Performance Of Extended Kalman Filter Research Articles

UWB/IMU integrated indoor positioning algorithm based on robust extended Kalman filter

Abstract As a fundamental method for integrated indoor positioning, Ultra wideband (UWB)/ Inertial Measurement Unit (IMU) offers more stable performance compared to separate UWB sensor and IMU sensor positioning and uses the least squares (LS) and extended Kalman filter (EKF) for positioning processing, however, the performance of conventional LS and EKF will be seriously affected when the contamination rate of measurement noise is high. To address this problem, this paper proposes a robust extended Kalman filter (REKF) based algorithm for robot-integrated indoor positioning, which combines UWB and IMU positioning methods to obtain a more robust system performance and optimal positioning accuracy. In this paper, a vehicle equipped with a UWB/IMU sensor and four anchor points is set up to perform linear, circular, and trajectory motions in an experimental environment with visible obstacles. The experimental results show that compared with EKF, REKF improves the localization precision and accuracy in the three motions by 20.98%, 35.51%, and 47.06%, respectively. REKF effectively improves the accuracy and robustness of the robot’s indoor positioning, and provides an improved and practical method for integrated indoor positioning algorithms to make indoor positioning more accurate and reliable.

Performance enhancement of PPP/SINS tightly coupled navigation based on improved robust maximum correntropy kalman filtering

Extended kalman filter (EKF) is widely used to integrated navigation system of global navigation satellite system (GNSS) and strapdown inertial navigation system (SINS). However, non-Gaussian noise and the uncertainty of measurement noise can seriously reduce the performance of EKF, so it is difficult to obtain an optimal GNSS/INS integration solution. At present, non-Gaussian noise processing is still a difficult issue in filter research. In this paper, an adaptive and robust maximum correntropy extended kalman filter (MCEKF) method based on Cauchy kernel function is proposed to solve the above problem. Thanks to the excellent properties of Cauchy kernel function, the proposed method can effectively avoid filter faults and has better stability. However, the performance of MCEKF depends on the select of kernel bandwidth parameter, which is a difficult problem in the engineering application of MCEKF. In this paper, the switching kernel bandwidth algorithm is employed to adaptively estimate the kernel bandwidth parameter to solve the tradeoff between convergence rate and steady-state misalignment in the MCEKF algorithm under constant kernel bandwidth. Finally, the performance of the proposed algorithm is verified by two sets of vehicle-mounted precise point positioning (PPP) and SINS tightly coupled integration experiments in urban environment. The results show that compared with EKF, the proposed method can significantly improve the positioning accuracy, that is, the PPP/SINS positioning accuracy based on GE, GR and GRE system is improved by 25.1 %, 2.5 % and 17.0 % in D196 experiment, and 23.5 %, 16.5 % and 31.8 % in D107 experiment, respectively. The velocity and attitude accuracy of the two methods are similar. The velocity errors of all schemes can reach cm/s level. The roll, pitch and heading errors of navigation-grade inertial sensor are all less than 0.12 degree. The roll and pitch errors of MEMS are less than 1.0 degree, the heading error of the G, GE, GR, and GRE systems are 1.719, 1.464, 1.676, and 1.475 degree, respectively.

A Novel Extended Unscented Kalman Filter Is Designed Using the Higher-Order Statistical Property of the Approximate Error of the System Model

A Novel Extended Unscented Kalman Filter Is Designed Using the Higher-Order Statistical Property of the Approximate Error of the System Model

A Comparison between Kalman Filtering Approaches in Aircraft Flight Signal Estimation

At present, the requirements for the accuracy of aircraft on-board measurement systems are constantly increasing, while sensors contain various errors in signal measurement, primarily random. Noisy signals from onboard measurements can be smoothed or filtered out in a variety of ways. One of the most popular approaches is Kalman filtering, the effectiveness of which has been proven by many studies. This paper presents a comparative analysis of the extended Kalman filter (EKF) and unscented Kalman filter (UKF), used to estimate the pitch angle of an aircraft using bench modeling data. During the simulation, the normal measurement noises are also generated. According to the results obtained in this paper, it can be noted that UKF performs better when a priori knowledge about the process noise is certain. However, the efficiency of UKF in estimating the signal deteriorates when a priori knowledge about the process becomes uncertain while the performance of EKF remains stable. This is due to the fact that UKF uses more sophisticated assumptions and therefore is more sensitive to these assumptions violation. The obtained results also show that various variants of Kalman filtering remain relevant in comparison with the smoothing methods that have spread in recent years, based on the ideas of optimal control and evolutionary algorithms for numerical optimization.

Real-time water demand pattern estimation using an optimized extended Kalman filter

This study presents a hybrid approach for the estimation of real-time water demand multipliers using the Kalman filter (KF) and extended Kalman filter (EKF). Multiple Linear Regression (MLR) and Nonlinear Regression (NLR) models were applied to predict water demand multipliers at each time step with historical flow data. The estimation performance of EKF is highly affected by the state noise covariance matrix (Q) and the measurement noise covariance matrix (R). An inappropriate value ofQandRsignificantly degrades the EKF’s performance and makes the filter diverge. So, the particle swarm optimization algorithm (PSO) was used to tune the noise covariance matricesQandRat each time step of EKF. Then the optimal values of noise covariance matrices are inserted in the real-time water demand multiplier estimation process. To find the optimal values ofQandR, the mean absolute percentage error (MAPE) between measured and simulated pressure was minimized. The proposed method was evaluated in Net1 and Net3 benchmark networks. The root means square error (RMSE) of EKF-PSO estimated water demand multiplier for Net1 and Net3 were 0.063 and 0.198, respectively. The simulation results indicated that the EKF-PSO algorithm was more accurate than the conventional EKF algorithm. Moreover, the KF-PSO performed poorly when dealing with nonlinear hydraulic systems.

Effects of Personalization on Gait-State Tracking Performance Using Extended Kalman Filters.

Emerging partial-assistance exoskeletons can enhance able-bodied performance and aid people with pathological gait or age-related immobility. However, every person walks differently, which makes it difficult to directly compute assistance torques from joint kinematics. Gait-state estimation-based controllers use phase (normalized stride time) and task variables (e.g., stride length and ground inclination) to parameterize the joint torques. Using kinematic models that depend on the gait-state, prior work has used an Extended Kalman filter (EKF) to estimate the gait-state online. However, this EKF suffered from kinematic errors since it used a subject-independent measurement model, and it is still unknown how personalization of this measurement model would reduce gait-state tracking error. This paper quantifies how much gait-state tracking improvement a personalized measurement model can have over a subject-independent measurement model when using an EKF-based gait-state estimator. Since the EKF performance depends on the measurement model covariance matrix, we tested on multiple different tuning parameters. Across reasonable values of tuning parameters that resulted in good performance, personalization improved estimation error on average by 8.5 ± 13.8% for phase (mean ± standard deviation), 27.2 ± 8.1% for stride length, and 10.5 ± 13.5% for ground inclination. These findings support the hypothesis that personalization of the measurement model significantly improves gait-state estimation performance in EKF based gait-state tracking (), which could ultimately enable reliable responses to faster human gait changes.

Improved Terahertz Time-Domain Spectroscopy via the Extended Kalman Filter

To implement terahertz time-domain spectroscopy (THz-TDS) systems that have short integration time and maintain performance, the extended Kalman filter (EKF) has been used. Performance of EKF with THz-TDS on vapor samples and solid samples is untested. Previous EKF methods were not adaptive for use on multiple THz-TDS systems. We provide an adaptive EKF method that can work on any THz setup, to improve maximum measurable absorption coefficient. Our adaptive EKF method responds to THz pulse properties. The adaptive EKF is exhaustively demonstrated for six different time-constant data sets spanning 1 ms to 300 ms for THz-TDS on vapor with electro-optic THz detection. The acquisition time saved is quantified and shown to significantly reduce acquisition time from 2.58 ms to 1 ms. This improvement of 2.58 times will have a significant effect to move spectral imaging from taking hours to taking minutes. Vapor absorption lines are maintained. We show the adaptive EKF maintain correct spectral information when compared to the high-resolution transmission molecular absorption (HITRAN) database. The adaptive EKF is also demonstrated for THz-TDS on vapor with photoconductive THz detection, thus demonstrating adaptability, and is applied for THz-TDS of a solid sample of polyethylene terephthalate glycol.

Optimized Kalman filters for sensorless vector control induction motor drives

<span lang="EN-US">This paper presents the comparison between optimized unscented Kalman filter (UKF) and optimized extended Kalman filter (EKF) for sensorless direct field orientation control induction motor (DFOCIM) drive. The high performance of UKF and EKF depends on the accurate selection of state and noise covariance matrices. For this goal, multi objective function genetic algorithm is used to find the optimal values of state and noise covariance matrices. The main objectives of genetic algorithm to be minimized are the mean square errors (MSE) between actual and estimation of speed, current, and flux. Simulation results show the optimal state and noise covariance matrices can improve the estimation of speed, current, torque, and flux in sensorless DFOCIM drive. Furthermore, optimized UKF present higher performance of state estimation than optimized EKF under different motor operating conditions.</span>

Interacting Multiple Model Filter with a Maximum Correntropy Criterion for GPS Navigation Processing

In order to deal with the uncertainty of measurement noise, particularly for outlier types of multipath interference and non-line of sight (NLOS) reception, this paper proposes a novel method for processing the navigation states of the Global Positioning System (GPS) that combines the maximum correntropy criterion (MCC) and the interacting multiple model (IMM), with an extended Kalman Filter (EKF). Multipath mitigation is essential for increased positioning accuracy since multipath interference is one of the primary sources of errors. Nonlinear filtering with IMM configuration uses filter structural adaptation. In processing time-varying satellite signal standards for GPS navigation, it offers an alternative for creating the adaptive filter. A collection of switching models built on a method of multiple model estimation can be used to characterize the uncertainty of the noise. Even though most noise in real life is non-Gaussian, time-varying, and of fluctuating strength, the standard EKF operates effectively when the noise is Gaussian. The performance of EKF will drastically decline if the signals appear non-Gaussian. The underlying system disrupted by heavy-tailed, non-Gaussian impulsive sounds could be better since the EKF employs second-order statistical information. The MCC is a method for comparing two random variables based on higher-order signal statistics. The maximum correntropy-extended Kalman filter (MCEKF), which uses the MCC rather than the minimal mean square error (MMSE) as the optimization criterion, is used to enhance performance in non-Gaussian situations. Finally, a performance evaluation will be conducted to compare the effectiveness of the suggested strategy in improving positioning to alternative system designs.

A Novel Extremum Seeking Hyperparameter Design for Joint State and Parameter Estimation of Nonlinear Systems

This paper introduces a novel hyperparameter design based on extremum seeking (ES) method to enhance the convergence speed of Extended-Kalman Filter (EKF). ES method produces a real-time optimization output based on the second-order gradient of performance function so that the estimation performance of EKF is simultaneously optimized. In addition to the convergence speed, the proposed hyperparameter reduces the effect of initial covariance matrices, and improves the accuracy of estimation for the fast changes without any knowledge about system dynamics. In numerical applications, EKF with and without the proposed hyperparameter were first used to estimate the unknown parameters of a linear time-varying system. Second, on a real-time collected data, they were applied for the joint estimation of velocity and payload mass of a real-time nonlinear servo-system where the performance improvement is provided almost 30%. Performance measurements are given in terms of the root-mean squared-error (RMSE) of estimation.

ECG enhancement using a modified Bayesian framework and particle swarm optimization

Extended Kalman filter (EKF) is a well-known nonlinear Bayesian framework deployed in various electrocardiogram (ECG) processing applications. However, it is not very effective in removing non-stationary noises, such as muscle artifacts (MA) that are common in ECG recordings. As a model-based framework, this filter relies on its predefined state space model. As a result, EKF fails when ECG dynamics don’t comply its state-space model. In order to solve the above issues, in this paper, we propose to use particle swarm optimization (PSO) to find a better and more accurate state-space model. In addition, in order to improve EKF performance in nonstationary environments, we propose a new measurement model. This Model is modified to include non-Gaussian non-stationary additive and stationary noises. However, in order for EKF to use this model, its equations should be reformulated. Two different approaches are proposed in this paper to reformulate EKF equations; 1-state augmentation and 2- measurement differencing strategies. The proposed formulations for the EKF algorithm in this paper enable it to perform better than standard EKF in removing non-stationary contaminants. The proposed filters also preserve the clinical characteristics of ECG signals better than standard EKF. In order to show the effectiveness of the proposed EKF algorithms, their denoising performances were evaluated on the MIT-BIH Normal Sinus Rhythm Database (NSRDB) in the presence of two different types of non-stationary contaminants; 1- synthetic pink noise and 2- real muscle artifact noise extracted from Physionet noise stress database. The results showed that the proposed modified EKF frameworks significantly outperformed the standard EKF framework in non-stationary environments.

Outlier-resilient iterative-extended Kalman filter based on maximum correntropy criterion

The extended Kalman filter (EKF) is the most popular tool for state estimation of nonlinear stochastic systems. The conventional EKF can be refined via iterative re-linearization, leading to the so-called iterative EKF (IEKF). The performance of either EKF or IEKF will deteriorate in the presence of outliers. In this article, an outlier-resilient IEKF method is proposed using a more robust cost function, the correntropy, to replace the traditional mean squared error criterion. An iterative procedure is derived to maximize the correntropy criterion in a similar way to the Gauss–Newton optimization. Simulation results demonstrate the superiority of the proposed method as compared to the existing methods.

Abridged Gaussian sum extended Kalman filter for nonlinear state estimation under non-Gaussian process uncertainties

Studies on Extended Kalman Filter (EKF) that explicitly consider non-Gaussian process uncertainties are scarce in the literature. In the current study, a novel approach referred to as Abridged Gaussian Sum-Extended Kalman Filter (AGS-EKF) is developed to improve EKF performance for such systems. AGS-EKF performs a modified version of the EKF formulation that accounts for non-zero mean process uncertainties. Contrary to the conventional Gaussian Sum Filter (GSF), the process uncertainties involved in the prior estimation step of AGS-EKF follow an overall Gaussian mixture model that approximates the actual non-Gaussian process uncertainty distribution. Hence, AGS-EKF computes the EKF calculation only once thus avoiding the need to perform multiple EKFs to capture all the Gaussian components in the mixture as in GSF approach. Since AGS-EKF considers the overall Gaussian mixture of the process uncertainties, the method avoids the biased estimations that may appear in GSF. In addition to AGS-EKF, an adaptation in the GSF framework is proposed to improve the estimation accuracy of GSF. Case studies have shown that AGS-EKF offers higher accuracy of the estimation in comparison with GSF in shorter computational times.

Comparative evaluation of Kalman filters and motion models in vehicular state estimation and path prediction

AbstractVehicle state estimation and path prediction, which usually involve Kalman filter and motion model, are critical tasks for intelligent driving. In vehicle state estimation, the comparative performance assessment, regarding accuracy and efficiency, of the unscented Kalman filter (UKF) and the extended Kalman filter (EKF) is rarely discussed. This paper is devoted to empirically evaluating the performance of UKF and EKF incorporating different motion models and investigating the models’ properties and the affecting factors in path prediction. Extensive real world experiments have been carried out and the results show that EKF and UKF have roughly identical accuracy in state estimation; however, EKF is faster than UKF generally; the fastest filter is about 2⋅6 times faster than the slowest. The path prediction experiments reveal that the velocity estimate and the used motion model affect path prediction; the more realistically the model reflects the vehicle's driving status, the more reliable its predictions.

SARSA in extended Kalman Filter for complex urban environments positioning

Nowadays, the Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) integrated navigation system is widely used in many applications. The extended Kalman Filter (EKF) is a popular data fusion method for the INS/GNSS integrated navigation system. However, the process and measurement noise covariance matrices of the EKF cannot be modelled accurately due to varied scenes and complicated GNSS signal errors in urban environments, which undermines or deteriorates the EKF's performance. To mitigate noise covariance uncertainties' influence, this paper proposes an adaptive EKF algorithm named SARSA EKF, which enables the State-Action-Reward-State-Action (SARSA) method in EKF to realise the autonomous selection of the noise covariance matrices based on the Q-value. Meanwhile, a pruning algorithm is designed to remove inappropriate selections of noise covariance matrices and enhance the performance. The simulation and field test results indicate that the positioning accuracy of the SARSA EKF is better than the traditional EKF and the Q-learning EKF (QLEKF). The positioning accuracy's mean error of the SARSA EKF decreases by 34.32% and 25.95% compared with the traditional EKF and the QLEKF, respectively. And the positioning accuracy's standard deviation of the SARSA EKF decreases by 41.74% and 32.99% compared with the traditional EKF and the QLEKF, respectively.

Lie group based nonlinear state errors for MEMS-IMU/GNSS/magnetometer integrated navigation

AbstractIn the integrated navigation system using extended Kalman filter (EKF), the state error conventionally uses linear approximation to tackle the commonly nonlinear problem. However, this error definition can diverge the filter in some adverse situations due to significant distortion of the linear approximation. By contrast, the nonlinear state error defined in the Lie group satisfies the autonomous equation, which thus has distinctively better convergence property. This work proposes a novel strapdown inertial navigation system (SINS) nonlinear state error defined in the Lie group and derives the SINS equations of the Lie group EKF (LG-EKF) for the MIMU/GNSS/magnetometer integrated navigation system. The corresponding measurement equations are also derived. A land vehicle field test has been conducted to evaluate the performance of EKF, ST-EKF (state transformation extended Kalman filter) and LG-EKF, which verifies LG-EKF's superior estimation accuracy of the heading angle as well as the other two horizontal angles (pitch and roll). The LG-EKF proposed in this paper is unlimited in the choice of sensors, which means it can be applied with both high-end and low-end inertial sensors.

Assessing the Impact of EKF as the Arrival Cost in the Moving Horizon Estimation under Nonlinear Model Predictive Control

In this work, we investigate the performance of nonlinear model predictive control (NMPC) and moving horizon estimation (MHE) in a feedback control system subject to different arrival cost (AC) approximation methods, process uncertainties with non-Gaussian distributions, and plant designs. In particular, we investigate the performance of an extended Kalman filter (EKF) as an AC estimator for large and complex applications. Considering the significant impact of state estimations as the initial condition of the NMPC problem, together with the importance of the AC approximation in the success of the MHE framework, it is expected that a poor approximation of the AC may lead to poor closed-loop performance. Different arrival cost estimation methods including the traditional EKF and constrained particle filtering were evaluated in this work. The closed-loop framework was tested on two industrial applications: a wastewater treatment plant and a high-impact polystyrene process. Error analysis on the convergence of the EKF-based AC estimator is presented in this work to provide insights into the performance of EKF as an AC estimator under different scenarios. The results show that an appropriate arrival cost estimation method such as EKF is adequate to maintain the operation of large and challenging systems in a closed-loop using an MHE–NMPC framework.

Low-cost GPS/INS integration with accurate measurement modeling using an extended state observer

The extended Kalman filter (EKF) is widely used for the integration of the global positioning system (GPS) and inertial navigation system (INS). It is well known that the EKF performance degrades when the system nonlinearity increases or the measurement covariance is not accurate. For the loosely coupled GPS/INS integration, accurate determination of the GPS measurement and its covariance is not a simple task. An extended state observer (ESO) is proposed for the first time to improve the navigation performance of the loosely coupled GPS/INS integration with accurate measurement modeling. The performance of the proposed method is comprehensively evaluated and analyzed, and comparisons were made with respect to the standard EKF method. Simulations and a field vehicular test were conducted to evaluate the performance of the integrated system using the proposed algorithm. The results demonstrate that the navigation performance of the proposed method can be improved significantly in terms of position and velocity when compared with the EKF method. In the simulation test, the RMS values of the positioning errors are reduced by 52.57%, 48.56%, and 34.16% in the north, east, and vertical directions, respectively. The corresponding percentage for the velocity errors are 48.20%, 43.17%, and 22.65%, respectively. In the field test, the RMS values of the positioning errors are decreased by 40.91%, 47.63%, and 12.21%, respectively. The corresponding percentage for the velocity errors are 42.13%, 31.38%, and 33.86%, respectively. The improvement of attitude accuracy is not obvious as it mainly relies on the quality of the inertial sensors.

Conditional equivalence between Extended Kalman filter and complementary filter for two-vector gyro-aided attitude determination

Extended Kalman Filter (EKF) and Complementary Filter (CF) are the two most commonly-used attitude determination algorithms in inertial and magnetic measurement units. It is known that the only difference between the a posterior attitude estimates provided by EKF and CF respectively is the gain matrix (GM) assigned to innovation for attitude update. Through mathematical derivation, it is concluded that the GM of EKF can be simplified to the one of CF, which means that CF is an approximation to EKF. Monte Carlo simulations were done to validate what influence of these simplifications is put on the performance of EKF. The main finding is EKF is more stable than CF in condition of low sampling rate, and hence CF must rely more on the measurements of gyroscope for attitude determination to improve its stability.

A Comparative Study on Adaptive EKF Observers for State and Parameter Estimation of Induction Motor

In this article, conventional extended Kalman filter (EKF) and adaptive extended Kalman filters (AEKFs) based on adaptive fading, strong tracking, and innovation are compared for state and parameter estimation problem of induction motor (IM) by considering their estimation performances and computational burdens. The estimation performance of EKFs depends on the proper selection of system and measurement noise covariance matrices. However, it is hard to select optimum elements of those matrices using the trial-and-error method, and those are affected by the operating conditions of IM. Therefore, different AEKF approaches with the ability to update those matrices online according to the operating conditions have been proposed in the literature. However, to the best of the author's knowledge, no comparison has been yet reported as to which observer is more effective for real-time state and parameter estimation problem of IM. This paper focuses on the detailed comparison of those observers and provides useful results to the literature.