Parameters Of Extended Kalman Filter Research Articles

Bayesian Optimization for Fine-Tuning EKF Parameters in UAV Attitude and Heading Reference System Estimation

In various applications, the extended Kalman filter (EKF) has been vital in estimating a vehicle’s translational and angular motion in 3-dimensional (3D) space. It is also essential for the fusion of data from multiple sensors. However, for the EKF to perform effectively, the optimal process noise covariance matrix (Q) and measurement noise covariance matrix (R) must be chosen correctly. The use of EKF has been challenging due to the need for an easy mechanism to select Q and R values. As a result, this research focused on developing an algorithm that can be easily applied to determine Q and R, allowing us to harness the full potential of EKF. Accordingly, an EKF innovation consistency statistics-driven Bayesian optimization algorithm was employed to achieve this goal. Q and R values were tuned until the expected result met the performance requirement for minimum error through improved measurement innovation consistency. The comprehensive results demonstrate that when the optimum Q and R, as tuned by the suggested technique, were used, the performance of the EKF significantly improved.

Evaluation of Various Offline and Online ECM Parameter Identification Methods of Lithium-Ion Batteries in Underwater Vehicles.

For underwater vehicles, the state of charge (SOC) of battery is often used to guide the optimal allocation of energy. An accurate SOC estimation can improve work efficiency and reliability of underwater vehicles. Model-based SOC estimation methods are still mainstream routes used in practical applications. Hence, accurate battery models are highly desirable, which depends not only on the circuit structure but also on the circuit parameters. Four-parameter identification algorithms, offline mechanism-based and least squared (LS) methods, as well as online recursive least-squares with forget factor (FFRLS) and extended Kalman filter (EKF) methods were analyzed in terms of SOC estimation under three different conditions. The results revealed that in the case without any disturbance, the predicted SOCs based on four-parameter identification circuits fitted well with the reference. Moreover, it is remarkable that the LS offline methods work better than the FFRLS online routes. In addition, the robustness has also been accessed through the other two conditions, i.e., measurement data with disturbance and initial SOC value with deviation. The results showed that maximum errors of SOC estimation based on the EKF approach are significantly lower than those of the other methods, and the values are 0.51% and 0.20%, respectively. Thus, the circuit model based on the EKF parameter identification approach possessed a stronger anti-interference performance during the SOC estimation process. This research can provide corresponding theoretical support on ECM parameter identification for lithium-ion batteries in underwater vehicles.

UAV navigation based on adaptive fuzzy backstepping controller using visual odometry

ABSTRACT This study investigates the 3D trajectory tracking of a quadrotor-type unmanned aerial vehicle (UAV) using a visual localization system integrated in the feedback control loop. First, adaptive stereo visual odometry (SVO) is proposed to solve the UAV localization problem. The proposed solution mainly employs adaptive iterative closest point speeded-up robust features. Second, a vision-based trajectory tracking algorithm is implemented using a backstepping controller, whose parameters are optimized using the particle swarm optimization algorithm. Finally, to avoid the limitations of visual localization (e.g. dark environment, uniform area, and dynamic scene), the visual pose is supported by the inertial pose obtained using a fuzzy adaptive Kalman filter (FAKF). Based on the number and average depth of the estimated 3D points, the FAKF algorithm adaptively tunes the extended Kalman filter parameters. The proposed algorithms are validated using simulation and experimental data. Many scenarios are considered with different trajectories. Good performance is achieved, confirming the efficiency of the proposed approach.

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Sparse Visual-Inertial Measurement Units Placement for Gait Kinematics Assessment.

This study investigates the possibility of estimating lower-limb joint kinematics and meaningful performance indexes for physiotherapists, during gait on a treadmill based on data collected from a sparse placement of new Visual Inertial Measurement Units (VIMU) and the use of an Extended Kalman Filter (EKF). The proposed EKF takes advantage of the biomechanics of the human body and of the investigated task to reduce sensor inaccuracies. Two state-vector formulations, one based on the use of constant acceleration model and one based on Fourier series, and the tuning of their corresponding parameters were analyzed. The constant acceleration model, due to its inherent inconsistency for human motion, required a cumbersome optimisation process and needed the a-priori knowledge of reference joint trajectories for EKF parameters tuning. On the other hand, the Fourier series formulation could be used without a specific parameters tuning process. In both cases, the average root mean square difference and correlation coefficient between the estimated joint angles and those reconstructed with a reference stereophotogrammetric system was 3.5deg and 0.70, respectively. Moreover, the stride lengths were estimated with a normalized root mean square difference inferior to 2% when using the forward kinematics model receiving as input the estimated joint angles. The popular gait deviation index was also estimated and showed similar results very close to 100, using both the proposed method and the reference stereophotogrammetric system. Such consistency was obtained using only three wireless and affordable VIMU located at the pelvis and both heels and tracked using two affordable RGB cameras. Being further easy-to-use and suitable for applications taking place outside of the laboratory, the proposed method thus represents a good compromise between accurate reference stereophotogrammetric systems and markerless ones for which accuracy is still under debate.

State of charge estimation of lithium-ion battery based on double deep Q network and extended Kalman filter

The state of charge (SOC), as an important parameter of the lithium-ion battery management system (BMS), is an important factor affecting the current battery detection and safety issues. Due to the non-linear characteristics of the lithium-ion battery charging and discharging process, it is difficult to model the BMS and estimate the SOC accurately. This paper takes lithium-ion battery as the research object, designs the Markov decision process (MDP) model of lithium-ion battery energy storage prediction, establishes the second-order RC equivalent circuit model (ECM) and extended Kalman filter (EKF), and proposes a method based on double deep Q network (double DQN) to optimize the EKF parameters SOC estimation method to solve the problem of dimensionality disaster and value function overestimation generated in deep reinforcement learning (DRL). Through the effective verification of the lithium-ion battery SOC estimation algorithm, the simulation results show that compared with the traditional deep Q network (DQN) algorithm, double DQN has better convergence, adaptive ability and better estimation accuracy. It can provide new ideas for the accurate estimation of SOC.

An efficient tuning framework for Kalman filter parameter optimization using design of experiments and genetic algorithms

The Extended Kalman Filter (EKF) is currently a dominant method of sensor fusion used for navigation of mobile devices, robotics and autonomous vehicles. One navigation system involves the EKF fusion of an Inertial Navigation System (INS) with a Global Navigation Satellite System (GNSS) to perform 3D pose estimation, which is essential to practical applications like autonomous vehicles and UAVs. This system involves using the INS to predict pose changes and uses GNSS measurements when available to correct for estimation drifts and sensor errors. The performance of the state estimation is heavily dependent on the accurate selection of EKF parameters, leading to the optimal selection of parameters being a critical factor in the design and use of the EKF. In this paper, a methodical and efficient method of EKF parameter tuning is presented. The tuning framework uses nominal parameters generated by Gauss Markov (GM) and Allan Variance (AV) methods that are tuned by Genetic Algorithms (GA) accelerated by a Design of Experiment (DoE) technique to efficiently optimize EKF parameters. This framework has been implemented in MATLAB and tested using simulations and real data. The results demonstrate that GA tuned parameters increases accuracy substantially, and that the DoE technique consistently improves the convergence behavior of the GA.

Self-Tuning Extended Kalman Filter Parameters to Identify Ankle's Third-Order Mechanics.

The estimation of human ankle's mechanical impedance is an important tool for modeling human balance. This work presents the implementation of a parameter-estimation approach based on a state-augmented extended Kalman filter (AEKF) to infer the ankle's mechanical impedance during quiet standing. However, the AEKF filter is sensitive to the initialization of the noise covariance matrices. In order to avoid a time-consuming trial-and-error method and to obtain a better estimation performance, a genetic algorithm (GA) is proposed to best tune the measurement noise (Rk) and process noise covariances (Q) of the extended Kalman filter (EKF). Results using simulated data show the efficacy of the proposed algorithm for parameter-estimation of a third-order biomechanical model. Experimental validation of these results is also presented. They suggest that age is an influencing factor in the human balance.

An adaptive filtering method based on EMD for X-ray pulsar navigation with uncertain measurement noise

Affected by the unstable pulse radiation and the pulsar directional errors, the statistical characteristics of the pulsar measurement noise may vary with time slowly and cannot be accurately determined, which cause the filtering accuracy of the extended Kalman filter(EKF) in pulsar navigation positioning system decline sharply or even diverge. To solve this problem, an adaptive extended Kalman filtering algorithm based on the empirical mode decomposition(EMD) is proposed. In this method, the high frequency noise is separated from measurement information of pulsar by the method of EMD, and the noise variance can be estimated to update the parameters of EKF. The simulation results demonstrate that compared with conventional EKF, the proposed method can adaptively track the change of the measurement noise, and still keeps high estimation accuracy with unknown measurement noise, the positioning accuracy of the pulsar navigation is improved simultaneously.

A Review on Tuning of Extended Kalman Filter using Optimization Techniques for State Estimation

estimation is the common problem in every area of engineering. There are different filters used to overcome the problem of state estimation like Kalman filter, Particle filters etc. Kalman Filter is popular when the system is linear but when the system is highly non-linear then the different derivatives of Kalman Filter are used like Extended Kalman Filter (EKF), Unscented Kalman filter. But these estimation techniques require tuning of process and noise covariance matrices. The different optimization techniques are used to tune the filter parameters of EKF. In this paper, various optimization techniques have been studied for non-linear state estimation based on EKF.

Sensorless Control of Permanent Magnet Synchronous Motors and EKF Parameter Tuning Research

This paper concerns the parameter tuning and the estimated results postprocessing of the extended Kalman filter for the sensorless control application of permanent magnet synchronous motors. At first an extended Kalman filter parameter tuning method is proposed based on the theoretical and simulation analysis of extended Kalman filter parameters. Furthermore, a sensorless control system is proposed based on the parameter tuning method and the simulation analysis of extended Kalman filter estimation results in different reference speeds and different load torques. The proposed sensorless control system consists of two parts. The first one is a module to self-regulate extended Kalman filter parameters. The second part can correct the estimated speed and the estimated rotation angle based on the reference speed and the electromagnetic torque. Finally, simulation results are presented to verify the feasibility and validity of the proposed sensorless control system.

Adaptive-tuning of extended Kalman filter used for small scale wind generator control

In this paper a small scale wind generator based on a permanent magnet synchronous machine (PMSM) and associated with an indirect maximum power point tracking (MPPT) algorithm is proposed. Choosing an energy conversion active structure and a sensorless PMSM, to control the system, a speed estimator is required. Facing to other methods, the extended Kalman filter (EKF) model-based estimator allows sensorless drive control in a wide speed range and estimates the rotation speed with a rapid response. The EKF parameters tuning is solved by introducing an adaptive method, i.e. adaptive-tuning EKF. This adaptive estimation approach is innovative by using a covariance matching technique. The experimental results prove that the proposed method is technically feasible with good performances within some limits.

Very-low speed control of PMSM based on EKF estimation with closed loop optimized parameters

When calculating the speed from the position of permanent magnet synchronous motor (PMSM), the accuracy and real-time are limited by the precision of the sensor. This problem causes crawling and jitter at very-low speed. Using the angle from the position sensor, an extended Kalman filter (EKF) designed in dq-coordinate is presented to solve this problem. The usage of position sensor simplifies the model and improves the accuracy of speed estimation. Specially, a closed loop optimal (CLO) method is devised to overcome the difficulty to adjust the parameters of the EKF. The EKF is the feedback link of speed control, CLO method is derived from the perspective of the speed step response to optimize the measurement covariance matrix and the system covariance matrix of EKF. Simulation and experimental results, comparing the low-speed performance of the EKF and sensor feedback methods, prove the effectiveness of the method to adjust the parameters of EKF and the advantages in eliminating the low speed jitter.

State Estimator Design for Multicomponent Batch Distillation Columns

In the control of batch distillation columns, one of the problems is the difficulty in monitoring the compositions. This problem can be handled by estimating the compositions from readily available online temperature measurements using a state estimator. In this study, a state estimator that infers the product composition in a multicomponent batch distillation column (MBDC) from the temperature measurements is designed and tested using a batch column simulation. An extended Kalman filter (EKF) is designed as the state estimator and is implemented for performance investigation on the case column with eight trays separating the mixture of cyclo-hexane, n-heptane and toluene. EKF parameters of the diagonal terms of process noise covariance matrix and those of measurement model noise covariance matrix are tuned in the range where the estimator is stable and selected basing on the least IAE score. Although NC-1 temperature measurements is sufficient considering observability criteria, using NC measurements spread through out the column homogeneously improves the performance of EKF estimator. The designed EKF estimator is successfully used in the composition—feedback inferential control of MBDC operated under variable reflux-ratio policy with an acceptable deviation of 0.5–3% from the desired purity level of the products.

A recursive algorithm based on the extended Kalman filter for the training of feedforward neural models

The extended Kalman filter (EKF) is a well-known tool for the recursive parameter estimation of static and dynamic nonlinear models. In particular, the EKF has been applied to the estimation of the weights of feedforward and recurrent neural network models, i.e. to their training, and shown to be more efficient than recursive and nonrecursive first-order training algorithms; nevertheless, these first applications to the training of neural networks did not fully exploit the potentials of the EKF. In this paper, we analyze the specific influence of the EKF parameters for modeling problems, and propose a variant of this algorithm for the training of feedforward neural models which proves to be very efficient as compared to nonrecursive second-order algorithms. We test the proposed EKF algorithm on several static and dynamic modeling problems, some of them being benchmark problems, and which bring out the properties of the proposed algorithm.

Aerodynamic Parameter Estimation for High-Performance Aircraft Using Extended Kalman Filtering

The estimation of aerodynamic coefficients in aircraft dynamic models from flight-test data is addressed in this paper. An extended Kalman filter (EKF), implementing the full nonlinear kinematics of the aircraft equations of motion, was used for this purpose. Flight-test data from NASA's X-31 Drop Model and High Angle-of-attack Research Vehicle (HARV) were analyzed. The EKF parameter estimates for the X-31 compared well with wind-tunnel data and flight-data results using other identification techniques. For the HARV, the assumption of pseudonoise in the parameter dynamic model substantially improved the state and parameter estimates. A residual correlation method was used to estimate the process noise intensity matrix for this aircraft's flight data.

Implementation issues concerning the EKF-based fault diagnosis techniques

The extended Kalman filter (EKF) is one of the most popular model-based techniques for fault detection and diagnosis. Although its effectiveness has been widely recognized, the practical applications of EKFs are still very limited. This is due to the fact that the estimates of EKF are often biased when the occurrence of multiple faults is possible. In this study, we have extended the findings of our previous research on diagnostic observability and diagnostic resolution concerning a set of parallel single-parameter EKFs (Chang et al., 1993, A.I.Ch.E. J. 39, 1146) to the multiple-parameter EKFs which are designed to identify more than one fault origin. The problems in implementing these EKFs, i.e. misdiagnosis due to biased estimates and heavy computation load due to the parallel configuration, have been solved with a selection strategy for proper combinations of sensor locations and EKF parameters. More importantly, simple procedures have been developed to quickly evaluate the performance of any given system and the reliability of the proposed approach has been repeatedly confirmed in extensive simulation studies without exceptions. As a result, it becomes feasible to construct appropriate fault monitoring schemes without extensive computational effort even for large and complex chemical processes.