Robust Adaptive Filtering Research Articles

Dynamic state awareness for distribution network based on robust adaptive cubature kalman filter

With the rapid development of the economy and society, the demand for power quality is constantly increasing. As a crucial part of grid situational awareness, distribution network state estimation plays a vital role in providing critical data support for other advanced applications, which is significant for ensuring the safe and reliable operation of the distribution network. Therefore, this paper proposes a dynamic state awareness method for distribution networks based on the robust adaptive cubature Kalman filter (RACKF). The proposed solution, grounded on the core computational concept of the cubature Kalman filter (CKF), constructs a robust noise statistical estimator (NSE) composed of a biased NSE and an unbiased NSE to adapt to the unknown and time-varying process noise parameters in the dynamic state estimation process. The proposed solution can ensure that the calculated process noise parameters always meet the constraints and guarantee the robustness of the algorithm. In addition, an estimation strategy for the fusion of multi-time scale measurement data is developed according to the RACKF-based dynamic state estimation features in order to realize system state corrections and updates. The results of simulation experiments and comparisons with traditional CKF methods demonstrate the accuracy and superiority of the proposed solution.

A robust adaptive error state Kalman filter for MEMS IMU attitude estimation under dynamic acceleration

Accurate estimation of attitude (pitch, roll) is a prerequisite for ensuring safe navigation during vehicle control execution. In dynamic environments, the presence of acceleration often degrades the accuracy and robustness of attitude estimation using traditional algorithms with Micro-Electro-Mechanical Systems (MEMS) Inertial Measurement Unit (IMU). This paper proposes a robust adaptive error state Kalman filter (RAESKF) algorithm for attitude estimation of MEMS IMU under dynamic acceleration conditions. The RAESKF algorithm decomposes the true attitude Direction Cosine Matrix (DCM) into nominal and error components. An error state Kalman filter is utilized to fuse real-time measurements from MEMS gyroscope and accelerometer, estimating the error component, which is then used to correct the nominal attitude DCM. Furthermore, within the error state Kalman filtering framework, a dynamic acceleration robust adaptive adjustment strategy is implemented. This strategy relies on real-time data monitoring, threshold-based decision-making, and switching mechanisms. It adaptively selects between dynamic acceleration model compensation and online adjustment of the measurement noise covariance matrix. The primary objective of this strategy is to mitigate the impact of disturbance induced by dynamic acceleration on attitude estimation, thereby enhancing the accuracy and robustness. Laboratory rotation experiments have demonstrated that the algorithm improved pitch and roll measurement accuracy by at least 8.81% and 11.69%, respectively, under rotational conditions. In dynamic acceleration conditions, pitch and roll measurement accuracy improved by at least 42.76% and 67.21%, respectively.

Robust Adaptive Filters and Smoothers for Linear Systems With Heavy-Tailed Multiplicative/Additive Noises

Robust Adaptive Filters and Smoothers for Linear Systems With Heavy-Tailed Multiplicative/Additive Noises

A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

Closed-loop state of charge estimation of Li-ion batteries based on deep learning and robust adaptive Kalman filter

The state of charge (SOC) is among the most crucial monitoring states in battery management systems. To accurately and robustly estimate the battery SOC, a closed-loop SOC estimation method based on deep neural networks is proposed in this study. Initially, a hybrid deep learning model, TGMA, is established by combining a temporal convolutional network (TCN) with a gated recurrent unit (GRU) and incorporating a multi-head self-attention mechanism (MHA) to estimate SOC. Subsequently, to further enhance the accuracy of estimating the battery SOC and the ability to resist outliers, the pre-estimated SOC from the deep learning model TGMA is used as the noisy observation in the Kalman filter, and robust factor and noise adaptive filtering are introduced into the Kalman filter, proposing a closed-loop estimation method based on deep learning and robust adaptive Kalman filter (RAKF). Finally, through comparison with other similar methods, the proposed TGMA-RAKF method is validated to have higher accuracy, generalization, and robustness against outliers under different operating conditions and temperatures, with root mean square error, mean absolute error, and maximum absolute error all less than 1 %, 1 %, and 2.5 % respectively.

A unified sensor and actuator fault diagnosis in digital twins for remote operations

This paper explores the development of a unified hybrid approach for sensor and actuator fault diagnosis in digital twins for remote operations. Central to this approach is the implementation of a robust adaptive Kalman filter algorithm, which forms the backbone of the proposed unified algorithm. The essence of this unified algorithm lies in its capability to effectively filter the sensor measurements. The algorithm is enriched with tuning parameters, offering flexibility in adjusting the convergence rate to suit operational requirements. Noteworthy for its robustness, our approach excels in handling uncertainties and diverse types of faults, including drift, bias, noise, and freeze fault scenarios. Through comprehensive simulation and experimental evaluations conducted on a small surface vessel, the method demonstrates remarkable proficiency in accurately identifying sensor and actuator faults. This precision enables early detection and prompt mitigation of anomalies, contributing to heightened operational resilience.

Robust hyperbolic tangent Geman-McClure adaptive filter based on NKP decomposition and its performance analysis

Robust hyperbolic tangent Geman-McClure adaptive filter based on NKP decomposition and its performance analysis

Robust adaptive non‐linear alignment algorithm for SINS/DVL integrated navigation system based on variational Bayesian

AbstractThe problem of dynamic attitude alignment for strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation has become a research hotspot. Underwater complex environment makes DVL output vulnerable to non‐Gaussian noise pollution, which makes it difficult to converge the SINS misalignment angle to within 1° based on analytical coarse alignment. This is to say, the performance of SINS fine alignment via Kalman filter will be degraded because the model of initial alignment exhibits non‐linearity. The inaccurate and/or unknown prior information of measurement noise statistical characteristics will also degrade the filtering performance. To ensure the SINS/DVL alignment accuracy under non‐linear, non‐Gaussian and uncertain conditions, this paper proposed a robust adaptive unscented Kalman filter (UKF) based on Variational Bayesian (VB) method (VBRAUKF). The proposed VBRAUKF improves the adaptability and robustness of UKF from the following two main aspects. Firstly, an adaptive estimation strategy for the measurement noise covariance is designed based on the VB algorithm, which can restrain the effect of inaccurate observation model and improve the adaptive ability of the filtering method. Secondly, an expansion factor is designed based on Mahalanobis distance algorithm, which can restrain the effect of non‐Gaussian noise and improve the robustness of the filtering method. The experimental results for the problem of the SINS/DVL dynamic alignment under mixed Gaussian noise and/or outlier conditions demonstrate the superiority of the proposed VBRAUKF over the traditional ones.

Improved performance of a shunt hybrid active power filter by a robust exponential functional link network-based nonlinear adaptive filter control to enhance power quality

This research article details the design and implementation of a nonlinear adaptive filtering (NAF) technique using an exponential functional link network (EFLN) for a shunt hybrid active power filter (SHAPF) control to solve the current-associated power quality issues on the utility side at the distribution level of electrical power systems. Separation of the fundamental component from the harmonics, achieving unity power factor operation, reducing the reactive power drawn from the source, balancing the currents during transients, and reduction of total harmonic distortion (THD) of the source current are the issues considered to resolve. The proposed technique solves these issues by generating the sinusoidal reference current and separating the fundamental current from the harmonics. When compared to conventional and existing adaptive filtering techniques such as least mean square (LMS), least mean fourth (LMF), and variable step size LMS (VSS-LMS), the proposed EFLN-NAF method excels in terms of speedy convergence, adaptability in noise-specific environments and reduced steady-state coefficient error. MATLAB/Simulink software is utilized to perform the simulations to examine the suggested strategy for the chosen SHAPF topology both in static and dynamic scenarios. For a 15 kW and 3kVAr requirement of the nonlinear load, simulation results proved that the designed PPF for 2kVAr is able to share the reactive power with the APF, thereby reducing its rating and cost. The proposed method of filtering has been proven to be fast converging with 0.049 s, and the THD in steady state is brought to 1.32 % in steady-state and to 3.77 % during transient conditions, which are under standard limits. A hardware prototype of the experimental setup is constructed at the laboratory scale with OPAL-RT (OP4510) as the controller. With an active and reactive power demand of 1.1 kW and 210VAr, the designed PPF supplies 110 VAr, whereas the rest is supplied by the APF. The practical THD in source current is observed to be 2.081 %, which meets the standards. The results from both simulations and experiments are validated, and the efficacy of the proposed technique in mitigating the aforementioned power quality issues is proved.

A novel robust adaptive Kalman filter with application to urban vehicle integrated navigation systems

This study addresses the formidable challenge presented by non-Gaussian, time-varying, heavy-tailed process noise in integrated vehicle navigation systems. While robust adaptive filtering methods exist, their efficacy is constrained, and certain algorithms exhibit suboptimal usability due to an excess of a priori parameters. We deduce an adaptive robust Kalman filter, characterizing process noise with a Student's t distribution and measurement noise adhering to a Gaussian distribution. To enhance robustness against unknown or varying noise statistics, our method simultaneously estimates the scale matrix, degrees of freedom parameters, state vector, and measurement noise covariance through the expectation–maximization (EM) algorithm and Bayesian variational inference theory. Rigorous simulations and empirical experiments validate its superior accuracy and stability, requiring minimal a priori parameter information. Vehicle-based experiments further demonstrate positioning error below 2.78 m, velocity error below 0.34 m/s, and heading error less than 1.28° after achieving a steady state. This approach exhibits significant potential for advancing the precision and reliability of vehicle navigation systems.

A robust adaptive decomposable Volterra filter based on the hyperbolic tangent Leclerc function and its performance analysis

SummaryMost of the existing adaptive filter algorithms pay more attention to improving performance while ignoring the computational complexity and the impact of the impulsive environment. When encountering the impulsive noise environments, the performance of traditional nonlinear adaptive filter may be significantly reduced and usually needs high computational cost. Therefore, this article proposes a hyperbolic tangent Leclerc robust nonlinear adaptive filter based on the low complexity decomposable Volterra model (HTLNAF‐DVM). The filter is implemented by imposing a rank‐one structure on the full Volterra model to get a product of linear filters, and employs a hyperbolic tangent Leclerc function as a robust norm to effectively improve the robustness against the impulsive noise. In addition, we give the theoretical analyses of the steady‐state mean‐square performance of the proposed HTLNAF‐DVM. Finally, the simulation results prove that the proposed HTLNAF‐DVM algorithm has better performance than the existing algorithms and fit well with the theory.

Robust adaptive Kalman filter for structural performance assessment

SummaryStructural performance assessment is a critical stage in the health monitoring for the maintenance and risk management of engineering structures, in which the interstory drift is a key indicator. In this paper, a robust adaptive Kalman filter is proposed for an interstory drift estimation problem to show the health condition of steel structures in the case that the statistics or internal dynamics describing the signals and measurements are not known precisely. More precisely, we build an adaptive current Jerk model (ACJM) where the model parameters are updated in each time step to presuppose the statistics characterization of the steel dynamic, while the unknown measurement noise covariance is adapted based on a fixed‐lag innovation with respect to measurements. Moreover, a robust adaptive Kalman filter is designed for the modelling uncertainties in each time increment by solving a minimax game: one player tries to select an “actual” model far from the proposed ACJM with an exponential decay tolerance, while its “hostile” player, namely, the optimum filter, is designed by minimizing the estimation error according to the selected “actual” model. Finally, some simulation and experimental results show the effectiveness of the proposed algorithm.

Research on Robust Adaptive RTK Positioning of Low-Cost Smart Terminals.

The performance of low-cost smart terminals is limited by the performance of their low-cost Global Navigation Satellite System (GNSS) hardware and chips, as well as by the impact of complex urban environments, which affect the positioning accuracy and stability of GNSS services. To this end, this paper proposes a robust adaptive Kalman filter for different environments that can be applied after data preprocessing. Based on the Kalman filter algorithm, a robust estimation approach is introduced into real-time kinematic (RTK) positioning to make judgments on the abnormal observation values of low-cost smart terminals, which amplifies the variance and covariance of the outlier observation equation, and reduces the impact of outliers on positioning performance. The Institute of Geodesy and Geophysics III (IGG III) function is used for regulation purposes, where prior information is modified and refreshed using the equivalent weight matrix and adaptive factors, thus reducing the impact of system model errors on system state estimation results. In addition, a robust factor is defined to adjust positioning deviation weighting between the pre- and post-test robust estimates. The experimental results show that after robust RTK positioning in the static experiments, the overall improvement in positioning accuracies of the Xiaomi 8, Huawei P40, Huawei mate40, and low-cost M8 receiver reached 29.6%, 31.3%, 32.1%, and 30.7%, respectively. Similarly, after applying the proposed robust method in the dynamic experiments, the overall positioning accuracies of the Xiaomi 8, Huawei P40, Huawei mate40, and the low-cost M8 receiver improved by 28.3%, 32.9%, 35.4%, and 26.2%, respectively. The experimental results reveal that an excellent positioning effect of a smartphone is positively correlated with robust RTK positioning performance. However, it is worth noting that when the positioning accuracy reaches a high level, such as the positioning results achieved using low-cost receivers, the robustness performance shows a relatively decreasing trend. This finding suggests that under the condition of high positioning accuracy, the sensitivity of specific positioning equipment to interference sources may increase, resulting in a decline in the effect of robust RTK positioning.

Robust augmented space recursive least-constrained-squares algorithms

This paper proposes a novel augmented space robust adaptive filter by reusing the errors for online applications. First, a batched augmented space constrained model (ASCM) is constructed to combat non-Gaussian noise. In ASCM, the errors are reused by k nearest neighbors (k-NN) estimation. Then, an augmented space recursive least-constrained-squares algorithm integrating with distance-based k-NN method (ARLCS-dk) is developed within the framework of ASCM for adaptive filtering. Finally, to curb the size of ever-growing error network, a sliding window ARLCS-dk (SW-ARLCS-dk) is proposed to reduce the computational burden. Theoretical analyses of excess mean square error (EMSE) and testing mean square error (TMSE) are carried out for performance evaluation. Examples on time-series prediction of simulated and real-world data are used to illustrate the advantages of proposed algorithms on robustness and prediction accuracy.

Robust logarithmic hyperbolic cosine adaptive filtering over graph signals

Graph signal processing (GSP) has two methods including graph Fourier transform (GFT) and graph shift-operator (GSO) for dealing with the graph signal used for adaptive filtering (AF). However, in order to perform feature decomposition, GFT requires the availability of a band-limited graph signal with a known bandwidth in advance. Therefore, a general model based on GSO is then derived for AF by introducing a mixture coefficient to combine the advantages of different GSOs, comprehensively. Since the existing algorithms using the mean square error and other robust error criteria in GSP cannot effectively fight against non-Gaussian noises, a robust logarithmic hyperbolic cosine adaptive filter over graph (GLHCAF) algorithm is proposed by applying the logarithmic hyperbolic cosine loss function to the designed general model. The significant performance improvement of GLHCAF in non-Gaussian noises is obtained by simply controlling the scaling parameter. To avoid the parameter selections including scaling parameter and step size, the adaptive GLHCAF (AGLHCAF) algorithm is therefore proposed to further improve the performance of GLHCAF. Moreover, the mean square performance analysis of GLHCAF is given. Simulations in the real-world data are provided to assess the reliability and accuracy for theoretical analysis, the universality of the designed general model, and superiorities of proposed algorithms.

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

This paper proposes a novel robust adaptive filter that combines smooth variable structure filter and extended Kalman filter for the spacecraft attitude estimation with model uncertainty originating from gyro drift, parameter error, and installation error. The proposed filter employs the extended Kalman filter based on quaternion and fuses an adaptive factor and smooth variable structure filter to improve robustness to the model uncertainty and noise. To improve the robustness of the extended Kalman filter, an adaptive factor that tunes the predicted covariance matrix is utilized to design the attitude estimation strategy. Moreover, to further decrease the impact of the suddenly rapid maneuvering and improve its robust effect of model uncertainty induced by dynamic error, gyro drift, and so on, a smooth variable structure estimation strategy founded on sliding mode theory is derived and utilized for the satellite attitude estimation. Thereby, a novel filtering algorithm is proposed by incorporating an adaptive factor and a smooth variable structure estimation strategy. Simulation results indicate that our proposed algorithm delivers exceptional robustness and achieves high precision and accuracy in satellite attitude estimation compared with the traditional extended Kalman filter.

Variational Bayesian and generalized maximum-likelihood based adaptive robust nonlinear filtering framework

An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation) to simultaneously handle the outliers and uncertain measurement noise covariance matrix (MNCM) for state estimation. This framework utilizes the cubature criterion to solve nonlinear integration problems. By embedding GM estimation in the VB method, the uncertain MNCM is modified while robust estimation is performed. The modified MNCM also provides more accurate model parameters for GM estimation, achieving the unity of adaptability and robustness. The VBCEECKF algorithm was obtained by applying the strong robust centered error entropy criterion to the adaptive robust nonlinear filtering framework. The simulation results of target tracking under different noise conditions verify the superiority of the adaptive robust filter compared to existing methods.

A modified federated Student’s t-based variational adaptive Kalman filter for multi-sensor information fusion

To overcome the problem of poor performance of multi-sensor fusion algorithm in linear systems with time-varying noise and outliers, a modified federated Student’s t-based variational robust adaptive Kalman filter (MFSTVRAKF) is proposed in this article. In this algorithm, an improved Student’s t-based variational robust adaptive Kalman filter (ISTVRAKF) is developed for adaptively mitigating the effects of time-varying noise and outliers of each local sensor, which improves the estimation accuracy of the algorithm. It reorganizes and derives a simplified variational filter to approximate the prior distribution of the measurement noise covariance via the Student’s t distribution to eliminate outliers. Subsequently, an adaptive factor is introduced into ISTVRAKF for adjusting the weights of prediction and measurement to further exclude outliers. Moreover, a modified adaptive information sharing factor is devised to adjust the multi-sensor fusion weights in accordance with the performance of local filter, which improves the fusion accuracy of the MFSTVRAKF algorithm. Simulations exhibit that the proposed algorithm is capable of resisting the effects of time-varying noise and outliers and achieving higher accuracy compared to other filtering algorithms and fusion algorithms.

A Robust Adaptive Extended Kalman Filter Based on an Improved Measurement Noise Covariance Matrix for the Monitoring and Isolation of Abnormal Disturbances in GNSS/INS Vehicle Navigation

Global Navigation Satellite Systems (GNSS) integrated with Inertial Navigation Systems (INS) have been widely applied in many Intelligent Transport Systems. However, due to the influence of various factors, such as complex urban environments, etc., accurately describing the measurement noise statistics of GNSS receivers and inertial sensors is difficult. An inaccurate definition of the measurement noise covariance matrix will lead to the rapid divergence of the position error of the integrated navigation system. To overcome this problem, this paper proposed a Robust Adaptive Extended Kalman Filter (RAKF) method based on an improved measurement noise covariance matrix. By analyzing and considering the position accuracy factors, measurement factor, and position standard deviation in GNSS measurement results, this paper constructed the optimal measurement noise covariance matrix. Based on the Huber model, this paper constructed a two-stage robust adaptive factor expression and obtained the robust adaptive factors with and without abnormal disturbances. And robust adaptive filtering was carried out. To assess the performance of this method, the author conducted experiments on land vehicles by using a self-developed POS system (GNSS/INS combined navigation system). The classic Extended Kalman Filter algorithm (EKF), Adaptive Kalman Filter (AKF) algorithm, Robust Kalman Filter (RKF) algorithm, and the proposed method were compared through data processing. Experimental results show that compared with the classical EKF, AKF, and RKF, the positioning accuracies of the proposed method were improved by 72.43%, 2.54%, and 47.82%, respectively, in the vehicle land experiment. In order to further evaluate the performance of this method, the vehicle data were subjected to different times and degrees of disturbance experiments. Experimental results show that compared with EKF, AKF, and RKF, the heading angle accuracy had obvious advantages, and its accuracy was improved by 34.65%, 31.53%, and 18.36%, respectively. Therefore, this method can effectively monitor and isolate disturbance and improve the robustness, reliability, accuracy, and stability of GNSS/INS integrated navigation systems in complex urban environments.

Vehicle state estimation using a maximum likelihood based robust adaptive extended kalman filter considering unknown white Gaussian process and measurement noise signal

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.