Noise Covariance Matrix Research Articles

Effect of Noise Covariance Matrices on State of Charge Estimation Using Extended Kalman Filter

The electrification of the transport sector increases the demand for a battery management system that allows the Li-ion battery to work in a sophisticated way to reach its maximum. The main focus of the battery management system is the estimation of the battery’s state of charge (SOC) which is an indicator to determine the driving range of an electric vehicle. However, battery modeling has a direct influence on SOC estimation. In this article, the equivalent circuit model (ECM) and extended Kalman filter (EKF) algorithm are combined for SOC estimation of the Li-ion battery. Since the performance of Kalman filter algorithms strictly depends on noise covariance matrices, incorrect values reduce the accuracy and make divergence in state estimation. Therefore, it is motivated to analyze the impact of process noise and measurement noise covariance matrix values on SOC estimation using Kalman filter algorithms. Ten different combinations of noise covariance matrices are employed to analyze the effect of these matrices on SOC estimation. As a result, the tuning of the filter is critical for improvement in state estimation regardless of the type of the battery model and filtering technique. The matrix values are chosen to take into account the convergence rate and estimation error. To validate the effectiveness of the chosen noise covariance matrices, the simulation results of the ECM based EKF estimation method is superimposed with the discharge curves available in the data sheet. The simulation results show minimal estimation error and a good convergence rate for tuned EKF.

Time-Varying System Identification of Precast Segmental Columns Subjected to Seismic Excitations

Precast segmental columns, as one structures, have attracted increasing attention in bridge and building construction. To understand the performance and dynamic characteristics of precast segmental columns subjected to earthquake excitations, this paper develops a novel approach for time-varying system stiffness identification of precast segmental columns under seismic excitations, based on the adaptive unscented Kalman filtering (AUKF) method. In the proposed approach, a precast segmental column model is considered as an equivalent single-degree-of-freedom (SDOF) system with time-varying system parameters. The AUKF method is employed to identify the time-varying stiffness parameters by using measured acceleration responses and then calculate dynamic displacement responses of the SDOF system to verify the accuracy of the identified stiffness parameters. Since the system parameter identification process and measurement noise covariance matrices are updated at each time step, the estimated results can be reliably obtained to evaluate the conditions of segmental columns subjected to seismic excitations. To verify the feasibility and effectiveness of using the proposed approach for time-varying system stiffness identification of segmental columns, numerical studies on a planar precast segmental column subjected to different intensities of ground motion excitations are conducted. Shake table tests on a scaled precast segmental column and a scaled monolithic column subjected to earthquake excitations are conducted in the laboratory to further verify the performance of the proposed approach. Measured acceleration responses are used for time-varying system identification. Both numerical and experimental results demonstrate that the proposed approach can successfully identify the time-varying stiffness values of precast segmental columns subjected to earthquake excitations, and the displacement responses of these columns are predicted accurately as compared with the measured ones.

Parameter identification of ductile timber beam-to-steel column connections: Procedure and assessment

Ductile beam–column connections in a moment-resistant timber frame are essential part that can affect the seismic performance of the timber frame. As the first step, this study presents a ductile timber beam-to-steel column joint connected by a steel link, herein designed as a box-shaped steel bracket. A robust unscented Kalman filter (UKF) algorithm was presented to identify the model parameters of the proposed the connection. In addition, a dual-scale assessment method is proposed to evaluate the accuracy of the identified results. UKF algorithm is limited to the problem of nonpositive definite matrices in high dimensional parameter identification. To prevent the interruption of the program and improve the stability of the program, the Cholesky decomposition in the UKF was superseded by singular value decomposition (SVD), a noise estimator was embedded into the UKF to self-adapt the noise covariance matrix during the iteration. The assessment was carried out for both the steel links and timber beam-to-steel column connections. Subsequently the framework was introduced for the parameter identification of the steel links. For the hysteretic curves, performance indices, and energy dissipation, there was good agreement between the experimental and numerical results. The steel bracket improves the ductility of the timber beam-to-steel column connection. The average ductility coefficient of the steel bracket with ribs can reach 7.11. The proposed parameter identification procedure is verified to be applicable in the field of ductile timber beam-to-steel column connections. The program stability is improved and the error of most of the performance parameters is within 10%. However, this method still need to be verified for dynamic analysis in the whole building.

An Adaptive Fuzzy Neural Network Based On Progressive Gaussian Approximate Filter with Variable Step Size

The nonlinear filtering problem is a hot spot in robot navigation research. As an advanced method that can effectively improve the robustness and accuracy of the system, the progressive Gaussian approximate filter with variable step size (PGAFVS) still has some shortcomings, how to resolve the nonlinear filtering problem in the application of tightly coupled integration under the premise of the prior uncertainty and further promote robustness high measurement accuracy, which becomes the purpose of this paper. This paper formulates the processing of trajectory tracking measurement noise problem as a Kalman filtering procedure and the measurement noise covariance matrix in controller, is jointly estimated based on the progressive Gaussian approximate filter (PGAF), after that, PGAFVS can be deduced. Then we proposed an adaptive fuzzy and backpropagation neural network controller based on PGAFVS (AFNPGA-VS) that can improve the application of tightly coupled integration under the premise of the prior uncertainty and further promote robustness high measurement accuracy. The simulation results show that the proposed algorithm outperforms the state-of-the-art methods.

Improving Localization Accuracy of Neural Sources by Pre-processing: Demonstration With Infant MEG Data.

We discuss specific challenges and solutions in infant MEG, which is one of the most technically challenging areas of MEG studies. Our results can be generalized to a variety of challenging scenarios for MEG data acquisition, including clinical settings. We cover a wide range of steps in pre-processing, including movement compensation, suppression of magnetic interference from sources inside and outside the magnetically shielded room, suppression of specific physiological artifact components such as cardiac artifacts. In the assessment of the outcome of the pre-processing algorithms, we focus on comparing signal representation before and after pre-processing and discuss the importance of the different components of the main processing steps. We discuss the importance of taking the noise covariance structure into account in inverse modeling and present the proper treatment of the noise covariance matrix to accurately reflect the processing that was applied to the data. Using example cases, we investigate the level of source localization error before and after processing. One of our main findings is that statistical metrics of source reconstruction may erroneously indicate that the results are reliable even in cases where the data are severely distorted by head movements. As a consequence, we stress the importance of proper signal processing in infant MEG.

A Rigorous Feature Extraction Algorithm for Spherical Target Identification in Terrestrial Laser Scanning

Precise and rapid extraction of spherical target features from laser point clouds is critical for achieving high-precision registration of multiple point clouds. Existing methods often use linear models to represent spherical target characteristics, which have several drawbacks. This paper proposes a rigorous estimation algorithm for spherical target features based on least squares configurations, in which the point-cloud data error is used as a random parameter, while the spherical center coordinates and radius are used as nonrandom parameters, emphasizing correlation between spherical parameters. The implementation details of this algorithm are illustrated by deriving calculation formulas for three variance–covariance matrices: variance–covariance matrices of the new observations, variance–covariance matrices of the new observation noise, and variance–covariance matrices of random parameters and the new observation noise. Experiments show that the estimation accuracy of sphere centers using our method is improved by at least 5.7% compared to classical algorithms, such as least squares, total least squares, and robust weighted total least squares.

Improved firefly algorithm–extended Kalman filter–least-square support-vector machine voltage sag monitoring and classification method based on edge computing

Aiming at the hardware reusability, multi-service carrying capacity, and computing resource limitations of edge devices, a light-weight voltage sag monitoring and classification method based on improved firefly algorithm optimization, extended Kalman filter, and least-square support-vector machine is proposed. The strategy of linearly decreasing inertia weight is introduced to optimize the state error of the extended Kalman filter algorithm and the measurement noise covariance matrix to achieve accurate monitoring of voltage sags. Extract characteristic quantities such as average value, duration of sag, minimum sag dispersion characteristics, number of sag phases, and flow direction of disturbance energy. As a model training data set, the least-square support-vector machine method optimized based on the improved firefly algorithm is used to create a multi-level classification model of voltage sag source to realize the classification of voltage sag sources. This method fully considers the influence of the limited resources of edge computing equipment on the algorithm, and effectively improves the use of computing resources by improving the optimization algorithm. Simulation and experimental results show that this method is suitable for edge computing equipment to monitor and distinguish voltage sags.

Localizing Submerged Acoustic Sources Under Adverse Conditions

This paper reviews various approaches for localizing submerged acoustic sources under adverse conditions. It is essential to obtain data of the highest possible quality when there are adverse conditions, such as uncertainties in the environment, source motion, and low signal-to-noise ratio. Focalization is an approach in which the source location and environmental parameters are treated as unknowns. Due to a parameter hierarchy in which source location outranks environmental parameters, there may be many realizations of the environment that bring the source into focus; the ambiguity in the environment can be an advantage if the primary objective is to localize the source. Environmental uncertainty is often associated with environmental complexity, which can be an advantage by reducing the ambiguity of the source location. Obtaining a high-quality estimate of the covariance matrix may be difficult when there is source motion, but the complexity of the received field from a moving source is another factor that can reduce ambiguity. It may be possible to localize a source that is buried in noise when an estimate of the noise covariance matrix is available. During the development of approaches for localizing submerged sources, much of the focus has been on one-dimensional vertical arrays. An extension of the multi-valued Bartlett processor to the case of a rectangular array was designed to take advantage of the extra dimension of the array and appears to have the potential to be the most powerful combination of hardware and signal processing to date.

Estimation algorithm for vehicle state estimation using ant lion optimization algorithm

In order to solve the problem of vehicle state estimation, an unscented Kalman filter state parameter estimator based on the Ant lion algorithm is proposed. Aiming at the uncertainty of the noise covariance matrix in the unscented Kalman filter (UKF) process, the Ant lion optimization algorithm (ALO) is used to optimize it. Based on the purpose, a 3-DOF nonlinear vehicle estimation model with Magic formula tire model was established firstly. Then the slalom road operating condition was simulated. The simulation results show that the estimated values of the key state variables are in better agreement with the virtual test values indicating the proposed algorithm having a good estimation performance. And also, compared with the estimation results of the UKF algorithm, the maximum error and the root mean square error of the estimation algorithm proposed in this paper are both smaller than the estimated value of the UKF algorithm. The results of a real-vehicle experiment demonstrate that the proposed method can be used effectively and accurately for solving the vehicle-state estimation problem. The study can provide precise status information for vehicle stability control under extreme conditions.

Trans-dimensional gravity and magnetic joint inversion for 3-D earth models

SUMMARY Studying 3-D subsurface structure based on spatial data is an important application for geophysical inversions. However, major limitations exist for conventional regularized inversion when applied to potential-field data. For example, global regularization parameters can mask model features that may be important for interpretation. In addition, 3-D inversions are typically based on data acquired in 2-D at the Earth’s surface. Such data may contain significant spatial error correlations in 2-D due to the choice of spatial sampling, acquisition geometry, ambient noise and model assumptions. These correlations can cause trade-offs with spatial resolution and should be accounted for. However, correlations are often ignored, particularly 2-D correlations in spatial data, such as potential field data recorded on the Earth’s surface. Non-linear Bayesian methods can address these shortcomings and we present a new hierarchical model for 2-D correlated errors. Nonetheless, limitations also exist. For example, non-linear Bayesian estimation requires numerical integration with a considerable computational burden to collect a posterior ensemble of models. For 3-D applications, this cost can be prohibitive. This paper presents a non-linear Bayesian inversion with trans-dimensional (trans-D) partitioning of space by a hierarchy of Voronoi nodes and planes (VP), and trans-D estimation of the data noise covariance matrix. The addition of planes permits the introduction of prior information which reduces non-uniqueness. The covariance matrix estimation uses a trans-D autoregressive (AR) noise model to quantify correlated noise on 2-D potential-field data. We address computational cost by wavelet compression in the forward problem and by basing susceptibility on an empirical relationship with density contrast. The method is applied to simulated data and field data from off-shore Abu Dhabi. With simulated data, we demonstrate that subsurface structures are well-resolved with the trans-D model that applies hierarchical VP partitioning. In addition, the model locally adapts based on data information without requiring regularization. The method is also successful in reducing 2-D error correlation via trans-D AR models in 2-D. From field data, the inversion efficiently resolves basement topography and two distinct salt diapirs with a parsimonious and data-driven parametrization. Results show a considerable reduction in 2-D spatial correlations of field data using the proposed trans-D AR model.

Experimental evaluation for fluxes, currents and speed estimation of induction motor

Induction motor drive control and estimation is a wide subject. The market for variable speed drives has grown dramatically in the last few years. Manufacturers have recognized the importance of not only managing the speed or torque range, but also reducing power consumption. This necessitates the development of new control algorithms and schemes to include these solutions. Indeed, the speed estimate must be employed in one or more regions of the control scheme, depending on the control objective. This concept, as well as the most common speed estimation methodologies, is investigated. Currently, many tools can be used for the evaluation of the rotor speed without a speed sensor. By modern signal processing methods, it is possible to implement an estimation scheme with the possibility of monitoring currents and voltages. Therefore, in this paper, the concept of currents, speed and fluxes estimation based on the extended Kalman filter is proposed. By monitoring the ratio of the theoretical residual to the actual residual, the measured noise covariance matrix is recursively corrected online to make it gradually approach the real noise level. So that the filter performs the optimal estimation, improves the accuracy of the speed estimation. The effect of the load change on the currents, fluxes and speed estimation was also studied. Simulation and experimental results show that the proposed improved adaptive extended Kalman estimator has a strong ability to suppress random measurement noise. The experimental and simulation results prove the accuracy of the proposed scheme towards the state estimation of an induction motor at different load levels. It can accurately estimate the speed of the motor and has a good anti-error ability to meet the actual needs of the project.

Target detection with persymmetric subspace models for steering vector mismatches in MIMO radars

In colocated multiple-input multiple-output radar, the problem of detecting a target embedded in Gaussian noise with unknown covariance matrix is examined for the mismatched case where the true transmit and receive steering vectors are not aligned with the nominal ones, respectively. We adopt subspace models to take into account the steering vector mismatches. With exploitation of persymmetry, adaptive detectors without requiring training data are proposed according to the criteria of generalized likelihood ratio test (GLRT), Wald test, and Rao test. The proposed GLRT and Wald test exhibit constant false alarm rate properties against the noise covariance matrix. Interestingly, we find out that the Rao test does not exist for the detection problem considered. Simulation results show that the proposed detectors bear stronger robustness to the steering vector mismatches than their counterparts.

On noise covariance estimation for Kalman filter-based damage localization

In Structural Health Monitoring, Kalman filters can be used as prognosis models, and for damage detection and localization. For a proper functioning, it is necessary to tune these filters with noise covariance matrices for process and measurement noise, which are unknown in practice. Therefore, in the presented work, we apply an autocovariance least-squares method with semidefinite constraints solely based on model parameters. We facilitate this novel approach by formulating the considered innovations covariance function in infinite horizon, which follows inherently from the assumption of linear time-invariant systems. For damage analysis, we adapt a framework based on state-projection estimation errors that was recently established, and yet only applied using H∞ filters. These estimators represent an alternative to Kalman filters, and are considered robust. Because of this property, the necessity of filter tuning is relaxed, and a naive design is often considered. Based on the damage analysis framework, we derive a new damage indicator that features a high sensitivity towards localized damage. We demonstrate the efficacy of the proposed schemes for noise covariance estimation and damage analysis in a series of simulations inspired by a preceding laboratory test. We finally offer experimental validation, based on vibration test data of a cantilever beam featuring damages at multiple positions, where high sensitivity towards small local stiffness changes is achieved. In our investigations, we compare the damage detection and localization performance of Kalman and H∞ filters as well as differences in mode shape curvatures (MSC). In the simulation studies, the proposed Kalman filter-based approach outperforms the alternative strategy using H∞ estimators. The experimental investigations demonstrate a significantly higher sensitivity of the filters towards localized damage compared to differences in MSCs. Considering the totality of investigations, the combined application of both estimators can lead to an increased robustness and sensitivity regarding damage detection and localization.

Detection and Tracking of Moving Object-Using Kalman Filter Enhancement (KF) by Grasshopper Optimization Algorithm

Today, the process of tracking moving objects in Video sequence has many real applications such as robots' systems, surveillance systems, and monitoring systems, visual information processing, and so more. The first stage in tracking moving object systems is detection the target in Video sequence and images and the second stage is to track the identified object. In this regard, Automatic detection and tracking of object is an attractive scope in now researches, so the proposed method based on the detection-tracking target moving objects by using the Kalman Improved Filter (KF) method. The Kalman filter, assuming initial state and noise covariance parameter for detection the object, which are critical parameters for estimating speed. For successful tracking by Kalman filter, the noise covariance matrix must be optimized. Therefore, in many studies, different methods based on optimization and metaheuristic algorithms have been proposed to increase the performance of Kalman filter method. In this research to adjust, the noise covariance is of the Kalman filter for object tracking and improve the initial parameters of it, using grasshopper optimization algorithm (GOA). Here considered not only the properties of the object, but also the estimation of the motion of the object to speed up the search process. To compare the new method's efficiency and accuracy, we used MATLAB R2019b software. The results show that the proposed method has improved at least 10% in accuracy compared to RMOT and CMOT and 20% in recovery compared to Recall. In addition, the proposed method has at least a 2% improvement in Recall parameters and accuracy compared to the evaluated article.

Robust Adaptive Beamforming Algorithm for Sparse Array Based on Covariance Matrix Reconstruction Technology

When the array structure of the sparse arrays (SA) cannot be determined, the existing beamforming algorithms designed according to specific formations such as coprime arrays (CA), nested arrays (NA), etc. will fail. To solve this problem, we propose two algorithms that are suitable for a variety of SA. In the first method, assuming that the desired signal is a non-Gaussian signal, the desired signal direction vector (DSDV) is estimated using the fourth-order cumulant, and then the interference plus noise covariance matrix (INCM) is reconstructed by integrating the area outside the desired signal. When the desired signal is a Gaussian signal, we propose the second method. The second method estimates the power and direction of arrival (DOA) of the signals by performing eigenvalue decomposition on the sampled covariance matrix (SCM) and finally calculates the weight vector. However, this method needs to estimate the DOA of the signals, so it has certain requirements for the SA structure design. The simulation results show that the proposed method has good performance and strong robustness under different SA.

Robust estimation of traffic density with missing data using an adaptive-R extended Kalman filter

Traffic density is a crucial indicator of traffic congestion, but measuring it directly is often infeasible and hence, it is usually estimated based on other measurements. However, a challenge in measuring traffic parameters is the high probability of sensor failure, which results in missing measurement or missing data. To overcome this difficulty, in this paper, we propose a novel adaptive-R extended Kalman filter (AREKF) combined with a model-based data imputation technique to estimate traffic density. We show analytically that the AREKF is able to accurately estimate the density even when the noise covariance matrices are not accurately known. Microscopic traffic simulations demonstrated the efficacy of the AREKF, where the estimated density is fed into a real-time ramp metering control algorithm to control vehicle flow on a merging road, which is highly susceptible to traffic congestion. The results show that the proposed AREKF with data imputation is able to accurately estimate the traffic density even when data is missing, and the ramp-metering controller significantly improves the traffic flow and thus, alleviates congestion.

A Compact Noise Covariance Matrix Model for MVDR Beamforming

Acoustic beamforming is routinely used to improve the SNR of the received signal in applications such as hearing aids, robot audition, augmented reality, teleconferencing, source localisation and source tracking. The beamformer can be made adaptive by using an estimate of the time-varying noise covariance matrix in the spectral domain to determine an optimised beam pattern in each frequency bin that is specific to the acoustic environment and that can respond to temporal changes in it. However, robust estimation of the noise covariance matrix remains a challenging task especially in non-stationary acoustic environments. This paper presents a compact model of the signal covariance matrix that is defined by a small number of parameters whose values can be reliably estimated. The model leads to a robust estimate of the noise covariance matrix which can, in turn, be used to construct a beamformer. The performance of beamformers designed using this approach is evaluated for a spherical microphone array under a range of conditions using both simulated and measured room impulse responses. The proposed approach demonstrates consistent gains in intelligibility and perceptual quality metrics compared to the static and adaptive beamformers used as baselines.

A Robust Digital Beamforming on Receive in Elevation for Airborne MIMO SAR System

The echo separation issue for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) is usually regarded as a more technical challenge. Spotlighted as a promising solution to the echo separation, the well-known short-term shift-orthogonal (STSO) beamforming scheme has become increasingly popular. However, for airborne MIMO SAR systems, the digital beamforming (DBF) involved in the STSO scheme usually encounters more issues, e.g., the direction of arrival (DOA) mismatch induced by topography variation. Up to now, relatively less research on robust DBF processing has been conducted for airborne MIMO SAR systems. In this respect, an adaptive DBF technique, based on interference plus noise covariance matrix (IPNCM) reconstruction and desired signal steering vector estimation, has been proposed in this paper. IPNCM reconstruction and steering vector estimation can not only cope with the DOA mismatch problem, but also remove the desired signal component in the training data cells to increase the beamformer convergence rates. Consequently, the proposed approach really improves the array output signal-to-interference-plus-noise ratio (SINR). Moreover, numerous discussions and simulations are carried out to prove the effectiveness of proposed DBF technique under various disturbance environments. Compared with the current DBF techniques, the proposed method provides a bright application prospect for the STSO scheme.

A Conditional One-Output Likelihood Formulation for Multitask Gaussian Processes

Multitask Gaussian processes (MTGP) are the Gaussian process (GP) framework's solution for multioutput regression problems in which the $T$ elements of the regressors cannot be considered conditionally independent given the observations. Standard MTGP models assume that there exist both a multitask covariance matrix as a function of an intertask matrix, and a noise covariance matrix. These matrices need to be approximated by a low rank simplification of order $P$ in order to reduce the number of parameters to be learnt from $T^2$ to $TP$. Here we introduce a novel approach that simplifies the multitask learning by reducing it to a set of conditioned univariate GPs without the need for any low rank approximations, therefore completely eliminating the requirement to select an adequate value for hyperparameter $P$. At the same time, by extending this approach with both a hierarchical and an approximate model, the proposed extensions are capable of recovering the multitask covariance and noise matrices after learning only $2T$ parameters, avoiding the validation of any model hyperparameter and reducing the overall complexity of the model as well as the risk of overfitting. Experimental results over synthetic and real problems confirm the advantages of this inference approach in its ability to accurately recover the original noise and signal matrices, as well as the achieved performance improvement in comparison to other state of art MTGP approaches. We have also integrated the model with standard GP toolboxes, showing that it is computationally competitive with state of the art options.

Reduced-Complexity FFT-Spread Multicarrier Faster-Than-Nyquist Signaling in Frequency-Selective Fading Channel

In this paper, we propose novel reduced-complexity fast Fourier transform (FFT)-spread multicarrier faster-than-Nyquist (MFTN) signaling with power allocation for a frequency-selective fading channel. The information rate of the proposed MFTN signaling is derived by relying on the circulant approximation of the FTN-specific intersymbol interference matrix and noise covariance matrix. This allows us to constitute efficient calculations of precoding and weighting matrices. The power allocation coefficients are optimized such that the approximated information rate is maximized. Our simulation results demonstrate that the proposed scheme with power allocation achieves the bit error ratio (BER) performance close to the conventional eigenvalue-decomposition (EVD)-precoded FTN signaling counterpart that is optimal in terms of an achievable information rate while significantly reducing the computational complexity as low as the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(N\log N)$ </tex-math></inline-formula> . While the proposed scheme exhibits a high peak-to-average-power ratio similar to the conventional EVD-precoded counterpart due to the effects of FFT-based precoding, it achieves better BER performance than the conventional open-loop single-carrier FTN signaling scheme and the Nyquist signaling scheme, employing the same root-raised cosine shaping filter. It is also confirmed that the proposed MFTN signaling scheme does not suffer from any significant bandwidth broadening.