Noise Covariance Research Articles

Distributed Sequential State Estimation Over Binary Sensor Networks with Inaccurate Process Noise Covariance: A Variational Bayesian Framework

Distributed Sequential State Estimation Over Binary Sensor Networks with Inaccurate Process Noise Covariance: A Variational Bayesian Framework

A comparison of indirect and direct filter designs from data for LTI systems: the effect of unknown noise covariance matrices

Existing literature on model-based filter design for stochastic LTI systems assumes complete correspondence between the system and its model. When the system is not completely known, the standard indirect model-based (two-steps) filtering solution consists of: (i) identify a model of the system from measured input/output data; (ii) design a Kalman filter based on the estimated model. The performance of this indirect approach are limited by the model and noise covariance matrices accuracy. To overcome such limitations, this paper investigates a direct (one-step) solution to the filtering problem for SISO LTI systems in the Prediction Error Method (PEM) identification framework. Simulation results indicate the effectiveness of the direct filtering approach, especially when the noise covariance matrices are misspecified.

A Noise Covariance Regulated Robust Modified Adaptive Extended Kalman Filter for State of Charge Estimation of Lithium-Ion Battery

A Noise Covariance Regulated Robust Modified Adaptive Extended Kalman Filter for State of Charge Estimation of Lithium-Ion Battery

A Stability Guaranteed Variational Bayesian Converted Measurement Kalman Filter for Radar Tracking with Unknown Noise Covariances

A Stability Guaranteed Variational Bayesian Converted Measurement Kalman Filter for Radar Tracking with Unknown Noise Covariances

Research of adaptive algorithms of recurrent filtration at processing data from GNSS when radio signals lose from navigation satellites

Algorithms for linear and adaptive Kalman filtering of navigation data received from satellite navigation systems are considered. A comparison of the Kalman linear filter algorithms, the Yazvinsky adaptive filter, the adaptive filter with feedback on the updated sequence and the adaptive filter without a priori information about the noise covariance matrices is made. The algorithms are tested in a practical experiment — navigation information from GNSS is obtained by using a GNSS receiver installed on a car moving in an urban environment. The comparative analysis results of the algorithms usage for adaptive modifications of the Kalman filter are presented. The results showed that the Yazvinsky filter works worse when radio signals from navigation satellites disappear, and the adaptive filter algorithm without a priori information about the noise covariance matrices does not actually filter the data. Keywords GNSS, navigation information, Kalman filter, Yazvinsky filter, adaptive Kalman filter

Structural Dynamic Response Reconstruction Based on Recurrent Neural Network–Aided Kalman Filter

In structural health monitoring (SHM), an important issue is the limited availability of measurement data due to the spatial sparsity of sensors installed on the structure. These measurements are insufficient to accurately depict the actual dynamic behavior and response of the structure. Therefore, full‐field (i.e., every degree of freedom) structural response reconstruction based on sparse measured data has drawn a lot of attention in recent years. Kalman filter (KF) is an effective technology for response reconstruction (also known as state estimation), providing an optimal solution for systems that can be well‐represented by a fully known Gaussian linear state‐space model. This implies that both the process noise and measurement noise follow known zero‐mean Gaussian distribution, which is impractical in many civil engineering applications considering the unavoidable modeling errors and variations of environmental conditions. To address this challenge, a data‐physics hybrid‐driven method, i.e., KalmanNet, is proposed in this study for response reconstruction of partially known systems. By integrating a recurrent neural network (RNN) module into the KF framework, KalmanNet can efficiently learn and compute the Kalman gain using available monitoring data, without any Gaussian assumptions or explicit noise covariance specifications (e.g., covariance matrices of process and measurement noise). Both numerical and experimental investigations are conducted to validate this method. The results demonstrate that under the influence of non‐Gaussian noise and modeling errors, KalmanNet can effectively and accurately reconstruct the structural response from sparse measurements in real‐time and has higher accuracy and robustness compared to traditional KF even with optimal parameter settings.

A Novel Adaptive Noise Covariance Matrix Estimation and Filtering Method: Application to Multiobject Tracking

This paper presents a novel online adaptive method for estimating the process and measurement noise covariance matrices in Kalman filters (KFs) to address the challenge of varying noise characteristics in practical applications. Specifically, the proposed method decomposes the noise covariance matrix into an element distribution matrix and a noise intensity and employs an improved Sage filter to estimate the element distribution matrix. Additionally, a calibration and correction method is introduced to accurately determine and adaptively correct the online bias of the noise intensity. The unbiasedness and convergence of the proposed method are mathematically proven under the condition that the system is detectable. Moreover, this method is applied to multiobject tracking (MOT) based on KFs and light detection and ranging (LiDAR), and it is evaluated on the KITTI dataset and the official KITTI server. The experimental results demonstrate that the proposed method achieves significantly improved MOT performance based on KFs and outperforms other LiDAR-based methods on the KITTI leaderboard. This method provides a new approach for enhancing the performance of KFs and assisting with MOT, and it has practical feasibility for real-world applications.

Fault-Tolerant Cubature Kalman Filter for Engineering Estimation Control Systems.

The cubature Kalman filter (CKF) overcomes the limitations of the Kalman filter in strong nonlinear systems, which has been widely used in many fields. However, in practical engineering, the abnormal measurement information obtained by the sensor causes the measurement noise covariance to change, which may deteriorate the filtering performance and even cause the filter failure. The fault-tolerant filter can deal with the state estimation problem for the systems with abnormal measurements. The key of the fault-tolerant filter is to forcefully correct filter innovation by using a fading factor. The fault-tolerant filter technology has been extensively applied in many practical systems, but it is still lack of reasonable theoretical analysis. To this end, the measurement noise model is established and the magnitude of the noise deviation is analyzed. The filtering performance under abnormal measurement is analyzed by three mean squared errors (MSEs), which are the ideal MSE, the filter calculated MSE and the true MSE. In order to solve the influence of sampling approximation deviation of CKF on fault detection, an improved fault detection algorithm is proposed. The performance of fault-tolerant CKF is analyzed from two views. The first view is about comparing the filter calculated MSEs of CKF and of fault-tolerant CKF, the second view is about comparing the relative closeness of the filter calculated MSE to the true MSE for the two algorithms. Numerical examples further verify these conclusions.

A robust GNSS sensors in presence of signal blockage for USV application

Unmanned surface vehicle (USV) can navigate autonomously via the global navigation satellite system (GNSS). However, the traditional GNSS scalar tracking loop easily loses lock in low carrier-to-noise ratio (CNR) situations, such as signal occlusion and weak signals. Meanwhile, an increase in the carrier/code phase error leads to an increase in the measurement error of the navigation filter, which decreases the accuracy of the position estimation. To solve this problem, this paper proposes a carrier and code tracking structure based on a forward and backward Kalman filter to dynamically adjust the gain of the vector tracking loop. The carrier and code phase errors calculated by the loop discriminators were linearly transformed into pseudo-range rate and pseudo-range errors after filtering and smoothing, which were used as the measurements of the navigation filter. The signal CNR was used to adaptively adjust the measurement noise covariance matrix of the loop filters. The field tests used a commercial receiver’s navigation solution as the reference. In the stationary test, the proposed structure reduced the localization error by 44.3% compared with the traditional methods. In kinematic experiments, the proposed structure reduced the carrier and code phase errors in a harsh signal environment and improved the positioning accuracy at the source. The test results demonstrate that the proposed GNSS tracking method can provide a possible solution for the development of navigation systems for USV.

An invariant error-based SINS/DVL/USBL tightly coupled integrated navigation algorithm and its robust state estimator

The existing strapdown inertial navigation system (SINS)/Doppler velocity log (DVL)/ultra-short baseline system (USBL) integrated navigation error models directly apply algebraic differences to define the vector error, which is not strictly accurate. Considering that the invariant error definitions derived from Lie group theory have been used in the navigation field to obtain more accurate linear error models, in this paper, a new SINS/DVL/USBL integrated navigation system is investigated based on the invariant error definition and tightly coupled structure. In order to suppress the effect of measurement outliers on navigation accuracy, a new statistical similarity measure (SSM)-based multiple adaptive outlier-robust state estimator (MAORSE) is proposed. It decomposes the noise covariance matrix into multiple sub-matrices. Through the estimation and adjustment of sub-matrices, the influence of abnormal observations on the filtering results is weakened while realizing the full utilization of normal observation information. The test results demonstrate the effectiveness and superiority of the proposed invariant error-based SINS/DVL/USBL tightly coupled integrated navigation algorithm and SSM-based MAORSE.

Equivalent circuit modeling and state-of-charge estimation of lithium titanate battery under low ambient pressure

The low ambient pressure during the flight of aircraft has a significant impact on the performance and safety of the onboard power battery. In order to ensure the safe operation of the battery system, it is very important to accurately estimate and manage the state-of-charge (SOC) of the battery. In this work, the equivalent circuit modeling (ECM) of lithium titanate battery (LTB) is studied in detail, and the influence of analog circuit model parameters in low ambient pressures is discussed for the first time. The forgetting factor recursive least square algorithm is introduced to accurately identify the ECM parameters of the LTB under different pressures online. The particle swarm optimization algorithm is innovatively proposed to optimize the covariance matrix of the Kalman filter algorithm. The verification shows that the root mean square error of the ECM of LTB under different ambient pressures is less than 0.025. In the SOC estimation process, the noise covariance matrixes of the extended Kalman filter and the unscented Kalman filter are optimized by the particle swarm algorithm. The optimized SOC estimation absolute error is less than 3 %, especially at 96 kPa and 30 kPa, where the absolute error is less than 2 %.

Bayesian Optimization for Fine-Tuning EKF Parameters in UAV Attitude and Heading Reference System Estimation

In various applications, the extended Kalman filter (EKF) has been vital in estimating a vehicle’s translational and angular motion in 3-dimensional (3D) space. It is also essential for the fusion of data from multiple sensors. However, for the EKF to perform effectively, the optimal process noise covariance matrix (Q) and measurement noise covariance matrix (R) must be chosen correctly. The use of EKF has been challenging due to the need for an easy mechanism to select Q and R values. As a result, this research focused on developing an algorithm that can be easily applied to determine Q and R, allowing us to harness the full potential of EKF. Accordingly, an EKF innovation consistency statistics-driven Bayesian optimization algorithm was employed to achieve this goal. Q and R values were tuned until the expected result met the performance requirement for minimum error through improved measurement innovation consistency. The comprehensive results demonstrate that when the optimum Q and R, as tuned by the suggested technique, were used, the performance of the EKF significantly improved.

Parameter Identification of Permanent Magnet Synchronous Motor with Dynamic Forgetting Factor Based on H∞ Filtering Algorithm

To address system parameter changes during permanent magnet synchronous motor (PMSM) operation, an H∞ filtering algorithm with a dynamic forgetting factor is proposed for online identification of motor resistance and inductance. First, a standard linear discrete PMSM parameter identification model is established; then, the discrete H∞ filtering algorithm is derived using game theory reducing state and measurement noise influence. A cost function is defined, solving extremes values of different terms. A dynamic forgetting factor is introduced to the weighted combination of initial and current measurement noise covariance matrices, eliminating identification issues from different initial values. On this basis, a dynamic forgetting factor is added to weigh the combination of the initial measurement noise covariance matrix and the current measurement noise covariance matrix, which eliminates the influence of the discrimination error caused by the different initial values. Finally, the identification model is built in MATLAB/Simulink for simulation analysis to verify the feasibility of the proposed algorithm. The simulation results show the proposed H∞ filtering algorithm rapidly and accurately identifies resistance and inductance values with significantly improved robustness. The forgetting factor enables quick stable recognition even with poor initial values, enhancing PMSM control performance.

Direction of Arrival Estimation With Gain-Phase Uncertainties in Unknown Nonuniform Noise

This paper considers the problem of direction-of-arrival (DOA) estimation for narrowband source signals under the coexistence of gain-phase uncertainties and nonuniform noise. Firstly, by exploiting the low-rank property of the covariance of signal components, and the diagonal property of noise covariance, an optimization problem with low-rank constraints is formulated to estimate the nonuniform noise covariance matrix, which is then solved efficiently by the alternating direction method of multipliers (ADMM). Secondly, a linear transformation operator is employed to construct a rank reduction (RARE) estimator, and subsequently an initial DOA and gain-phase uncertainties are obtained via one-dimensional (1-D) spectral search. With initial estimates, an augmented DOA estimation is finally achieved by constructing a weighted and structured sparse total least-squares (WSS-TLS) optimization problem, which is solved using the block coordinate descent algorithm. Simulation results show the superior performance of the proposed method, and it achieves better tradeoff between computational complexity and performance, compared to existing methods.

Soc Estimation of Li-ion Battery Based on Adaptive CKF Algorithm

A second-or der RC equivalent circuit model was established to improve the estimation accuracy of state of charge (SOC) of power Li-ion batteries, and the model parameters were identified by the recursive least square method with forgetting factor (FFRLS). On this basis, an adaptive cubature kalman filter (ACKF) algorithm was proposed to adaptively modify the process noise covariance matrix and the measurement noise covariance matrix to improve the SOC estimation accuracy. Finally, the SOC estimation algorithm was verified by MATLAB simulations. The results show that compared with UKF and CKF algorithms, the proposed algorithm has higher estimation accuracy and robustness, and can meet the application requirements.

Multi-sensor information fusion localization of rare-earth suspended permanent magnet maglev trains based on adaptive Kalman algorithm.

Since the positioning accuracy of sensors degrades due to noise and environmental interference when a single sensor is used to localize a suspended rare-earth permanent magnetically levitated train, a multi-sensor information fusion method using multiple sensors and self-correcting weighting is proposed for permanent magnetic levitated train localization. A decay memory factor is introduced to reduce the weight of the influence of historical measurement data on the fusion estimation, thus enhancing the robustness of the fusion algorithm. The Kalman filtering results suffer from inaccuracy when process noise is present in the system. In this paper, we use a covariance adaptive scheme that replaces the prediction step of the Kalman filter with covariance. It uses the covariance adaptive scheme to search the posterior sequence online and reconstruct the prior error covariance. Since the process noise covariance is not used in the new adaptive scheme, the negative impact of the mismatch noise statistics is greatly reduced. Simulation and experimental results show that the use of multi-sensor information fusion and covariance adaptive Kalman algorithm has significant advantages in terms of adaptability, accuracy and simplicity.

Efficiently building receive arrays with electromagnetic simulations and additive manufacturing: A two-layer, 32-channel prototype for 7T brain MRI.

We propose a comprehensive workflow to design and build fully customized dense receive arrays for MRI, providing prediction of SNR and g-factor. Combined with additive manufacturing, this method allows an efficient implementation for any arbitrary loop configuration. To demonstrate the methodology, an innovative two-layer, 32-channel receive array is proposed. The design workflow is based on numerical simulations using a commercial 3D electromagnetic software associated with circuit model co-simulations to provide the most accurate results in an efficient time. A model to compute the noise covariance matrix from circuit model scattering parameters is proposed. A 32-channel receive array at 7 T is simulated and fabricated with a two-layer design made of non-geometrically decoupled loops. Decoupling between loops is achieved using home-built direct high-impedance preamplifiers. The loops are 3D-printed with a new additive manufacturing technique to speed up integration while preserving the detailed geometry as simulated. The SNR and parallel-imaging performances of the proposed design are compared with a commercial coil, and in vivo images are acquired. The comparison of SNR and g-factors showed a good agreement between simulations and measurements. Experimental values are comparable with the ones measured on the commercial coil. Preliminary in vivo images also ensured the absence of any unexpected artifacts. A new design and performance analysis workflow is proposed and tested with a non-conventional 32-channel prototype at 7 T. Additive manufacturing of dense arrays of loops for brain imaging at ultrahigh field is validated for clinical use.

SOC estimation for lithium-ion battery based on AGA-optimized AUKF

The window size for covariance matching (CM) of the adaptive unscented Kalman filter (AUKF) affects the state of charge (SOC) estimation performance due to changes with time in the distribution of error innovation sequence (EIS). A new adaptive genetic algorithm (AGA) to address this problem is proposed in this paper. The proposed AUKF (AGA-AUKF1) obtains its best window size determined by the AGA. A novel AUKF (AGA-AUKF2) is proposed to prevent the uncertainty caused by time-varying EIS with the combination of AGA and CM methods. Firstly, the influence of different temperatures on the prediction performance of the algorithm is investigated by FUDS data. The influence of various parameters on the algorithm is further analyzed by FUDS. For different temperatures, initial SOC values, and initial measurement noise covariance, the SOC estimation results show that the accuracy of AGA-AUKFs is better than AUKF. The population size and termination algebra simulation results indicate that the proposed AGA performs well in parameter optimization. Subsequently, the SOC estimation capability of two proposed methods in different working conditions is analyzed by BJDST and US06. The results show that AGA-AUKF2 has better accuracy and robustness than AGA-AUKF1.

A fast convergence strategy based on gray wolf optimization algorithm for co-estimation of battery state of charge and capacity

Under the same initial noise covariance, the extended Kalman filter (EKF) algorithm and the adaptive extended Kalman filter (AEKF) algorithm show different convergence rates in the battery state estimation experiments. It can be concluded from the experimental results that the convergence rate of the EKF algorithm is usually faster than that of the AEKF algorithm, but the estimation accuracy of the AEKF algorithm is usually better than that of the EKF algorithm. In response to this issue, this article proposes a fast convergence strategy based on the grey Wolf optimization (GWO) algorithm for the co-estimation of battery SOC and capacity. Based on battery parameter identification, the proposed algorithm utilizes the GWO to optimize the initial noise covariance of the EKF algorithm. Then, the EKF algorithm with optimized initial noise covariance is used to quickly pull the SOC estimation results into a stable region and switch to the AEKF algorithm to jointly estimate the SOC and capacity of the battery. Through data validation under different working conditions, it is shown that the proposed target algorithm has a much faster convergence ability than the comparison algorithm, and the proposed algorithm also exhibits excellent robustness under different initialization errors and temperatures.

Mitigating the effect of 1/f noise on the detection of the H i intensity mapping power spectrum from single-dish measurements

ABSTRACT We present and compare several methods to mitigate time-correlated (1/f) noise within the H i intensity mapping component of the MeerKAT Large Area Synoptic Survey (MeerKLASS). By simulating scan strategies, the H i signal, foreground emissions, white and correlated noise, we assess the ability of various data-processing pipelines to recover the power spectrum of H i brightness temperature fluctuations. We use MeerKAT pilot data to assess the level of 1/f noise expected for the MeerKLASS survey and use these measurements to create realistic levels of time-correlated noise for our simulations. We find the time-correlated noise component within the pilot data to be between 10 and 20 times higher than the white noise level at the scale of $k = 0.04 \, {\rm {Mpc}}^{-1}$. Having determined that the MeerKAT 1/f noise is partially correlated across all the frequency channels, we employ Singular Value Decomposition (SVD) as a technique to remove both the 1/f noise and Galactic foregrounds but find that over-cleaning results in the removal of H i power at large (angular and radial) scales; a power loss of 40 per cent is seen for a 3-mode SVD clean at the scale of $k = 0.04 \, {\rm {Mpc}}^{-1}$. We compare the impact of map-making using weighting by the full noise covariance (i.e. including a 1/f component), as opposed to just a simple unweighted binning, finding that including the time-correlated noise information reduces the excess power added by 1/f noise by up to 30 per cent.