Extended Kalman Filter Technique Research Articles

Cumulative error correction of inertial navigation systems using LIDAR sensors and extended Kalman filter

Autonomous robots have gained significant attention in research due to their ability to facilitate human work. Navigation systems, particularly localization, present a challenge in autonomous robots. The inertial navigation system is a localization system that uses inertial sensors and a wheel odometer to estimate the robot’s relative position to the initial position. However, the system is susceptible to continuous error accumulation over time due to factors like sensor noise and wheel slip. To address these issues, external sensors are required to measure the robot’s position in the environment. The extended Kalman filter (EKF) method is utilized to estimate the robot’s position based on wheel odometer and light detection and ranging (LIDAR) sensor measurements. In the prediction stage, the input to the EKF is the position measurement from the wheel odometer, while the LIDAR sensor’s position measurement is used in the update stage to improve the prediction stage results. The test results reveal that the EKF’s estimated position has a lower average error compared to the position measurement using the wheel odometer. Therefore, it can be concluded that the EKF technique is effectively applied to the robot and can correct the wheel odometer's cumulative error with the assistance of the LIDAR sensor.

An Extended Kalman Filter Design for State-of-Charge Estimation Based on Variational Approach

State of charge (SOC) is a very important variable for using batteries safely and reliably. To improve the accuracy of SOC estimation, a novel variational extended Kalman filter (EKF) technique based on least square error method is herein provided by establishing a second-order equivalent circuit model for the battery. It was found that when SOC decreased, resistance polarization occurred in the electrochemical model, and the parameters in the equivalent RC model varied. To decrease the modeling error in the equivalent circuit model, the system parameters were identified online depending on the SOC’s estimated result. Through the SOC-estimation process, the variation theorem was introduced, which enabled the system parameters to track the real situations based on the output measured. The experiment results reveal the comparison of the SOC-estimation results of the variational EKF algorithm, the traditional EKF algorithm, the recursive least square (RLS) EKF algorithm, and the forgotten factor recursive least square (FFRLS) EKF algorithm based on different indices, including the mean square error (MSE) and the mean absolute error (MAE). The variational EKF algorithm provided in this paper has higher estimation accuracy and robustness than the traditional EKF, which verifies the superiority and effectiveness of the proposed method.

Stochastic Default Risk Estimation Evidence from the South African Financial Market

AbstractThis paper provides empirical studies of the estimation of defaultable bonds in the South African financial markets. The key objective is to estimate the unobservable factors affecting bond yields for South African major banks. The maximum likelihood approach is adopted for the estimation methodology. Multi-dimensional Cox–Ingersoll–Ross (CIR)-type factor models are considered and compared. Extended Kalman filtering techniques are employed in order to tackle the situation that the factors cannot be observed directly. We find empirical evidence that default risk varies with the business cycle, increased sharply in the South African financial market during COVID-19 and the $$\alpha$$ α -CIR model performs better than the classical CIR model.

A Fast Variational Bayesian Adaptive Extended Kalman Filter for Robust Underwater Direction-of-Arrival Tracking

The underwater direction-of-arrival (DOA) tracking using hydrophone array is an important research subject in passive sonar signal processing. To deal with the unknown measurement noise results from underwater environmental noise, the existing variational Bayesian adaptive extended Kalman filter (VB-AEKF) technique for robust underwater DOA tracking jointly estimates the measurement noise covariance matrix and the bearing angle of a target. The iteration process and the nonlinear measurement model result in significant computational complexity of the VB-AEKF. By deriving computational process which is equivalent to VB-AEKF but more computationally efficient, a fast variational Bayesian adaptive extended Kalman filter (FVB-AEKF) for robust DOA tracking is proposed. The proposed method is tested via Monte Carlo simulations of an underwater DOA tracking scenario and an experiment in the South China Sea in July 2021. The results of the simulations and the experiment verified the accuracy and the computational efficiency of the FVB-AEKF.

Securing Multi-User Uplink Communications Against Mobile Aerial Eavesdropper via Sensing

In this paper, we propose a secure multi-user uplink communicaion scheme against a mobile aerial eavesdropper (AE) in Integrated Sensing and Communication (ISAC) systems, where the ISAC base station transmits radar signals to track and jam the AE. For tracking mobile AE, we adopt an extended Kalman filter technique to predict AE's motion state. Based on the tracking information we formulate an optimization problem to jointly design radar signal and receiver beamformer for improving the secrecy performance. To deal with the non-convex constraints and the coupled variables, we propose an alternating optimization based algorithm via iteratively solving a Fractional Programming (FP) problem and a Semidefinite Program (SDP) problem. Numerical results show that the proposed algorithm can achieve higher secrecy capacity and better fairness, compared to the state-of-the-art techniques.

A Novel State Estimation Method for Smart Grid Under Consecutive Denial of Service Attacks

Persistent data packet losses induced by consecutive denial-of-service (DoS) attacks could fail traditional state estimation (SE) algorithms that highly rely on the completeness of dataset. To solve the problem, this article explores a novel SE algorithm with enhanced SE accuracy for power systems against consecutive DoS attacks. First, according to the characteristics of data packet losses induced by DoS attacks, we design a strategy by using the latest received measurement packet to compensate for consecutive data packet losses, and reconstruct the power system model. Second, by integrating Holt’s two-parameter exponential smoothing and extended Kalman filter techniques, a new enhanced SE algorithm is proposed, where the statistical properties of data packet losses are contained in the recursion formulas of the state prediction and state filtering processes. Third, the boundedness of estimation error covariance matrix and prediction error are proved. Finally, the proposed algorithm is compared with traditional SE algorithms via three IEEE testing systems and verified in a real power system. Simulation results illustrate the effectiveness and efficiency of the proposed algorithm under various data packet losses scenarios.

Tikhonov regularization-based extended Kalman filter technique for robust and accurate reconstruction in diffuse optical tomography.

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

Geodetic first order data assimilation using an extended Kalman filtering technique

Geodetic first order data assimilation using an extended Kalman filtering technique

Square-root cubature Kalman filter based power system dynamic state estimation

The state estimator’s real-time state information plays a vital role in monitoring and control of the power system. As a result, one of the primary requirements of the estimator is to provide accurate state estimates with good convergence under varied system operating conditions. In this context, dynamic state estimation (DSE) consistently tracks the power system dynamics and delivers real-time system state evolution. In literature, this dynamic state estimation (SE) problem is generally solved using an extended Kalman filter (EKF). The EKF approach neglects the non-linear mathematical functions of network equations by linearly approximating the measurement equations. This leads to degradation of SE accuracy during a sudden change in load conditions. In this paper, a new derivative-free method based on square-root cubature Kalman filter (SCKF) is proposed to overcome the limitations of the EKF technique and achieves improved performance. The proposed SCKF technique has been tested on IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus systems under various operating conditions. The effectiveness of the SCKF technique has been compared with the traditional EKF and cubature Kalman filter (CKF) techniques using different performance indices. The obtained results demonstrate the versatility of the proposed SCKF technique.

Towards robust reduction of nonlinear errors in dynamic spectrum spectroscopy for effective noninvasive optical detection of blood components

Most conventional noninvasive optical methods for blood component detection suffer from individual subjects’ variability interferences. Dynamic spectrum (DS) is a spectroscopy technique that can eliminate these limitations and improve the accuracy of blood component assessment. The DS method is an adaptive technique that can extract blood information from multiple and different spectral wavelengths of the pulsating arterial part of the photoplethysmography (PPG) signal. However, high concentrations of human blood have strong scattering properties that result in a nonlinear effect during spectral analysis. There is still a paucity of robust techniques to address this nonlinear effect in DS and noninvasive optical detection of blood components. This investigation proposed a novel optimized extended Kalman filter (O-EKF) technique and radial basis function neural network (RBF-NN) to address the nonlinear effect in spectroscopy measurements. The O-EKF and RBF-NN were considered nonlinear algorithms with the adaptive ability to approximate the nonlinear relationship between spectral absorbance and concentration. Hemoglobin samples with concentration levels between 120 g/L and 175 g/L acquired from 231 volunteer subjects were used for sample prediction and spectrum accuracy evaluation. The spectrum extraction from single positioning obtained a correlation coefficient of prediction (Rp) = 0.721 and a root mean square error of prediction (RMSEp) = 10.023 with the partial least square (PLS) model. Further evaluation with the original dual-position spectrum extraction without optimized filtering recorded Rp = 0.636 and RMSEp = 10.630. The results of the dual-position spectrum extraction with O-EKF and the RBF-NN model proved to be effective with a significant increase in Rp = 0.976 and a decrease in RMSEp = 8.132. The results represent a 35% increase in hemoglobin prediction and 31% reduction in prediction error when compared to spectrum detection in single-position. The results demonstrate that nonlinearity from scattering can be reduced through multi-position spectrum detection and optimized filtering. The present study could provide a robust alternative to eliminate nonlinearity and thus improve the linear concentration detection of blood components.

Application and Testing of the Extended-Kalman-Filtering Technique for Determining the Planetary Boundary-Layer Height over Athens, Greece

We investigate the temporal evolution of the planetary boundary-layer (PBL) height over the basin of Athens, Greece, during a 6-year period (2011–2016), using data from a Raman lidar system. The range-corrected lidar signals are selected around local noon (1200 UTC) and midnight (0000 UTC), for a total of 332 cases: 165 days and 167 nights. In this dataset, the extended-Kalman filtering technique is applied and tested for the determination of the PBL height. Several well-established techniques for the PBL height estimation based on lidar data are also tested for a total of 35 cases. The lidar-derived PBL heights are compared to those derived from radiosonde data. The mean PBL height over Athens is found to be 1617 ± 324 m at 1200 UTC and 892 ± 130 m at 0000 UTC for the period examined, while the mean PBL-height growth rate is found to be 170 ± 64 m h−1 and 90 ± 17 m h−1 during daytime and night-time, respectively.

Subcriticality estimation by extended Kalman filter technique in transient experiment with external neutron source at Kyoto University Critical Assembly

The monitoring subcriticality by the extended Kalman filter (EKF) is evaluated in the presence of an external neutron source through transient analyses and compares with that by inverse kinetic method at Kyoto University Critical Assembly. Throughout the transient experiment, subcriticality is deduced with the use of neutron counts measured every 1 s. For ensuring the initial condition of the EKF technique, the basic transient experiment is carried out by dropping a control rod into the core at a critical state, and the result by the EKF technique shows remarkably accurate subcriticality as compared with the reference value obtained by the rod drop method with less fluctuation than by the inverse kinetic method. In the ADS transient experiment with the 14 MeV stable neutron source, the subcriticality is set as target subcriticality of the accelerator-driven system ($$k_\mathrm{eff}= 0.97$$); the external neutrons are then injected from outside the core. The EKF technique reveals significantly good agreement with MCNP6.1, whereas subcriticality by the inverse kinetic method fluctuates widely during the transient experiment. Thus transient experiment shows that the EKF technique is applicable to subcriticality monitoring with a high time resolution and a high degree of precision.

Finite-time optimized robust control with adaptive state estimation algorithm for autonomous heavy vehicle

Structured and unstructured uncertainties coupled with external disturbances usually pose considerable challenges in realizing heavy vehicle automatic lane guidance control. This paper presents a novel solution paradigm for the lateral control of autonomous heavy vehicle. The proposed control framework consists of an adaptive state estimator and a finite-time optimized ℋ∞ state feedback regulator. Firstly, based on the dual extended Kalman filter (DEKF) technique, which can estimate model time-varying parameters and unknown states at the same time, the adaptive state estimation algorithm is proposed and investigated to improve state estimation adaptivity against uncertain time-varying general front/rear axle cornering stiffnesses. Then, using zero-sum dynamic game theory as the general framework, we analyze the minimax controller design problem and introduce the finite-time optimized robust regulator design method. The autonomous heavy vehicle automatic lane guidance controller is designed in the framework of robust optimal state feedback control to make it robust against external disturbance. Finally, results of various driving scenarios from both simulation and hardware-in-loop (HIL) implementation show that the proposed finite-time optimized robust and adaptive state estimation control paradigm can robustly obtain satisfactory automated lateral control performance for heavy vehicle when the control system is characterized by both time-varying model parameters and uncertain external energy-bounded disturbance. A comparative study is also conducted to investigate cases to show its effectiveness when the adaptive state estimation is used and when it is not.

Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems

In this paper, we propose a new technique—called Ellipsoidal and Gaussian Kalman filter—for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system’s state (and the optimal ellipsoid for describing the systems’s uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better—the state estimation technique usually applied to such nonlinear problems.

An on-line extended Kalman filtering technique for reconstructing the transient heat flux and temperature field in two-dimensional participating media

Accurate measuring of the surface time-dependent heat flux and internal temperature of the participating media is significant in the fields of solar energy and aerospace. In this study, an on-line extended Kalman Filtering (EKF) technique was developed to reconstruct the surface time-varying heat flux and internal temperature field in two dimensions (2D) participating media simultaneously. The forward nonlinear conduction-radiation problem was solved by employing the finite volume method combined with discrete ordinate method. On this basis, the inverse problem for retrieving the surface time-varying heat flux and internal temperature field was solved by the EKF. The performance of the proposed EKF is tested thoroughly by appending different forms of time-varying heat flux on the left surface of the 2D participating media. The effect of medium thickness, time step, measurement noise, process noise, measurement noise covariance, process noise covariance on the stability and accuracy of the reconstructed results are investigated, respectively. All the research outcomes indicate that the time-varying surface heat flux and internal temperature field in the 2D participating medium can be reconstructed accurately and effectively by the EKF technique.

Incorporating neuro-fuzzy with extended Kalman filter for simultaneous localization and mapping

Extended Kalman filter is well-known as a popular solution to the simultaneous localization and mapping problem for mobile robot platforms or vehicles. In this article, the development of a neuro-fuzzy-based adaptive extended Kalman filter technique is presented. The objective is to estimate the proper values of the R matrix at each step. We design an adaptive neuro-fuzzy extended Kalman filter to minimize the difference between the actual and theoretical covariance matrices of the innovation consequence. The parameters of the adaptive neuro-fuzzy extended Kalman filter is then trained offline using a particle swarm optimization technique. With this approach, the advantages of high-dimensional search space can be exploited and more effective training can be achieved. In the experiments, the mobile robot navigation with a number of landmarks under two benchmark situations is evaluated. The results have demonstrated that the proposed adaptive neuro-fuzzy extended Kalman filter technique provides the improvement in both performance efficiency and computational cost.

Mitigating the Effect of Noise Uncertainty on the Online State-of-Charge Estimation of Li-Ion Battery Cells

Real-time battery state-of-charge (SOC) estimation is critical in many applications. The extended Kalman filter (EKF) has been successfully deployed in SOC estimation allowing real-time SOC monitoring. However, modeling inaccuracies, measurement faults, and wrong initialization can cause the estimation algorithm to diverge. The precise knowledge of statistical information about process and measurements noise is crucial for accurate system modeling and estimation. This paper presents a novel SOC estimation approach based on maximum-likelihood estimation (MLE). The process and measurements models are transformed to an error state propagation system where the innovation covariance is utilized to maximize the likelihood of the multivariate innovation distribution with respect to process and measurement covariances. The MLE formulation allows the estimation of the process and measurement noise covariance magnitudes, which are used to obtain an optimal SOC estimate. The proposed method is validated experimentally using a number of Li-ion battery cells under various testing conditions. The estimation performance is compared with that of the conventional EKF technique as well as previously published results based on autocovariance least-squares measurements noise estimation. The results indicate an enhanced performance for the new algorithm over the traditional EKF across all conducted tests.

State of charge estimation based on adaptive algorithm for Lead-Acid battery

The usage of batteries in recent years has become widespread in many fields e.g. in electric vehicles, energy renewable and stand-alone systems which require a robust approach for estimation of the state of charge (SOC). The SOC represents an important factor to guaranty safe operations. A lot of methods have been used to predict the state of charge. The coulomb counting method is the famous and widely used among them, but have limitation due to its accuracy. Another used approach is the Kalman Filter, which improves the estimation efficiency, to reach a good performance in SOC prediction. The version of adaptive extended Kalman filter (AEKF) technique is applied in this paper. This paper presents an experimental performance of technique of Kalman filter, for solving the problem of accurate SOC. The method is used to compute the terminal voltage in such a way to estimate the SOC. The proposed algorithm is based on preselected Thevenin model after the identification of its parameters. It has been used to predict the SOC based on nonlinear equations, and evaluation of the approach is verified with the experimental results. The final results signify that the estimation matched with the proposed model and the algorithm is performed optimally, thus the maximum soc estimation error is the finest

State of charge estimation based on adaptive algorithm for Lead-Acid battery

The usage of batteries in recent years has become widespread in many fields e.g. in electric vehicles, energy renewable and stand-alone systems which require a robust approach for estimation of the state of charge (SOC). The SOC represents an important factor to guaranty safe operations. A lot of methods have been used to predict the state of charge. The coulomb counting method is the famous and widely used among them, but have limitation due to its accuracy. Another used approach is the Kalman Filter, which improves the estimation efficiency, to reach a good performance in SOC prediction. The version of adaptive extended Kalman filter (AEKF) technique is applied in this paper. This paper presents an experimental performance of technique of Kalman filter, for solving the problem of accurate SOC. The method is used to compute the terminal voltage in such a way to estimate the SOC. The proposed algorithm is based on preselected Thevenin model after the identification of its parameters. It has been used to predict the SOC based on nonlinear equations, and evaluation of the approach is verified with the experimental results. The final results signify that the estimation matched with the proposed model and the algorithm is performed optimally, thus the maximum soc estimation error is the finest

Fuzzy-Controller-Designed-PV-Based Custom Power Device for Power Quality Enhancement

In this paper, a three-phase series hybrid active filter (SEHAF) interconnected with photovoltaic (PV) system and dc–dc boost converter is proposed to minimize sag, swell, and harmonics caused due to nonlinear power electronic loads. The SEHAF consists of a voltage source inverter (VSI) with a capacitor connected across it to provide consistency in managing and compensating the reactive power. This minimizes the sag, swell, and harmonics present in the source and load voltages. With the integration of PV, the voltage across the dc-link capacitor of VSI is controlled effectively, which helps in better compensation. Reference current generation is done using the proposed robust extended complex Kalman filter (RECKF) technique. The performance of the PV-integrated-HAF is analyzed using a synchronous reference frame with proportional-integral (PI) as well as fuzzy logic controller (FLC) and is compared with the proposed RECKF technique. The PV-integrated hybrid power system is developed using MATLAB/SIMULINK. Further, real-time digital simulation using OPAL-RT OP5142 is also carried out to support the simulation results. It is observed that the proposed control scheme provides better harmonic compensation compared to conventional PI and FLC.