Extended Kalman Filter Approach Research Articles

LEO-Enhanced GNSS/INS Tightly Coupled Integration Based on Factor Graph Optimization in the Urban Environment

Precision point positioning (PPP) utilizing the Global Navigation Satellite System (GNSS) is a traditional and widely employed technology. Its performance is susceptible to observation discontinuities and unfavorable geometric configurations. Consequently, the integration of the Inertial Navigation System (INS) and GNSS makes full use of their respective advantages and effectively mitigates the limitations of GNSS positioning. However, the GNSS/INS integration faces significant challenges in complex and harsh urban environments. In recent years, the geometry between the user and the satellite has been effectively improved with the advent of lower-orbits and faster-speed Low Earth Orbit (LEO) satellites. This enhancement provides more observation data, opening up new possibilities and opportunities for high-precision positioning. Meanwhile, in contrast to the traditional extended Kalman filter (EKF) approach, the performance of the LEO-enhanced GNSS/INS tightly coupled integration (TCI) can be significantly improved by employing the factor graph optimization (FGO) method with multiple iterations to achieve stable estimation. In this study, LEO data and the FGO method were employed to enhance the GNSS/INS TCI. To validate the effectiveness of the method, vehicle data and simulated LEO observations were subjected to thorough analysis. The results suggest that the integration of LEO data significantly enhances the positioning accuracy and convergence speed of the GNSS/INS TCI. In contrast to the FGO GNSS/INS TCI without LEO enhancement, the average enhancement effect of the LEO is 22.16%, 7.58%, and 10.13% in the north, east, and vertical directions, respectively. Furthermore, the average root mean square error (RMSE) of the LEO-enhanced FGO GNSS/INS TCI is 0.63 m, 1.21 m, and 0.85 m in the north, east, and vertical directions, respectively, representing an average improvement of 41.91%, 13.66%, and 2.52% over the traditional EKF method. Meanwhile, the simulation results demonstrate that LEO data and the FGO method effectively enhance the positioning and convergence performance of GNSS/INS TCI in GNSS-challenged environments (tall buildings, viaducts, underground tunnels, and wooded areas).

Estimating the Optimal State of Charge for Electric Car Batteries Using an Extended Kalman Filter

The efficient management of battery state of charge (SOC) is crucial for maximizing the performance, range, and longevity of electric vehicle (EV) batteries. This paper presents a novel approach for estimating the optimal state of charge of electric car batteries using an Extended Kalman Filter (EKF). The EKF is a recursive algorithm that combines measurements from various sensors with a dynamic battery model to estimate the current SOC and predict future SOC values with high accuracy. The paper provides a detailed explanation of the EKF algorithm and its application to battery SOC estimation, highlighting its ability to handle nonlinearities, uncertainties, and measurement noise inherent in battery systems. Furthermore, this research presents a simulation-based validation of the proposed EKF approach using real-world driving data from electric vehicles. The simulation results demonstrate the effectiveness of the EKF algorithm in accurately estimating the SOC of electric car batteries under various operating conditions, including different driving patterns, temperatures, and battery degradation scenarios.

Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory.

This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group (SE(3)) and 3-sphere space (S3) are used to express the pose (position and attitude) and misalignment, respectively. SE(3) contains position and attitude transformation matrices, and S3 comprises unit quaternions. The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). The previous EKF approach without Lie theory is based on the assumption that a non-differentiable space can be approximated as a differentiable space when the increments are sufficiently small. On the contrary, the proposed Lie theory approach enables exact differentiation in a differentiable space, thus enhances the accuracy of the navigation. Furthermore, the convergence and stability of the internal parameters, such as the Kalman gain and measurement innovation, are improved.

Nonlinear roll damping coefficients and natural frequency estimation via augmented extended Kalman filtering for floating body

ABSTRACT The nonlinear roll damping coefficients and natural frequency of a floating body are discussed in this article using an augmented Extended Kalman Filtering (EKF) method. This paper presents a non-linear model-based observer for the combined estimation of free roll decay motion states and damping coefficients. The identification framework uses an improved extended Kalman filter (EKF) to deal with model parameter variability and noisy measurement input. The estimated error was compared to the theoretical results obtained from the covariance matrix for filtering correctness. It is found that the nonlinear damping coefficients and natural frequency obtained from the EKF approach are a more realistic representation of the roll dynamics from the general estimation procedure given by the literature. The proposed method also has the built-in capability to remove random noise from the measured roll. The influence of noise levels in the measurements on the identification accuracy was investigated and discussed.

Reduce state of charge estimation errors with an extended Kalman filter algorithm

Li-ion batteries (LiBs) are accurately estimated under varying operating conditions and external influences using extended Kalman filtering (EKF). Estimating the state of charge (SOC) is essential for enhancing battery efficiency, though complexities and unpredictability present obstacles. To address this issue, the paper proposes a second-order resistance-capacitance (RC) battery model and derives the EKF algorithm from it. The EKF approach is chosen for its ability to handle complex battery behaviors. Through extensive evaluation using a Simulink MATLAB program, the proposed EKF algorithm demonstrates remarkable accuracy and robustness in SOC estimation. The root mean square error (RMSE) analysis shows that SOC estimation errors range from only 0.30% to 2.47%, indicating substantial improvement over conventional methods. These results demonstrate the effectiveness of an EKF-based approach in overcoming external influences and providing precise SOC estimations to optimize battery management. In addition to enhancing battery performance, the results of the study may lead to the development of more reliable energy storage systems in the future. This will contribute to the wider adoption of LiBs in various applications.

The adaptive extended kalman filter approach for the Lotka-Volterra model and application to economic variables

The adaptive extended kalman filter approach for the Lotka-Volterra model and application to economic variables

A Customized Extended Kalman Filter for Removing the Impact of the Magnetometer's Measurements on Inclination Determination.

Normally, a three-dimensional orientation determination algorithm that is used in a magnetic and inertial measurement unit calculates the inclination (including both the pitch and roll) of rigid bodies by fusing the measurements of the gyroscope, as well as the measurements of both the accelerometer and the magnetometer. The measurements of the magnetometer can be helpful in improving the inclination estimation accuracy; however, once the measurements of the magnetometer are disturbed by ferromagnetic materials, the inclination estimation accuracy could be significantly decreased. Hence, a better approach should be followed in terms of not employing the measurements of the magnetometer for inclination determination. In order to achieve this goal, the component of the measurement of the magnetometer that is used for the improvement of the inclination estimation accuracy, along with the measurement of the accelerometer at each sampling time instant, is abandoned. Consequently, the remaining component of the measurement of the magnetometer, which is perpendicular to the measurement of the accelerometer, is used for the azimuth determination. After applying this process, the extended Kalman filter (EKF) is proposed for the inclination and azimuth estimations. Through experiments, the EKF is compared with three algorithms that were recently proposed with the same objective as this work, and the extracted outcomes show that the EKF approach clearly outperforms these three algorithms.

Partition‐based distributed extended Kalman filter for large‐scale nonlinear processes with application to chemical and wastewater treatment processes

AbstractIn this article, we address a partition‐based distributed state estimation problem for large‐scale general nonlinear processes by proposing a Kalman‐based approach. First, we formulate a linear full‐information estimation design within a distributed framework as the basis for developing our approach. Second, the analytical solution to the local optimization problems associated with the formulated distributed full‐information design is established, in the form of a recursive distributed Kalman filter algorithm. Then, the linear distributed Kalman filter is extended to the nonlinear context by incorporating successive linearization of nonlinear subsystem models, and the proposed distributed extended Kalman filter approach is formulated. We conduct rigorous analysis and prove the stability of the estimation error dynamics provided by the proposed method for general nonlinear processes consisting of interconnected subsystems. A chemical process example is used to illustrate the effectiveness of the proposed method and to justify the validity of the theoretical findings. In addition, the proposed method is applied to a wastewater treatment process for estimating the full‐state of the process with 145 state variables.

Estimation of nonlinear mixed-effects continuous-time models using the continuous-discrete extended Kalman filter.

Many intensive longitudinal measurements are collected at irregularly spaced time intervals, and involve complex, possibly nonlinear and heterogeneous patterns of change. Effective modelling of such change processes requires continuous-time differential equation models that may be nonlinear and include mixed effects in the parameters. One approach of fitting such models is to define random effect variables as additional latent variables in a stochastic differential equation (SDE) model of choice, and use estimation algorithms designed for fitting SDE models, such as the continuous-discrete extended Kalman filter (CDEKF) approach implemented in the dynr R package, to estimate the random effect variables as latent variables. However, this approach's efficacy and identification constraints in handling mixed-effects SDE models have not been investigated. In the current study, we analytically inspect the identification constraints of using the CDEKF approach to fit nonlinear mixed-effects SDE models; extend a published model of emotions to a nonlinear mixed-effects SDE model as an example, and fit it to a set of irregularly spaced ecological momentary assessment data; and evaluate the feasibility of the proposed approach to fit the model through a Monte Carlo simulation study. Results show that the proposed approach produces reasonable parameter and standard error estimates when some identification constraint is met. We address the effects of sample size, process noise variance, and data spacing conditions on estimation results.

Multi-directional Interaction Force Control with an Aerial Manipulator Under External Disturbances

To improve accuracy and robustness of interactive aerial robots, the knowledge of the forces acting on the platform is of uttermost importance. The robot should distinguish interaction forces from external disturbances in order to be compliant with the firsts and reject the seconds. This represents a challenge since disturbances might be of different nature (physical contact, aerodynamic, modeling errors) and be applied to different points of the robot. This work presents a new hbox {extended Kalman filter (EKF)} based estimator for both external disturbance and interaction forces. The estimator fuses information coming from the system’s dynamic model and it’s state with wrench measurements coming from a Force-Torque sensor. This allows for robust interaction control at the tool’s tip even in presence of external disturbance wrenches acting on the platform. We employ the filter estimates in a novel hybrid force/motion controller to perform force tracking not only along the tool direction, but from any platform’s orientation, without losing the stability of the pose controller. The proposed framework is extensively tested on an omnidirectional aerial manipulator (AM) performing push and slide operations and transitioning between different interaction surfaces, while subject to external disturbances. The experiments are done equipping the AM with two different tools: a rigid interaction stick and an actuated delta manipulator, showing the generality of the approach. Moreover, the estimation results are compared to a state-of-the-art momentum-based estimator, clearly showing the superiority of the EKF approach.

Early estimation of the number of hidden HIV infected subjects: An extended Kalman filter approach

In the last decades several epidemic emergencies have been affecting the world, influencing the social relationships, the economics and the habits. In particular, starting in the early '80, the Acquired Immunodeficiency Syndrome, AIDS, is representing one of the most worrying sanitary emergency, that has caused up to now more than 25 million of dead patients. The infection is caused by the Human Immunodeficiency Virus, HIV, that may be transmitted by body fluids; therefore with wise behaviours the epidemic spread could rapidly be contained. This sanitary emergency is peculiar for the long incubation time: it can reach even 10 years, a long period in which the individual can unconsciously infect other subjects. The identification of the number of infected unaware people, mandatory to define suitable containment measures, is here obtained by using the extended Kalman filter applied to a noisy model in which, reasonably, only the number of infected diagnosed patients is available. Numerical simulations and real data analysis support the effectiveness of the approach.

Extended Kalman filter for fish weight estimation using augmented fish population growth model*

The fish weight, which indicates the growth rate of fish, is a crucial factor that optimizes the feeding rate and shapes the life history of fish in recirculating aquaculture systems. Estimating or predicting fish weight is essential for achieving better control of the output of an aquaculture system. However, many difficulties arise from the lack of direct measurement of fish weight. Currently, aquaculture sensors that directly estimate the fish's weight are unavailable. Additionally, the fish growth model that relies on the fish weight is affected by various environmental factors like water temperature, dissolved oxygen, salinity, and light, increasing the difficulty in estimating the weight. This paper proposes an extended Kalman filter approach for assessing the fish weight from directly available measurements of the fish stocking density and dissolved oxygen. The extended Kalman approach relies on a new version of the fish population growth model, which includes the fish population and dissolved oxygen dynamics. The simulation results demonstrate that the extended Kalman filter algorithm achieves good weight estimation in the nominal case and the presence of process and measurement noises.

Brake Pressure Estimation of the Integrated Braking System Considering Vehicle Dynamics

The integrated braking control system (IBC) has become one of the most popular brake-by-wire (BBW) solutions due to its compactness and versatility. Accurate monitoring of wheel cylinder pressure in real time is the basis for brake pressure control, and pressure estimation is a low-cost and reliable method. However, the IBC is an electromechanical hydraulic coupling system that has significant nonlinear behaviors; moreover, vehicle dynamics also have a critical impact on the accuracy of pressure estimation. To solve this problem, this paper proposes a novel adaptive extended Kalman filter (EKF) approach that combines a hydraulic model and a single-wheel model. This novel strategy has better estimation than the hydraulic model when the pressure is accurately estimated by the single-wheel model, while when the single-wheel model is not accurate, the EKF degrades to the hydraulic model. Finally, vehicle experimental data under high- and low-mu braking are collected. The pressure estimation error of the EKF is within 0.4 MPa in the low-mu road and 2 MPa in the high-mu road. It is proven that the proposed pressure estimation strategy is highly effective.

Experimental Validation of State of Charge Estimation by Extended Kalman Filter and Modified Coulomb Counting

The operation of batteries in energy storage systems (SAE) is controlled by the battery management system (BMS). Within the scope of research related to the functions of the BMS, there is attention to the methods of estimating the state of charge (SOC) that use state estimators. Among the estimators, there is the algorithm known as the extended Kalman filter (EKF). This work proposes the implementation of the EKF for SOC estimation of a lithium ion 18650 single-cell battery, with experimental validation. The algorithm is embedded in BMS composed of Arduino MEGA 2560 microcontroller and auxiliary hardware. The battery is modeled using a simple model, which aims to facilitate implementation in embedded systems. The results revealed that the SOC estimation via EKF embedded in BMS showed maximum errors around 4%, a result compatible with other references in the literature. Based on the EKF approach, an alternative method, called a modified Coulomb counting, was defined, which uses parameters calculated in the EKF to establish a adaptive Coulomb counting to the unknown initial SOC. This new method is also capable of reducing estimation fluctuations, a common feature found in the EKF implementation. The use of the modified counting proved to be useful in several cases, often reducing the maximum estimation error to values less than 1%. Finally, the use of the simple model with EKF proved to be adequate in terms of the balance between precision and simplicity.

State of charge estimation of lithium‐ion battery based on extended Kalman filter and unscented Kalman filter techniques

AbstractLithium‐ion batteries (LIBs) are currently the most widely used energy storage technologies in electric vehicles (EVs) due to their higher power density, greater energy density, longer life, fast charging capabilities, and low discharge rate. The brain of rechargeable batteries is referred to be the battery management system (BMS). The operation of the battery is monitored & regulated by an electronic system called BMS. Most significantly, it prevents the battery from exceeding its safety limits. One of the important parameters of BMS is the state of charge (SOC); it determines the battery's remaining capacity of accessible stored energy, battery lifespan, and cell balancing. As a result, an accurate SOC calculation is essential for BMS, and it is used for safer operations that avoid overcharging and discharging for the optimum battery life. The primary ambition of this article is to find an accurate and robust SOC estimation based on extended Kalman filter (EKF) and unscented Kalman filter (UKF) techniques. RMS error, average error, minimum error, and maximum error are used to compare the EKF method and UKF method. Two resistor‐capacitor (2RC) equivalent circuit model has been considered for the dynamic performance of the battery. The waveforms are displayed, and errors are simulated for SOC estimate using the EKF and UKF algorithms, taking the same initial SOC into consideration at a time. The UKF algorithm outperforms the EKF approach in terms of dynamic results when comparing the two methods.

Lebesgue Sampling-Based Li-Ion Battery Simplified First Principle Model for SOC Estimation and RDT Prediction

The state-of-charge (SOC) estimation and remaining-dischargeable-time (RDT) prediction are critical and challenging to safe operation of Li-ion batteries. The main challenges are the limited accuracy of traditional equivalent circuit model and computation-inefficiency of electrochemical battery models. To address this problem, this article proposes a Lebesgue-sampling-based extended Kalman filter (LS-EKF) approach that integrates the high fidelity of a simplified first principle (SFP) model with the low computation of Lebesgue sampling (LS) in a Bayesian estimation framework. In this framework, the SFP model is first introduced along with its design and validation. The LS-EKF is employed with the SFP model to estimate the SOC and predict the RDT. The proposed method is verified with a series of experiments under different operating conditions. The results and comparisons demonstrate the effectiveness of the proposed method in terms of the accuracy of estimation and prediction, as well as the computational efficiency.

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.

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.

State estimation algorithms for electric vehicle 48 V battery management system

The estimation of the State of Charge (SOC) is the most important function of the battery management system (BMS) of a vehicle. The algorithms for this estimation are conventionally based on adaptive methods but now improved with adaptive and conventional methods. The paper presents SOC estimation based on second order equivalent circuit and open circuit voltage-based capacity estimation models with extended Kalman filter approach for accurate estimation at pack level simulated in MATLAB. The BMS measures the voltage, current and temperature of the battery pack. The estimation of the equivalent circuit parameters is done using a nonlinear least squares solver from the measured quantities of the pack. The equivalent circuit parameter estimation is done using real time hybrid pulse power characterization (HPPC) data and the drive cycle data. The test data for the look up table is for charging and discharging at C/50 of a Lithium Iron Phosphate (LFP) chemistry at pack level. The SOC estimation using modified Leunberger observer with dynamic observer gain and extended Kalman filter algorithm has been tested for 0.1C and 0.5C rates. With input data available at 25 °C the accuracy for SOC estimation is 95%. With data from different temperatures the accuracy improved to 98%.

Extended Kalman Filter State Estimation for Aerial Continuum Manipulation Systems

The primary goal of this letter is to address the state estimation problem for dual-arm tendon-driven aerial continuum manipulation systems (ACMSs). While the state estimation problem for conventional rigid aerial manipulation systems (AMSs) has been addressed, parameter estimation remains a significant challenge for the recently introduced ACMS platform. Compared to AMSs that utilize arms’ encoder data, ACMSs with flexible arms are not equipped with such sensors. As a result of the requirement for external sensors such as vision systems, measurement challenges may arise in ACMSs cases. Additionally, the dynamics of ACMSs are substantially more complicated, coupled, and nonlinear, posing additional barriers to tackling the estimating problem at hand. This letter proposes integrating deep neural networks with the extended Kalman filter (EKF) technique to enable real-time applications of the method. Simulation results demonstrate the performance of the suggested learning-based EKF approach.