmic framework is developed to solve the resulting nonconvex optimization problem. In order to find a feasible point in the intersection of the unit-modulus, and robustness constraint sets in each iteration, an alternating projection algorithm is also devised. More importantly, the closed-form expressions of the projection onto the two sets are derived, which only need a low complexity of O(M) with M being the number of antennas. Convergence of the alternating projection is analyzed, and the local linear convergence rate is established. Simulation results demonstrate the fast convergence rate, and accuracy of the GP, as well as the simplicity and robustness of the PO-RMD.

The Research on Distributed Fusion Estimation Based on Machine Learning

Multi-sensor distributed fusion estimation algorithms based on machine learning are proposed in this paper. Firstly, using local estimations as inputs and estimations of three classic distributed fusion (weighted by matrices, by diagonal matrices and by scalars) as the training sets, three distributed fusion algorithms based on BP network (BP net-based fusion weighted by matrices, by diagonal matrices and by scalar) are proposed and the selection basis of the number of nodes in hidden layer is given. Furthermore, by using local estimations as inputs and centralized fusion estimation as training set, another recurrent net-based distributed fusion algorithm is proposed, in the case that neither true states nor cross-covariance matrices is available. This method is not limited to the linear minimum variance (LMV) criterion, so its accuracy is higher than the classical three distributed fusion algorithms. A radar tracking simulation verifies the effectiveness of the proposed fusion networks.

Event-Triggered State Estimation for Wireless Sensor Network Systems With Packet Losses and Correlated Noises

In this article, an event-triggered state estimation problem for wireless sensor network systems affected by random packet losses and correlated noises is considered. A set of independent Bernoulli variables are used to describe the random packet losses in the measurement transmission. An event-triggered transmission strategy is introduced to decrease limited network bandwidth consumption, and the measurement noise is correlated with the process noises of the same moment and the previous moment. Event-triggered estimator of process noises under the linear minimum variance criterion is derived. Then, an event-triggered state estimation algorithm related to the packet loss rate, noise correlation coefficient and triggering threshold is designed. Sufficient conditions are provided to guarantee convergence of the estimation error covariances of the proposed estimator. Finally, comparative simulation verifies the effectiveness of our algorithm.

基于线性约束最小方差准则和合成孔径连续声束合成的内镜超声成像算法

基于线性约束最小方差准则和合成孔径连续声束合成的内镜超声成像算法

SPICE-ML Algorithm for Direction-of-Arrival Estimation.

Sparse iterative covariance-based estimation, an iterative direction-of-arrival approach based on covariance fitting criterion, can simultaneously estimate the angle and power of incident signal. However, the signal power estimated by sparse iterative covariance-based estimation approach is inaccurate, and the estimation performance is limited to direction grid. To solve the problem above, an algorithm combing the sparse iterative covariance-based estimation approach and maximum likelihood estimation is proposed. The signal power estimated by sparse iterative covariance-based estimation approach is corrected by a new iterative process based on the asymptotically minimum variance criterion. In addition, a refinement procedure is derived by minimizing a maximum likelihood function to overcome the estimation accuracy limitation imposed by direction grid. Simulation results verify the effectiveness of the proposed algorithm. Compared with sparse iterative covariance-based estimation approach, the proposed algorithm can achieve more accurate signal power and improved estimation performance.