Conventional Extended Kalman Filter Research Articles

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.

LSTM을 이용한 항법시스템의 확장칼만필터 공분산 튜닝

Noise covariances in the EKF (Extended Kalman Filter) act as tuning parameters due to modeling errors, such as the error generated in the process of linearizing the nonlinear system equation. Filter designers traditionally prefer the trial-and-error method. However, because the noise covariances require retuning in concert with changes in trajectories or changes in system equations, human tuning is very time consuming. Accordingly, this study proposes an automation method for real-time parameter tuning using an LSTM (Long Short-Term Memory) neural network. The proposed method consists of two stages: 1) generating residual and state error covariances from an EKF using fixed-noise covariances and 2) producing a state estimate from an EKF using tuned time-varying noise covariances obtained from an LSTM neural network. This scheme is applied to navigation systems to calculate accurate velocity, attitude, and IMU bias estimates under challenging maneuvering situations. Using simulation, we showed that the proposed method outperforms the conventional EKF of navigation systems in suppressing estimation error in different trajectory scenarios.

An USBL/DR Integrated Underwater Localization Algorithm Considering Variations of Measurement Noise Covariance

Ultrashort baseline (USBL) positioning system is an important part of the integrated navigation for underwater vehicles. The single USBL positioning system has problems such as reduced accuracy of azimuth measurement due to target motion and large impact of small angular variations, especially in the region where the target is close to the conical boundary, that is, the low-elevation region. To improve the positioning accuracy of the USBL-based integrated navigation system, a tightly coupled USBL/Dead Reckoning (DR) integrated localization algorithm that considers the time varying characteristics of the measurement noise was proposed, and the filtering model of the algorithm was designed. The algorithm exploits the mechanism of the azimuth measurement covariance variation of the USBL system, constructs an adaptive measurement noise estimator for the USBL system, and applies it to the integration filtering of USBL/DR data. A nonlinear extended Kalman filtering (EKF) model was used to fuse the USBL positioning and dead reckoning trajectories. A number of simulation tests with different elevation angle settings were performed to compare the performance of the proposed algorithm with that of a conventional EKF for underwater localization. The test results reveal that the proposed algorithm can effectively reduce the positioning error caused by the change in the relative azimuth of the acoustic signal owing the motion of the mother ship and the motion of the underwater vehicle.

Partial-Update Kalman Filter for Permanent Magnet Synchronous Motor Estimates Under Intermittent Data

The partial-update Kalman filter (PKF) is an extension of the Schmidt Kalman filter, which can improve the capabilities of the conventional extended Kalman filter for handling model uncertainties and nonlinearities. Herein, we adapt the PKF to estimate the states and parameters of electric machines, particularly in cases with intermittent observations. To account for missing data within the filter, the arrival of new measurements is treated as a Bernoulli process. We show that the estimation error of the proposed filter remains bounded if the system satisfies mild assumptions. Moreover, we show that the prediction error covariance matrix is guaranteed to be bounded if the observation arrival rate has a lower bound. Hardware experiments validate this technique for a surface-mounted permanent magnet synchronous motor.

Design of power lithium battery management system based on digital twin

The accurate estimation of the State of Charge (SoC) of batteries has always been the focus of Battery Management System (BMS). However, the current BMS has problems such as difficult data sharing, weak data processing capability and limited data storage capacity, so the simplest ampere-time integration method is used to estimate the SoC, and the estimation results are highly biased. In this paper, an innovative digital twin-driven battery system framework is proposed and successfully developed. A joint HIF-PF online algorithm for estimating SoC under the experimental condition Beijing Bus Dynamic Stress Test (BBDST) is also proposed, which is comparable to the conventional Extended kalman filter (EKF), HIF and Particle Filter (PF). The results demonstrate the superiority of the algorithm. Then, we applied the algorithm to estimate SoC. In addition, the system implements functions such as real-time voltage and current monitoring and visualization.

Factor graph optimization for GNSS/INS integration: A comparison with the extended Kalman filter

<h3>Abstract</h3> Factor graph optimization (FGO) recently has attracted attention as an alternative to the extended Kalman filter (EKF) for GNSS-INS integration. This study evaluates both loosely and tightly coupled integrations of GNSS code pseudorange and INS measurements for real-time positioning, using both conventional EKF and FGO with a dataset collected in an urban canyon in Hong Kong. The FGO strength is analyzed by degenerating the FGO-based estimator into an “EKF-like estimator.” In addition, the effects of window size on FGO performance are evaluated by considering both the GNSS pseudorange error models and environmental conditions. We conclude that the conventional FGO outperforms the EKF because of the following two factors: (1) FGO uses multiple iterations during the estimation to achieve a robust estimation; and (2) FGO better explores the time correlation between the measurements and states, based on a batch of historical data, when the measurements do not follow the Gaussian noise assumption.

PFIN: An Efficient Particle Filter-Based Indoor Navigation Framework for UAVs

The utilization of Unmanned Aerial Vehicles (UAVs) like drones for indoor data gathering or sensing applications have gained popularity over the last decade. Indoor UAV navigation is a complex process, which involves several tasks such as mapping, localization, and path planning with obstacle avoidance. In this paper, a Particle Filter-based Indoor Navigation (PFIN) framework is proposed for the drone navigation process. In PFIN, Quadcopter Mapping Algorithm (QMA) is proposed using particle filter analysis to aid in mapping for indoor navigation. In addition, particle filter-based Optimized Localization Algorithm (OLA) and Adaptive Velocity Procedure (AVP) are proposed for the purpose of enhancing the precision in localization and to improve the velocity estimation for collision avoidance, respectively. Thus, the proposed PFIN framework is experimented using Software-In-The-Loop (SITL) tools such as Robot Operating System (ROS) and Gazebo for visualizing its behavior, and Crazyflie 2.0 drone assisted Hardware-In-The-Loop (HITL) simulation in verifying the correctness of the algorithms in a laboratory setup. The PFIN framework reduces position error on an average by 14% than the conventional Extended Kalman Filter (EKF) model. The SITL and HITL simulations demonstrate the efficiency of the algorithms through improved precision in UAV exploration.

Infrared focal plane array attitude measurement method based on adaptive fault-tolerant extended Kalman filter

To improve the anti-jamming ability of infrared attitude measurement methods, the infrared focal plane array (IRFPA) fault diagnosis method was investigated with regard to small-region and full-region infrared interference, respectively. An adaptive fault-tolerant extended Kalman filter algorithm is proposed to actively remove the infrared interference data in the case of small-region infrared interference and carry out attitude estimation with the mathematical model under full-region infrared interference. The results reveal that the adaptive fault-tolerant extended Kalman filter has stronger anti-jamming ability compared with the conventional extended Kalman filter. Additionally, the adaptive fault-tolerant extended Kalman filter can maintain the attitude estimation accuracy of ±0.8° when full-region infrared interference doesn't exist or if most IRFPA data are reliable. Apart from missile navigation, the framework of the adaptive fault-tolerant extended Kalman filter can be applied to almost all applications using extended Kalman filter, such as aircraft, vehicular navigation, indoor positioning, and target tracking, etc.

Stochastic filtering based transmissibility estimation of novel coronavirus

In this study, the transmissibility estimation of novel coronavirus (COVID-19) has been presented using the generalized fractional-order calculus (FOC) based extended Kalman filter (EKF) and wavelet transform (WT) methods. Initially, the state-space representation for the bats-hosts-reservoir-people (BHRP) model is obtained using a set of fractional order differential equations for the susceptible-exposed-infectious-recovered (SEIR) model. Afterward, the EKF and Kronecker product based WT methods have been applied to the discrete vector representation of the BHRP model. The main advantage of using EKF in this system is that it considers both the process and the measurement noise, which gives better accuracy and probable states, which are the Markovian (processes). The importance of proposed models lies in the fact that these models can accommodate conventional EKF and WT methods as their special cases. Further, we have compared the estimated number of contagious people and recovered people with the actual number of infectious people and recovered people in India and China.

Global Sensitivity Analysis on Temperature-Dependent Parameters of A Reduced-Order Electrochemical Model And Robust State-of-Charge Estimation at Different Temperatures

In this paper, a robust estimator is designed based on a reduced-order electrochemical model to achieve accurate state-of-charge estimation of lithium ion batteries at different ambient temperatures. The reduced-order electrochemical model, containing only two estimation states, describes the first principles within the battery and incorporates temperature-dependent properties, making it an ideal candidate for accurate estimation applications. A global sensitivity analysis based on Sobol indices is then conducted, investigating the impact of different temperatures on the model performance by changing the electrochemical properties of lithium ion batteries. The first-order and total Sobol indices obtained by Monte Carlo method show that variations of temperature-dependent parameters make different influence on the overall model uncertainties at different temperatures. Then, a robust adaptive extended Kalman filter based on the electrochemical model is designed for state-of-charge estimation to actively compensate such potential model uncertainties. Results against multiple experimental datasets at 45, 25 and 0°C indicate that the proposed state-of-charge estimation algorithm is robust to imposed initial estimation errors, different driving cycle inputs and ambient temperatures. An extensive comparative analysis between the adaptive extended Kalman filter and a conventional extended Kalman filter is also presented.

A state-of-charge estimation method of the power lithium-ion battery in complex conditions based on adaptive square root extended Kalman filter

The control strategy of electric vehicles mainly depends on the power battery state-of-charge estimation. One of the most important issues is the power lithium-ion battery state-of-charge (SOC) estimation. Compare with the extended Kalman filter algorithm, this paper proposed a novel adaptive square root extended Kalman filter together with the Thevenin equivalent circuit model which can solve the problem of filtering divergence caused by computer rounding errors. It uses Sage-Husa adaptive filter to update the noise variable, and performs square root decomposition on the covariance matrix to ensure its non-negative definiteness. Moreover, a multi-scale dual Kalman filter algorithm is used for joint estimation of SOC and capacity; the forgetting factor recursive least-square method is used for parameter identification. To verify the feasibility of the algorithm under complicated operating conditions, different types of dynamic working conditions are performed on the ternary lithium-ion battery. The proposed algorithm has robust and accurate SOC estimation results and can eliminate computer rounding errors to improve adaptability compared to the conventional extended Kalman filter algorithm.

Tightly coupled integrated navigation system via factor graph for UAV indoor localization

Due to the widely use of the rotorcrafts in civil applications, the highly accurate positioning is paid more attentions. The ultra-wide band (UWB) receiver plays a crucial role in navigating the unmanned aerial vehicle (UAV) in indoor areas, because of its low cost and low power consumption. However, the positioning accuracy of UWB is drastically affected by the infamous multipath effect. Therefore, the Ultra Wideband (UWB)/Inertial Navigation System (INS) integrated indoor navigation is an effective approach to reduces the positioning errors. This paper proposes a tightly-coupled UWB/INS integration navigation based on factor graph optimization (FGO). For the loosely-coupled integration, the linear and nonlinear least square methods are employed to obtain the well-performed single point positioning. The Allan-variance analysis is used to estimate the process noise covariance of INS. Besides, to reduce the computational load of nonlinear optimization in factor graph, this paper employs the IMU preintegration factor. The location performance of the proposed FGO method is compared with an extended Kalman Filter (EKF). The results show that the proposed tightly-coupled UWB/INS integration method can realize the better positioning performance than that of the conventional EKF in Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) combined indoor environments.

Distributed Extended Kalman Filtering Based Techniques for 3-D UAV Jamming Localization.

Wireless networks are vulnerable to jamming attacks. Jamming in wireless communication becomes a major research problem due to ease in Unmanned Aerial Vehicle (UAV) launching and blocking of communication channels. Jamming is a subset of Denial of Service Attack (DoS) and an intentional interference where the malicious node disrupts the wireless communication by increasing the noise at the receiver node through transmission interference signal towards the target channel. In this work, the considered jammer is a UAV hovering around the target area to block the communication channel between two transceivers. We proposed a three-dimensional (3-D) UAV jamming localization scheme to track and detect the jammer position at each time step by employing a single boundary node observer. For this purpose, we developed two distributed Extended Kalman Filter (EKF) based schemes: (1) the Distributed EKF (DEKF) scheme using the information of the received power from the jammer at a single nearby boundary node only and (2) Distance Ratio aided Distributed EKF (DEKF-DR) based scheme utilizing an edge node in addition to a single boundary node. Extensive simulations are conducted in order to evaluate the performance of the proposed distributed algorithms for a 3-D trajectory and compared with that of the conventional Centralized EKF (EKF-Centr) based method (which is also modified for the 3-D scenario). The results show the clear supremacy of the proposed distributed algorithms with much lesser complexity in contrast to the conventional EKF-Centr technique.

Comparison of SI-ANN and Extended Kalman Filter-Based Sensorless Speed Controls of a DC Motor

In this study, a speed sensorless algorithm was developed to control a single-link manipulator connected to DC motor. The armature voltage value can be obtained by using duty cycle information generated by the controller without using any sensor. Thus, the proposed system does not require any additional measurement sensor. This paper presents a study for artificial neural network (ANN)-based speed estimation algorithm which has a closed-loop speed control with the first and second inputs generated via support of system identification (SI). The second SI input was obtained as a simple transfer function with discrete time. The performances of the SI-input ANN structure and the conventional extended Kalman filter (EKF) method were compared in the MATLAB/Simulink environment. It was observed that the proposed method revealed better results than the EKF method in the steady and transient states. Thus, it was shown that high-performance sensorless speed control could be performed with SI-ANN structure in applications.

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.

A Parameter Extraction Method for the Li-Ion Batteries With Wide-Range Temperature Compensation

An accurate battery model is essential for precise estimation of battery performance indicators, such as state of charge (SoC), state of health (SoH), etc. It helps in determining the optimum energy management and therefore, optimum utilization of the battery capacity. Some of the battery model parameters may change with the variation of environmental conditions, such as operating temperature, and therefore, accurate temperature compensated model estimation is necessary to minimize the error in battery model and SoC estimation. This article presents a novel parameters extraction method for the Thevenin equivalent circuit model of Li-ion batteries considering their resiliency on temperature effect. The proposed approach represents each of the RC parallel circuits of the Thevenin-based equivalent circuit battery model as a first-order linear time-invariant (LTI) system. The resistance and capacitance values for each of the RC circuits in the model have been identified as the parameters of a standard LTI system using the system identification theory and represented them as the temperature-compensated model parameters. The proposed model can be applied to various applications, such as SoC, SoH estimation, and battery energy management. In order to demonstrate the suitability of the proposed modeling approach, the model is augmented with the conventional extended Kalman filter to enable accurate SoC estimation under varying operating temperatures. The accuracy and effectiveness of the proposed modeling approach and its suitability to enhance SoC estimation under a wide operating temperature range ( $-$ 5 to 45 $^\circ$ C) have been validated through laboratory experiments in the LabVIEW platform.

Heading angle estimation using rotating magnetometer for mobile robots under environmental magnetic disturbances

The heading angle plays a vital role in the localization and mapping of mobile robots. It is generally obtained by fusing measurements from gyroscope and magnetometer. However, ferromagnetic objects in real-world environments will disturb the magnetic field and will, therefore, cause significant errors in the estimated heading angles. This work proposes a novel method that employs a rotating magnetometer to detect ambient spatial magnetic disturbances and corrects the heading angle. The algorithm is based on the extended Kalman filter (EKF). Firstly, a criterion named spatial disturbance index is defined to characterize the disturbance quantitatively. And then the magnetometer measurement error covariance of the EKF is tuned adaptively according to the proposed criterion, so that a relatively reliable heading angle can be obtained even under strong spatial dynamic magnetic disturbances. In addition, the estimated heading angle can quickly restore to the correct value when the spatial disturbances disappear. The proposed algorithm has the benefit of adjusting the fusing degree of gyroscope and magnetometer adaptively to reject spatial disturbances and avoid the adverse impact of inherent gyroscope drift. The algorithm is evaluated under static and dynamic conditions in real-world indoor/outdoor environments. The results show that our algorithm outperforms the conventional EKF with fixed measurement error covariance and also the algorithm using only gyroscope.

Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective

Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Stratonovich stochasticity is embedded into a vector ‘bilinear’ time-varying stochastic differential equations. Then, coupled non-linear filtering equations are achieved. Finally, the non-linear filtering results are applied to an appealing bilinear stochastic Ćuk converter circuit. This paper also encompasses a system of coupled bilinear filtering equations for the vector input Brownian motion case. This paper brings the notions of systems theory, that is, bilinearity, Stratonovich stochasticity, non-linear filtering techniques and switched electrical networks together. Numerical simulation results are presented to demonstrate that the proposed bilinear filter can achieve much better and accurate filtering performance than the conventional Extended Kalman Filter (EKF).

Invariant extended Kalman filter on matrix Lie groups

We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the group configuration which, in turn, provides a uniform estimate of the region of convergence. The proposed IEKF differs from existing techniques in literature on the account that it is derived using minimal tools from differential geometry that simplifies its representation and derivation to a large extent. The filter error dynamics is defined on the Lie algebra directly instead of identifying the Lie algebra with an Euclidean space or defining the error dynamics in local coordinates using exponential map, and the associated differential Riccati equations are described on the corresponding space of linear operators using tensor algebra. The proposed filter is implemented for the attitude dynamics of the rigid body, which is a benchmark problem in control, and its performance is compared against a conventional extended Kalman filter (EKF). Numerical experiments support that the IEKF is computationally less intensive and gives better performance than the EKF.

Improved Pedestrian Positioning with Inertial Sensor Based on Adaptive Gradient Descent and Double-Constrained Extended Kalman Filter

The Foot-mounted Inertial Pedestrian-Positioning System (FIPPS) based on the Micro-Inertial Measurement Unit (MIMU) is a good choice for the forest fire fighters when the Global Navigation Satellite System is unavailable. Zero Velocity Update (ZUPT) provides a solution for reducing cumulative positioning errors caused by the integral calculation of the inertial navigation. However, the performance of ZUPT is highly affected by the low accuracy and high noise of the MIMU. The accuracy of conventional ZUPT for attitude alignment is reduced by the zero offset of acceleration and the drift of a gyroscope during the standing phase. An initial alignment algorithm based on Adaptive Gradient Descent Algorithm (AGDA) is proposed. In the stepping phase, the extended Kalman filter (EKF) is often used to correct attitude and position in track estimation. However, the measurement noise of the EKF is influenced by the high-frequency acceleration and angular velocity. Thus, the accuracy of the attitude and position will decrease. A double-constrained extended Kalman filtering (DEKF) is proposed. An adaptive parameter positively correlated with the acceleration and angular velocity is set, and the measurement noise in the DEKF is adaptively adjusted. The performance of the proposed method is verified by implementing the pedestrian test trajectory using MPU-9150 MIMU manufactured by InvenSense. The results show that the attitude error of the AGDA is 33.82% less than that of the conventional GDA. The attitude error of DEKF is 21.70% less than that of the conventional EKF. The experimental results verify the effectiveness and applicability of the proposed method.