Robust Unscented Kalman Filter Research Articles

Robust UKF orbit determination method with time-varying forgetting factor for angle/range-based integrated navigation system

The angle/range-based integrated navigation system is a favorable navigation solution for deep space explorers. However, the statistical characteristics of the measurement noise are time-varying, leading to inaccuracies in the derived measurement covariance even causing filter divergence. To reduce the gap between theoretical and actual covariances, some adaptive methods use empirically determined and unchanged forgetting factors to scale innovations within the sliding window. However, the constant weighting sequence cannot accurately adapt to the time-varying measurement noise in dynamic processes. Therefore, this paper proposes an Adaptive Robust Unscented Kalman Filter with Time-varying forgetting factors (TFF-ARUKF) for the angle/range integrated navigation system. Firstly, based on a statistically linear regression model approximating the nonlinear measurement model, the M-estimator is adopted to suppress the interference of outliers. Secondly, the covariance matching method is combined with the Huber linear regression problem to adaptively adjust the measurement noise covariance used in the M-estimation. Thirdly, to capture the time-varying characteristics of the measurement noise in each estimation, a new time-varying forgetting factors selection strategy is designed to dynamically adjust the adaptive matrix used in the covariance matching method. Simulations and experimental analysis compared with EKF, AMUKF, ARUKF, and Student’s t-based methods have validated the effectiveness and robustness of the proposed algorithm.

Improved State-of-Charge Estimation of Lithium-Ion Battery for Electric Vehicles Using Parameter Estimation and Multi-Innovation Adaptive Robust Unscented Kalman Filter

In this study, an improved adaptive robust unscented Kalman Filter (ARUKF) is proposed for an accurate state-of-charge (SOC) estimation of battery management system (BMS) in electric vehicles (EV). The extended Kalman Filter (EKF) algorithm is first used to achieve online identification of the model parameters. Subsequently, the identified parameters obtained from the EKF are processed to obtain the SOC of the batteries using a multi-innovation adaptive robust unscented Kalman filter (MIARUKF), developed by the ARUKF based on the principle of multi-innovation. Co-estimation of parameters and SOC is ultimately achieved. The co-estimation algorithm EKF-MIARUKF uses a multi-timescale framework with model parameters estimated on a slow timescale and the SOC estimated on a fast timescale. The EKF-MIARUKF integrates the advantages of multiple Kalman filters and eliminates the disadvantages of a single Kalman filter. The proposed algorithm outperforms other algorithms in terms of accuracy because the average root mean square error (RMSE) and the mean absolute error (MAE) of the SOC estimation were the smallest under three dynamic conditions.

Autonomous Asteroid Characterization Through Nanosatellite Swarming

This paper first defines a class of estimation problem called simultaneous navigation and characterization (SNAC), which is a superset of simultaneous localization and mapping (SLAM). A SNAC framework is then developed for the Autonomous Nanosatellite Swarming (ANS) mission concept to autonomously navigate about and characterize an asteroid including the asteroid gravity field, rotational motion, and 3D shape. The ANS SNAC framework consists of three modules: 1) multi-agent optical landmark tracking and 3D point reconstruction using stereovision, 2) state estimation through a computationally efficient and robust unscented Kalman filter, and 3) reconstruction of an asteroid spherical harmonic shape model by leveraging a priori knowledge of the shape properties of celestial bodies. Despite significant interest in asteroids, there are several limitations to current asteroid rendezvous mission concepts. First, completed missions heavily rely on human oversight and Earth-based resources. Second, proposed solutions to increase autonomy make oversimplifying assumptions about state knowledge and information processing. Third, asteroid mission concepts often opt for high size, weight, power, and cost (SWaP-C) avionics for environmental measurements. Finally, such missions often utilize a single spacecraft, neglecting the benefits of distributed space systems. In contrast, ANS is composed of multiple autonomous nanosatellites equipped with low SWaP-C avionics. The ANS SNAC framework is validated through a numerical simulation of three spacecraft orbiting asteroid 433 Eros. The simulation results demonstrate that the proposed architecture provides autonomous and accurate SNAC in a safe manner without an a priori shape model and using only low SWaP-C avionics.

Online estimation of state-of-charge inconsistency for lithium-ion battery based on SVSF-VBL

It is of great significance to estimate cell inconsistency for improving the service life and safety performance of the power battery pack. To accurately estimate the state-of-charge (SOC) inconsistency of cells with different performance parameters and working states, a method combining adaptive robust unscented Kalman filter and smooth variable structure filter with time-varying smoothing boundary layer (SVSF-VBL) is proposed. The cell mean-difference model is used to simulate the behavior characteristics of the battery module, including the cell mean model expressed by the dual polarization (DP) model and the cell difference model characterized by the hypothetical Rint model. Firstly, the improved forgetting factor recursive least square is applied to identify parameters of the DP model, and the unscented Kalman filter incorporating robust estimation and adaptive filter tuning is employed to estimate the SOC of the battery module. Then, SVSF-VBL is used to estimate the SOC difference between each cell and module based on the Rint model for improving the estimation accuracy and robustness. In addition, the comprehensive inconsistency of the cells can be captured by the secondary performance indicator inherent in SVSF-VBL, which contributes to the in-depth study of cell inconsistency. Finally, a series of tests are carried out to verify the performance of the proposed method, and the results show that the method can improve the estimation accuracy and convergence performance while effectively suppressing the system disturbance.

Robust UKF Relative Positioning Approach for Tightly Coupled Vehicle Ad Hoc Networks Based on Adaptive M-Estimation

Huber M-estimation, as an estimation method based on mixed norm as cost function, provides an effective method for robust filtering to deal with measurement outliers. Based on statistical linear regression model approximating nonlinear measurement model, M-estimation algorithm is used to realize measurement update of states. However, when the measurement noise pollution rate is high, the filtering performance will be seriously degraded. In order to further improve the actual performance of data fusion under abnormal measurement noise, a vehicle cooperative positioning scheme based on adaptive M-estimation robust unscented Kalman filter (AMRUKF) was proposed. This algorithm combines Huber’s linear regression problem with covariance matching method, and calculates the adaptive matrix through the innovation covariance estimator based on fading memory index weighting to adaptively adjust the measurement noise covariance used in Huber M estimation method. The analytical and experimental results of tightly-coupled vehicle relative positioning show that the proposed AMRUKF method can effectively improve the robustness and accuracy of relative positioning and provide a practical control scheme for vehicle cooperative positioning.

Intelligent Fusion Structure for Wi-Fi/BLE/QR/MEMS Sensor-Based Indoor Localization

Due to the complexity of urban environments, localizing pedestrians indoors using mobile terminals is an urgent task in many emerging areas. Multi-source fusion-based localization is considered to be an effective way to provide location-based services in large-scale indoor areas. This paper presents an intelligent 3D indoor localization framework that uses the integration of Wi-Fi, Bluetooth Low Energy (BLE), quick response (QR) code, and micro-electro-mechanical system sensors (the 3D-WBQM framework). An enhanced inertial odometry was developed for accurate pedestrian localization and trajectory optimization in indoor spaces containing magnetic interference and external acceleration, and Wi-Fi fine time Measurement stations, BLE nodes, and QR codes were applied for landmark detection to provide an absolute reference for trajectory optimization and crowdsourced navigation database construction. In addition, the robust unscented Kalman filter (RUKF) was applied as a generic integrated model to combine the estimated location results from inertial odometry, BLE, QR, Wi-Fi FTM, and the crowdsourced Wi-Fi fingerprinting for large-scale indoor positioning. The experimental results indicated that the proposed 3D-WBQM framework was verified to realize autonomous and accurate positioning performance in large-scale indoor areas using different location sources, and meter-level positioning accuracy can be acquired in Wi-Fi FTM supported areas.

Magnetic-Free Quaternion-Based Robust Unscented Kalman Filter for Upper Limb Kinematic Analysis

Human motion analysis is a field of increasing interest. In most applications, an accurate estimation of joint angles is needed. Inertial measurement units (IMUs) represent a very promising technology for motion capture. Unfortunately, their performances are strongly influenced by different sources of error (e.g., gyroscopes biases). To limit the effect of these sources of error, several algorithms (usually defined as “sensor fusion” algorithms) are used. The proposed work aims to validate a magnetic-free quaternion-based robust unscented Kalman filter (UKF) for upper limb kinematic analysis (i.e., estimation of the articular joint angles), using an inertial body sensor network, in a set of complex 3-D movements (i.e., the yoga poses). The algorithm was tested on ten expert yoga practitioners during the execution of the sun salutation sequence. Joint angle estimations were compared with the ones obtained from an optoelectronic reference system by evaluating the root mean square errors (RMSEs) and Pearson’s correlation coefficients. The achieved worst case was 8.41°, while the best one was 2.96° for RMSEs mean values. The accuracy of the algorithm was further confirmed by the high values of Pearson’s correlation coefficients (lowest mean value of 0.80). In addition, the comparison with one of the most used filters for attitude estimation [extended Kalman filter (EKF)] showed no significant differences between the two methods. Up to authors knowledge, the scientific literature lacks the development of a complete magnetic-free version of the UKF for human motion capture and analysis in complex movements, such as the one introduced here. The proposed work aims at filling this gap.

Robust Unscented Kalman Filter-Based Decentralized Multisensor Information Fusion for INS/GNSS/CNS Integration in Hypersonic Vehicle Navigation

INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integration is a favourable navigation mode for hypersonic vehicles. However, since the measurements from GNSS and CNS are easily interfered during highly dynamic maneuvers, this integration is very difficult to achieve optimal navigation solution with existing information fusion techniques. This paper proposes a new method of decentralized multi-sensor information fusion based on robust UKF (unscented Kalman filter) for INS/GNSS/CNS integration to solve the above issue. Firstly, a fault detection-based robust UKF is established for local state estimation, in which a hypothesis test is constructed via the Mahalanobis distance of innovation to detect abnormal measurements in GNSS and CNS; and subsequently, a scalar factor is determined and further introduced into the innovation covariance to decrease the Kalman gain to improve the UKF robustness against abnormal measurements. Secondly, the traditional multi-sensor optimal data fusion technique is extended to nonlinear systems by use of unscented transformation in the framework of minimum variance estimation to fuse the local state estimations from INS/GNSS and INS/CNS subsystems. The proposed information fusion method can achieve the globally optimal fusion estimation results against abnormal measurements for hypersonic vehicle navigation with INS/GNSS/CNS integration. Semi-physical simulations and comparison analysis have validated the superior performance of the proposed method.

Extended kernel Risk-Sensitive loss unscented Kalman filter based robust dynamic state estimation

The traditional unscented Kalman filter (UKF) with mean square error (MSE) criterion for dynamic state estimation (DSE) is sensitive for unknown non-Gaussian noise and outliers. Leading to biased state estimates. This paper proposes a novel robust UKF with extended kernel risk-sensitive loss (EKRSL) for DSE considering unknown non-Gaussian process and measurement noises. Instead of MSE criterion, a novel robust EKRSL via the generalized Gaussian density is defined in KRSL framework, and we further develop a new robust UKF using the EnKRSL(called EKRSL-UKF). To obtain the recursive form of EKRSL-UKF, the statistical linear regression model is used and the fixed-point iteration is further utilized to iteratively get the optimal state estimate. An error constrained method is also introduced to restrict the error to address the numerical instability problem caused by large outliers. Furthermore, an enhanced EKRSL-UKF is established by using an exponential function of innovation to improve the estimation accuracy in the presence of noise uncertainties. Numerical results carried out on the IEEE 39-bus test system demonstrate that the proposed method can achieve desired robustness without loss of estimation accuracy under various conditions.

Robust state estimation of the anaerobic digestion process for municipal organic waste using an unscented Kalman filter

The stable and sustainable operation of anaerobic digestion (AD11Anaerobic digestion.) plants is crucial for their feasible long-term operation. Due to the high non-linearity of the AD process, the main contribution of this paper is to investigate the performance of a robust unscented Kalman filter (UKF) for dynamic process state estimation for the organic fraction of municipal solid waste (OFMSW22Organic fraction of municipal solid waste.). A traditional UKF performance degrades in case of dynamical model uncertainties or the presence of unknown Gaussian and non-Gaussian noises. The utilized robust UKF proposed by Zhao and Mili (2019) addresses this issue by improving the accuracy of state estimation using the H-infinity filtering theory. The performance of the utilized estimator is tested for the case of uncertainties within the AD model and the substrate feed, as well as unknown Gaussian and non-Gaussian process and measurement noise. Results show that the developed robust UKF estimator achieves higher accuracy and presents higher robustness against uncertainties. Besides, the mathematical model considered for the simulation and the state estimator both rely on the extended version of the AD model No. 2 (E-AM233Extended version of the anaerobic digestion model No. 2 including a hydrolysis step.) including a hydrolysis step. This model is a simplified AD model, which is a suitable choice for control and estimation purposes providing a reasonable trade-off between complexity and accuracy. In this paper, the developed E-AM2 model is adapted for the AD process of OFMSW.

Robust Initial Alignment Based on Unscented Information Kalman Filter

The velocity of the odometer (OD) and Doppler velocity log (DVL) is easily contaminated by non-Gaussian noise, and the prior information of the state vector is usually hard to estimate accuracy enough, which will lead to the performance of alignment to decline or even divergent. Considering the error characteristic model has very significant nonlinear characteristics, a robust unscented information Kalman filter (RUIKF) algorithm for dynamic initial alignment is proposed in this article to suppress the influence of interference noise. The RUIKF algorithm first calculates the Mahalanobis distance (MD) between observation and the innovation of observation, and an amplification factor is designed to modify the estimation of the measurement noise covariance matrix and then take the modified measurement noise covariance matrix to update the measurement. The state error is estimated by the RUIKF to modify the strapdown inertial navigation system (SINS) navigation solution. Initial alignment experiments are carried out by the RUIKF and unscented information Kalman filter (UIKF) algorithm, respectively, under the conditions of outliers and mixed Gaussian distribution noise. The results show that the RUIKF can suppress the effect of outliers and non-Gaussian noise when the velocity of the OD (or DVL) is contaminated. The experiment results also verify the feasibility and effectiveness of the RUIKF algorithm on the SINS/DVL/OD integrated dynamic initial alignment.

Adaptive robust unscented Kalman filter-based state-of-charge estimation for lithium-ion batteries with multi-parameter updating

State-of-charge (SOC) estimation is one of the key technologies for the development and application of battery management system (BMS). To achieve high accuracy in SOC estimation, which can adapt to any conditions, an adaptive robust unscented Kalman filter (ARUKF) based on multi-parameter update is proposed herein. First, the DP battery model is applied to replicate the dynamic behavior of lithium-ion batteries, and the model parameters are identified online by the improved forgetting factor recursive least square (IFFRLS). Then, the Institute of Geodesy and Geophysics (IGGIII) weight function is introduced into unscented Kalman filter (UKF) as the form of a robust factor to adjust the weights of observation residuals, and receding horizon based adaptive filter tuning is employed to obtain the time-varying noise covariance. Subsequently, joint estimation of battery model parameters and SOC with capacity updating is implemented which can suppress the system disturbance caused by outliers, mistuning, unknown initial value, and aging. Finally, the superior performance of accuracy and convergence is verified by cycle and aging tests. The maximum absolute error of SOC estimation under the proposed method is kept within 2%. The convergence speed of SOC estimation utilizing ARUKF is nearly 80 s faster than that of robust UKF (RUKF) and UKF under a 20% SOC initial error.

Maximum Correntropy with Variable Center Unscented Kalman Filter for Robust Power System State Estimation.

The robust Kalman filter with correntropy loss has received much attention in recent years for forecasting-aided state estimation in power systems, since it efficiently reduces the negative influence of various abnormal situations, such as non-Gaussian communication, changing environment, and instrument failures, and obviously improves the stability of power systems. However, the existing correntropy-based robust Kalman filters usually use the Gaussian function with a fixed center as the kernel function in correntropy, which may not be a suitable choice in practical applications of power system forecasting-aided state estimation (PSSE). To address this issue, a new and robust unscented Kalman filter, called the maximum correntropy with variable center unscented Kalman filter (MCVUKF), is proposed in this paper for PSSE. Specifically, MCVUKF adopts an extended version of correntropy, whose center can be located at any position, to replace the original correntropy in an unscented Kalman filter to improve the performance in PSSE. Moreover, by using an exponential function of the innovation vector to adjust a covariance matrix, an enhanced MCVUKF (En-MCVUKF) method is also developed for suppressing the influence of bad data to the innovation vector and further improving the accuracy of PSSE. Finally, extensive simulations have been conducted on IEEE 14-bus, 30-bus, and 57-bus test power systems, and the simulation results have shown the superiority of the proposed MCVUKF and En-MCVUKF methods compared with several related state-of-the-art Kalman filter methods.

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.

Robust Power System Forecasting-Aided State Estimation With Generalized Maximum Mixture Correntropy Unscented Kalman Filter

As an effective method for power system forecasting-aided state estimation (FASE), the unscented Kalman filter (UKF) based on correntropy has been widely used in recent years, ensuring the safe and reliable operation of power systems. In this article, to address the impulsive noise, Laplacian noise, bad measurement data, and sudden load change, a robust UKF algorithm based on generalized maximum mixture correntropy (GMMC-UKF) criterion is proposed for FASE, in which the kernel is composed of two generalized Gaussian functions. Specifically, we use a statistical linearization technique to unify the state error and measurement error in the cost function and obtain the optimal value of state estimation by fixed-point iteration. The effectiveness of the proposed algorithm for FASE is verified on IEEE 14-, 30-, and 57-bus test systems under a variety of abnormal situations. Compared with traditional correntropy algorithms, the GMMC-UKF shows more accurate estimation and stronger robustness.

Robustification of Unscented Kalman Filtering to Identify Faults in Gas Turbine Engine

A methodology is proposed to improve the robustification of the Unscented Kalman Filtering by adjusting the measurement noise covariance matrix by introducing two adaptive factors. The combined effect of the two adaptive factors helps to identify and filter the outliers more prominently. Improvement in the proposed robust UKF algorithm is established by analyzing the percentage reduction of accumulation error for different conditions with the larger measurement noise covariance. In addition, a method of fault identification of gas turbine engines is developed by the proposed robust UKF approach in the presence of system and measurement noises. The proposed fault identification method deals with the analysis of the residual signature of different states along with the cost function of the derived algorithm. Different component and sensor anomalies are introduced in the nonlinear dynamic model of the gas turbine engine to produce the faulty situations. The deviations in performances are compared with the nominal behavior to obtain the residual signature. A comparative study is performed to identify the faulty scenarios.

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.

Adaptive robust unscented Kalman filter with recursive least square for state of charge estimation of batteries

Adaptive robust unscented Kalman filter with recursive least square for state of charge estimation of batteries

Constrained fault-tolerant control for hypersonic vehicle subject to actuator failure and with unmeasurable states

In this article, a novel constrained fault-tolerant control (FTC) scheme is proposed to solve the attitude tracking control problem of the hypersonic vehicle (HSV) subject to multiple constraints, actuator faults, and disturbances. The reentry model of HSV with state constraints and the fault model of aerodynamic surface considering surface deflection constraints are constructed firstly. The adaptive robust unscented Kalman filter (ARUKF)-based estimation algorithm is designed, which can quickly estimate state variables, stuck faults, partial loss of effectiveness (PLOE) faults, and disturbances at the same time. By utilising the improved model predictive static programming (MPSP) technique, the complexity of processing multiple constraints and the computation are significantly reduced. Moreover, the closed-loop control system stability of HSV is analysed and the simulation results under two fault cases are given to demonstrate the effectiveness of the presented FTC scheme.

An Adaptive and Robust UKF Approach Based on Gaussian Process Regression-Aided Variational Bayesian

In this study, both adaptive and robust one is proposed, considering that the properties of a classic unscented Kalman filter (UKF) can be degraded severely by the outliers measured in the contamination distribution and the effects of time-varying noise. An adaptive and robust UKF approach on Gaussian process regression- assisted Variational Bayesian is proposed. The Variable Bayesian (VB) method is used to statistically approximate the time-varying noise due to the strong nonlinearity and inaccuracy of the system model. At the same time, Gaussian Process Regression (GPR) has the advantage of machine learning. The observation information trained by the GPR model performs real-time prediction of the sliding window. Based on the above two points, the output source of the measurement information is estimated to realize the robustness of the filter measurement update. When the noise is uncertain and there are outliers in the measurement information, simulation and SINS/GPS integrated navigation of actual tests were performed, respectively. The test outcomes indicate that the algorithm has better nonlinear estimation performance than the traditional method, the effectiveness of the filtering algorithm proposed is verified.