Adaptive 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.

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 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.

Robust adaptive Unscented Kalman Filter with gross error detection and identification for power system forecasting-aided state estimation

Owing to the effect of measurement noise and sudden changes in the power system, the robustness of state estimation for power system becomes very important. The Unscented Kalman Filter (UKF) is widely used for state estimation. However, it does not consider the influence of different kinds of gross errors. To better deal with gross errors, a robust adaptive UKF with gross error detection and identification (RAUKF-GEDI) is proposed, which uses the robust generalized correntropy loss in the UKF framework. The RAUKF-GEDI detects gross errors by hypothesis testing, and then uses the moving window to identify and classify three kinds of gross errors. Subsequently, the RAUKF-GEDI estimates the magnitudes of the gross errors to further compensate the measurements, and finally uses the compensated measurements to re-estimate the state to obtain precise estimated states. In addition, RAUKF-GEDI also introduces adaptive covariance matching method for state estimation. The RAUKF-GEDI is applied to the state estimation for power systems where the measurements are contaminated by three kinds of gross errors. Finally, the RAUKF-GEDI is also applied to the practical power system of Zhejiang Juchuang Smart Technology Company Park. The results show that the RAUKF-GEDI can detect and identify gross errors and enhance the robustness of UKF.

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.

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.

State estimation of radar tracking system using a robust adaptive unscented Kalman filter

State estimation of radar tracking system using a robust adaptive unscented Kalman filter

Adaptive unscented Kalman filter for neuronal state and parameter estimation.

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

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.

A Robust Adaptive Unscented Kalman Filter for Floating Doppler Wind-LiDAR Motion Correction

This study presents a new method for correcting the six degrees of freedom motion-induced error in ZephIR 300 floating Doppler Wind-LiDAR-derived data, based on a Robust Adaptive Unscented Kalman Filter. The filter takes advantage of the known floating Doppler Wind-LiDAR (FDWL) dynamics, a velocity–azimuth display algorithm, and a wind model describing the LiDAR-retrieved wind vector without motion influence. The filter estimates the corrected wind vector by adapting itself to different atmospheric and motion scenarios, and by estimating the covariance matrices of related noise processes. The measured turbulence intensity by the FDWL (with and without correction) was compared against a reference fixed LiDAR over a 25-day period at “El Pont del Petroli”, Barcelona. After correction, the apparent motion-induced turbulence was greatly reduced, and the statistical indicators showed overall improvement. Thus, the Mean Difference improved from −1.70% (uncorrected) to 0.36% (corrected), the Root Mean Square Error (RMSE) improved from 2.01% to 0.86%, and coefficient of determination improved from 0.85 to 0.93.

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.

State estimation of distributed electric vehicle based on robust adaptive UKF

The key to achieving active safety and automatic driving is accurate parameters of the vehicle state. The unscented Kalman filter (UKF) algorithm will seriously affect the vehicle state’s estimation accuracy if the noise of measurement is high or the covariance of noise does not suit. A robust adaptive UKF algorithm based on fault detection mechanism is proposed to estimate the state of distributed drive electric vehicle. The algorithm uses the residual vector of observation noise to identify whether there is a fault in the system, determines whether the observation noise covariance and the process noise covariance need to be adjusted adaptively according to the statistical function, and updates the covariance based on the weight factors. A robust adaptive UKF estimator is designed to estimate three important state variables: longitudinal speed, lateral speed, and sideslip angle. The algorithm is eventually tested based on the co-simulation of CarSim and MATLAB/Simulink. The results showed that the proposed robust adaptive UKF algorithm can significantly reduce the estimation error of three state variables, and is better than the standard accuracy and robustness of the UKF algorithm. This lays an important foundation for advanced driving assistance systems and precise automatic driving movement control.

Adaptive Robust Unscented Kalman Filter for AUV Acoustic Navigation.

Autonomous underwater vehicle (AUV) acoustic navigation is challenged by unknown system noise and gross errors in the acoustic observations caused by the complex marine environment. Since the classical unscented Kalman filter (UKF) algorithm cannot control the dynamic model biases and resist the influence of gross errors, an adaptive robust UKF based on the Sage-Husa filter and the robust estimation technique is proposed for AUV acoustic navigation. The proposed algorithm compensates the system noise by adopting the Sage-Husa noise estimation technique in an online manner under the condition that the system noise matrices are kept as positive or semi positive. In order to control the influence of gross errors in the acoustic observations, the equivalent gain matrix is constructed to improve the robustness of the adaptive UKF for AUV acoustic navigation based on Huber’s equivalent weight function. The effectiveness of the algorithm is verified by the simulated long baseline positioning experiment of the AUV, as well as the real marine experimental data of the ultrashort baseline positioning of an underwater towed body. The results demonstrate that the adaptive UKF can estimate the system noise through the time-varying noise estimator and avoid the problem of negative definite of the system noise variance matrix. The proposed adaptive robust UKF based on the Sage-Husa filter can further reduce the influence of gross errors while adjusting the system noise, and significantly improve the accuracy and stability of AUV acoustic navigation.

Correlation-Aided Robust Decentralized Dynamic State Estimation of Power Systems With Unknown Control Inputs

This paper proposes a correlation-aided robust adaptive unscented Kalman filter (UKF) for power system decentralized dynamic state estimation with unknown inputs, termed as robust AUKF-UI. The temporal and spatial correlations among the unknown inputs are used to derive a vector auto-regressive (VAR) model in an adaptive manner. This VAR model is further integrated together with state transition and measurement models for joint state and unknown inputs estimation. This allows taking into account the implicit cross-correlations between the states and the unknown inputs. As a result, the rank requirement for unknown input vector estimation is relaxed and the local generator frequency measurement is not required. The temporal correlations of time series innovation vectors, predicted state and input vectors are also leveraged by the robust AUKF-UI to detect, identify and process bad data. Without these correlations, it is very challenging to address bad data with unknown inputs. Simulation results carried out on the IEEE 39-bus system demonstrate that, thanks to the use of hidden system temporal and spatial correlations, the proposed robust AUKF-UI has lower requirement of the number of measurements for dynamic state estimation while achieving better robustness against bad data as compared to the existing UKF methods with unknown inputs.

Robust adaptive unscented Kalman filter for bearings-only tracking in three dimensional case

This paper proposes an improved version of Unscented Kalman Filter (UKF), namely Robust Adaptive UKF (RAUKF), with a special focus on Bearings-Only Target Tracking for three-dimensional case (3DBOT). The automatic tuning of the noise covariance matrices and the robust estimation of the target states form a critical point for the performance of the Kalman-type filtering algorithms, especially in the variable environmental conditions exposed in underwater. The key idea of the proposed filter is to combine robust aspects of UKF and adaption of the process and measurement noise covariance matrices with low computational complexity. The main contribution of this paper is to adjust these matrices by means of the steepest descent algorithm, and the H∞ technique is embedded to achieve superior performance in terms of accuracy and robustness against initial conditions and model uncertainties. Different experiments are performed to evaluate the performance of the proposed algorithm in the 3DBOT problem with a single moving observer. Simulations demonstrate that the proposed filter produce more accurate results with satisfactory computational burden in comparison with other methods.

A New Adaptive Robust Unscented Kalman Filter for Improving the Accuracy of Target Tracking

In target tracking, the tracking process needs to constantly update the data information. However, during data acquisition and transmission of sensors, outliers may occur frequently, and the model is disturbed by non-Gaussian noise, that affects the performance of system state estimation. In this paper, a new filtering algorithm is proposed based on QR decomposition and singular value decomposition (SVD) method, namely adaptive robust unscented Kalman filter (QS-ARUKF) to suppress the interference of outliers, nonGaussian noise as well as a model error to achieve high accuracy state estimation. An adaptive filtering algorithm based on strong tracking idea is used in modifying the state equation of unscented Kalman filter (UKF), so that the algorithm can effectively improve the tracking ability of the state model. By using the robust filtering method to construct a new cost function used to modify the measurement covariance formula of the Kalman filter, the error of measurement model can be effectively suppressed. The QR decomposition is introduced to the time update and measurement update to avoid the covariance non-positive definite. We propose the SVD method to address the problem of numerical sensitivity in the filtering process. The purpose of this method is to replace the calculation of the inverse of the filter gain matrix and further improve the robustness of the algorithm. The simulation results showed that the proposed algorithm has higher accuracy and better robustness than the traditional filtering method.

Robust adaptive unscented Kalman filter and its application in initial alignment for body frame velocity aided strapdown inertial navigation system.

In the in-motion alignment of a strapdown inertial navigation system (SINS), the unscented Kalman filter (UKF) is usually used to solve non-linear problems. The measurement noise covariance R has a direct influence on the filtering results of the alignment of the SINS. The measurement noise is assumed to follow Gaussian distribution with a constant covariance R . However, these assumptions are often not realistic, neither the Gaussianity nor the constant covariance. This will degrade the performance of the UKF. To solve this problem, this paper proposes a novel adaptive robust UKF (NARUKF). In the NARUKF, a sliding window is used in estimating the covariance R in real-time. The NARUKF is divided into three main steps, the first step is to use the Mahalanobis distance algorithm to robustify the UKF. The second step is to use the projection statistics algorithm to reweight the abnormal stored innovations. Finally, the covariance R is adaptively estimated. The simulation and experimental results for the problem of the body frame velocity aided SINS in-motion alignment under heavier-tail distribution and/or outlier conditions demonstrate the superiority of the proposed method over the traditional ones.

Adaptive Robust Unscented Kalman Filter via Fading Factor and Maximum Correntropy Criterion.

In most practical applications, the tracking process needs to update the data constantly. However, outliers may occur frequently in the process of sensors’ data collection and sending, which affects the performance of the system state estimate. In order to suppress the impact of observation outliers in the process of target tracking, a novel filtering algorithm, namely a robust adaptive unscented Kalman filter, is proposed. The cost function of the proposed filtering algorithm is derived based on fading factor and maximum correntropy criterion. In this paper, the derivations of cost function and fading factor are given in detail, which enables the proposed algorithm to be robust. Finally, the simulation results show that the presented algorithm has good performance, and it improves the robustness of a general unscented Kalman filter and solves the problem of outliers in system.

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance.

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results.