Unscented Kalman Filter Research Articles

A novel nonlinear observer for inertial parameters of lightweight electric vehicle through adaptive dual unscented Kalman filter

A novel nonlinear observer for inertial parameters of lightweight electric vehicle through adaptive dual unscented Kalman filter

Interacting Multiple Model Estimators for Fault Detection in a Magnetorheological Damper.

This paper proposes a novel estimator for the purpose of fault detection and diagnosis. The interacting multiple model (IMM) strategy is effective for estimating the behaviour of systems with multiple operating modes. Each mode corresponds to a distinct mathematical model and is subject to a filtering process. This paper applies various model-based filters in combination with the IMM strategy. One such estimator employs the recently introduced extended sliding innovation filter (ESIF) known as the IMM-ESIF. The ESIF is an extension of the sliding innovation filter for nonlinear systems based on the sliding mode concept. In the presence of modeling uncertainties, the ESIF has been proven to be more robust compared to methods such as the extended Kalman filter (EKF). The novel IMM-ESIF strategy is also compared with the IMM strategy, which incorporates the unscented Kalman filter (UKF), referred to herein as IMM-UKF. While EKF uses Taylor series approximation to linearize the system model, the UKF uses sigma point to calculate the system's mean and covariance. The methods were applied to an experimental magnetorheological (MR) damper setup, which was designed for testing control and estimation theory. Magnetorheological dampers exhibit a diverse array of applications in the automotive and aerospace sectors, with particular relevance to attenuating vibrations through adaptive suspension systems. Applied to a magnetorheological (MR) damper with distinct operating modes determined by the damper's current, the results showcase the effectiveness of IMM-ESIF. In mixed operational conditions, IMM-ESIF demonstrates a notable 80% to 90% reduction in estimation error compared to its counterparts. Furthermore, it exhibits a 4% to 5% enhancement in correctly classifying operational modes, establishing IMM-ESIF as a promising and efficient alternative for adaptive estimation in electromechanical systems. The improved accuracy in estimating the system's behaviour, even amidst uncertainties and mixed operational scenarios, signifies the potential of IMM-ESIF to significantly enhance the overall robustness and efficiency of estimations.

Multisensor Integrated Autonomous Navigation Based on Intelligent Information Fusion

A major inadequacy of the Kalman filter is the necessity of accurate measurement models, which may not be possible in the case of complicated disturbances. A new solution to multisensor integrated autonomous navigation based on intelligent information fusion technology for launch vehicles is proposed in this paper, which can improve navigation performance based on the existing measurement models. Artificial neural networks (ANNs) are designed to discover the hidden relationship between the available data and trajectory parameters. The tracking, telemetry, and control system can provide centimeter-level accuracy of the launch vehicle after every flight. While postprocessing data is irrelevant to real-time navigation using traditional methods, it is crucial for ANNs to learn the rules of information fusion and identify the inaccuracy of the input variables. In this way, artificial-intelligence-modified trajectory parameters are expected to be closer to the truth value. The experimental results indicate that the proposed method can significantly improve navigation performance compared with the unscented Kalman filter, and ANNs can achieve good performance in various situations.

A Model-Based Bayesian Inference Approach for On-Board Monitoring of Rail Roughness Profiles: Application on Field Measurement Data of the Swiss Federal Railways Network

According to the International Union of Railways, railway networks count more than one million kilometers of tracks worldwide, a number that is to rise further as the goal is to promote rail transportation as a sustainable means to face the challenge of increased mobility. However, such a vast expansion further necessitates efficient and reliable infrastructure monitoring schemes able to guarantee the quality and safety of rail transportation. Traditional monitoring approaches, relying on visual inspection and portable measuring devices, cannot rise to the task as they do not allow for continuous inspection of extended portions of rail infrastructure. Therefore, mobile monitoring methodologies based on dedicated diagnostic vehicles have emerged as an alternative. Despite revolutionizing traditional monitoring methods, such vehicles are usually expensive and can only operate under the suspension of regular rail service. In this work, we propose an alternative approach for mobile sensing of railway infrastructure based on on-board monitoring data collected from low-cost vibration sensors, e.g., accelerometers, which can be mounted on in-service trains. Specifically, we focus on identifying the roughness profile of the tracks and propose a fusion of reduced-order vehicle models with a Bayesian inference approach for joint input-state estimation. To enhance the inference, we opt for a prior updating of the vehicle model parameters on the basis of an unscented Kalman filter and available measurements from a diagnostic vehicle. The key contributions of this work are (i) the consideration of the dynamic interaction between trains and tracks, which is usually ignored in rail roughness estimation, (ii) the adoption of reduced train vehicle models that decrease the computational effort of the identification task, (iii) the updating of the vehicle parameters to account for inconsistencies in the model used, and (iv) the application of the proposed methodology to actual acceleration measurements collected from a diagnostic vehicle of the Swiss Federal Railways network.

A data and physical model joint driven method for lithium-ion battery remaining useful life prediction under complex dynamic conditions

Accurate remaining useful life (RUL) prediction of batteries plays an important role in battery management. The existing methods mainly rely on the battery test data under ideal operating conditions to show good performance. However, the actual operating conditions of batteries are usually complex, which bring great challenges to the RUL prediction. To improve the accuracy and the generalization ability of RUL prediction method, a fusion method of electrochemical–thermal model (ECT) and unscented kalman filter (UKF) is proposed for lithium-ion battery. Firstly, an ECT–based capacity degradation model is established by coupling pseudo two dimensions (P2D) electrochemistry model, 3D thermal model and solid electrolyte interface (SEI) formation model. Secondly, the UKF method is used to update iteratively the parameters of model to improve its accuracy. Finally, several sets of operating data of lithium-ion battery under different conditions are used for RUL prediction, followed by the comparative analysis of different models and algorithms. As a result, the proposed fusion method not only exhibits better accuracy in RUL prediction under ideal conditions, but also shows excellent accuracy and generalization for other dynamic stochastic operating conditions.

Maximum capacity and state of health estimation based on equivalent circuit model for degraded battery

In real-time systems, state of health (SOH) and maximum capacity need to be updated regularly as battery degrades with time. Incorrect estimation of SOH or maximum capacity leads to inaccurate state of charge (SOC) estimation, especially for degraded batteries. Maximum capacity or SOH is usually obtained by constant-current discharging test, which is impractical in real-time battery management system (BMS). Therefore, it is meaningful to find an adaptive method to estimate SOH or maximum capacity in real-time BMS instead of discharging test. This paper proposes a two-step approach to estimate SOC and SOH. In the first step, SOC and battery electrical parameters (such as resistance, capacitor, etc.) are estimated simultaneously with fixed maximum capacity by using (dual) extended Kalman filter model. In the second step, the maximum capacity of degraded battery is estimated based on estimated electrical parameters using (dual) unscented Kalman filter, which rending estimated SOH. The above two step could be deployed on real-time applications to improve the accuracy of SOC estimation even when battery degrades.

Time‐varying reliability analysis based on hybrid Kalman filtering and probability density evolution

AbstractThe study introduces a novel approach for time‐varying reliability analysis of structures called “hybrid UKF‐PDEM” by integrating the unscented Kalman filter (UKF) and the probability density evolution method (PDEM). The UKF estimates the displacement, velocity, stiffness, and damping parameters of a structure at each time step subjected to dynamic loading for structural damage quantification. The estimated parameters at each time step are then input into the PDEM to calculate the time‐varying probability density function (PDF) of the estimated states. The estimated PDF is used to update the uncertainty matrix of the estimated states in each iteration and to determine the time‐varying reliability curves of the structure. To demonstrate the effectiveness of the proposed method, we applied it to a numerical model of a three‐degree‐of‐freedom system and a full‐scale seven‐story building with different damage scenarios. The method is used to estimate the level of damage and calculate the corresponding reliability curve of the system over time for each damage scenario, utilizing the estimated structural responses and stiffness values. The extracted reliability values for each damage scenario follow the level of damage over time. This study shows that the newly developed method is computationally efficient for building a digital twin and enables real‐time damage identification and reliability analysis in various structural systems. The method's applicability to different types of structures highlights its versatility and potential for widespread use in assessing the integrity of buildings and infrastructure.

Open circuit voltage - state of charge curve calibration by redefining max–min bounds for lithium-ion batteries

The relationship between open circuit voltage (OCV) and state of charge (SoC) is essential for SoC estimation of lithium-ion batteries, which can be secured by either low-current OCV test or incremental OCV test, with incremental OCV test demonstrating better results. Nevertheless, low current always leads to a discharge capacity that is inconsistent with maximum available capacity, which is a key parameter in SoC estimation. Therefore, the resultant OCV-SoC curve fails to provide a consistent SoC range and thus affects SoC estimation. In this paper, OCV-SoC curves obtained from low-current OCV tests are calibrated by redefining max–min bounds to improve SoC estimation accuracy. Max–min bounds of SoC are redefined by measuring, calculating and resetting upper and lower cut-off voltages of the OCV-SoC curve. Based on second-order RC model, model parameters are identified online and adaptive square-root unscented Kalman filter (ASRUKF) algorithm is introduced to perform SoC estimation, which is proved to be precise and adaptive. The calibrated OCV-SoC curve achieves an overall better SoC estimation performance than that obtained from the low-current OCV test and incremental OCV test, which is validated by experiments of LiNiMnCoO2 (NMC) batteries at 0°C and 25°C.

Adaptive Bayesian filter with data-driven sparse state space model for seismic response estimation

The present work proposes a seismic response estimation framework for post-earthquake structural condition assessment via acceleration measurements. An augmented sparse state space model is first derived to represent the underlying governing equations of the system of interest with hysteresis nonlinearity. A Bayesian filter is then utilized to provide the displacement estimate under an earthquake excitation by fusing the identified sparse state space model with the measured system acceleration. To avoid subjective assumptions on the process and observation noises in the Bayesian filter, a double-loop process is proposed, where the inner loop is an online Bayesian filtering by the unscented Kalman filter with Robbins-Monro algorithm, while the outer loop is an offline Bayesian updating by the transitional Markov chain Monte Carlo method. The feasibility of the framework is demonstrated on a simple illustrative example and a followed engineering application to the state estimation of a bridge pier finite element model. The results indicate the capability of the framework to properly infer the system displacement, including its residual components.

Utilizing Probabilistic Maps and Unscented-Kalman-Filtering-Based Sensor Fusion for Real-Time Monte Carlo Localization

An autonomous car must know where it is with high precision in order to maneuver safely and reliably in both urban and highway environments. Thus, in this paper, a reliable and relatively precise position estimation (localization) technique for autonomous vehicles is proposed and implemented. In dealing with the obtained sensory data or given knowledge about the vehicle’s surroundings, the proposed method takes a probabilistic approach. In this approach, the involved probability densities are expressed by keeping a collection of samples selected at random from them (Monte Carlo simulation). Consequently, this Monte Carlo sampling allows the resultant position estimates to be represented with any arbitrary distribution, not only a Gaussian one. The selected technique to implement this Monte-Carlo-based localization is Bayesian filtering with particle-based density representations (i.e., particle filters). The employed particle filter receives the surrounding object ranges from a carefully tuned Unscented Kalman Filter (UKF) that is used to fuse radar and lidar sensory readings. The sensory readings are used to detect pole-like static objects in the egocar’s surroundings and compare them to the ones that exist in a supplied detailed reference map that contains pole-like landmarks that are produced offline and extracted from a 3D lidar scan. Comprehensive simulation tests were conducted to evaluate the outcome of the proposed technique in both lateral and longitudinal localization. The results show that the proposed technique outperforms the other techniques in terms of smaller lateral and longitudinal mean position errors.

Systematic use of nonlinear data filtering methods in forecasting tasks

The article describes an approach to the systematic use of nonlinear data filtering methods in tasks of intelligent data analysis and machine learning. The concepts of filtering and non-linear filtering are considered. The analysis of modern methods of optimal and probabilistic nonlinear filtering of statistical data and the peculiarities of their application in solving the problems of estimating the states of dynamic systems is carried out. The application of the Kalman filter and its variants for solving nonlinear filtering problems is analysed. The classification of nonlinear filtering methods is given. In the basis of the classification are digital, optimal and probabilistic filters. Non-recursive and recursive digital filters are studied. The formulation of the problem of optimal filtering based on the Kalman filter is considered. The filtering equation for a free dynamic system based on the state space model of a discrete system is given. The extended Kalman filter and its modifications are considered. The Bayesian method of estimating the state of a nonlinear stochastic system is presented. The problem of linear and nonlinear probabilistic filtering is considered. Three filters are considered as examples of probabilistic filters: an unscented Kalman filter, a point mass filter, and a granular filter. The granular filtering algorithm and its modifications are considered in detail. The architecture of the information-analytical system for solving forecasting problems has been developed. The system consists of the following main components: user interface, information storage subsystem, data analysis and pre-processing subsystem, modelling subsystem, forecast construction and evaluation subsystem, visualization subsystem. As an example of forecasting based on the systematic use of non-linear filtering methods, the task of forecasting the prices of Google shares is considered. A comparison of the quality assessment results of basic models and forecast values without filtering and with different options for applying filters was carried out. To improve the quality of forecasting based on prepared data and based on nonlinear filtering methods, a method based on combined forecasts was used to solve the forecasting problem. The results of forecasting using the combined model are presented

Correction of Misalignment Errors in the Integrated GNSS and Accelerometer System for Structural Displacement Monitoring

Structural health monitoring (SHM) systems are widely deployed to monitor the dynamic behaviors of large civil infrastructures such as bridges and tall buildings. Global Navigation Satellite System- (GNSS-) based technologies are often a key component in such an SHM system considering the unique capability of GNSS in determining real-time displacements. GNSS often integrates with an accelerometer to achieve complementary advantages. However, due to the various error sources in GNSS measurements and accelerometer, accuracies of GNSS and accelerometer fusion results often cannot meet the requirements of SHM. We propose to integrate a multi-antenna GNSS and an accelerometer with an unscented multi-rate Kalman filter (UMRKF-MA) to correct the system misalignment errors between the sensors, aiming to produce a much more accurate real-time displacement measurement technology for monitoring large civil infrastructures. Extensive experiments with datasets gathered using a shaking table have indicated that the proposed method was able to improve the accuracy of real-time displacement measurements by up to about 40–65% compared to some existing approaches, and that a 1 mm level of real-time monitoring of displacements could be achieved with the method. The method has also been applied to process a dataset from a real-world long-span bridge when heavy vehicles passed through the bridge in a loading test and significantly improved results were obtained.

Adaptive hybrid Kalman filter for attitude motion parameters estimation of space non-cooperative tumbling target

Attitude motion parameters estimation of the space non-cooperative tumbling target is the premise of the on-orbit target capture task. However, existing methods cannot balance the estimation accuracy and efficiency. In this paper, an adaptive hybrid Kalman filter is presented to estimate the attitude, angular velocity and inertia motion parameters of the space non-cooperative tumbling target. First, the dynamic model of the non-cooperative tumbling target is derived, and the nonlinear discrete state-space equation is obtained. Then, a hybrid Kalman filter is designed by combining the extended Kalman filter and the unscented Kalman filter. The adaptive technique is introduced to track time-varying uncertain measurement noise caused by complex space disturbances. After that, based on the first-order linearization technique, the sufficient condition for the local convergence of the proposed method is proved. Finally, the numerical simulation experiment was conducted to compare the proposed method with the adaptive extended Kalman filter and the adaptive unscented Kalman filter. The experimental results show that the estimation accuracy of the proposed method is much higher than that of the adaptive extended Kalman filter and slightly lower than that of the adaptive unscented Kalman filter, and the iteration-average Central-Processing-Unit time is 64.2% smaller than that of the adaptive unscented Kalman filter and slightly longer than that of the adaptive extended Kalman filter. The proposed method achieves a much higher accuracy with a slight loss of iteration-average Central-Processing-Unit time.

Heating and cooling supply estimation to control buildings temperature using resistor-capacitor thermal model, unscented kalman filter, and nonlinear least square method.

This research provides a valuable contribution to modern building industry professionals by offering a precise method for estimating heating and cooling supply for temperature control in buildings. By equipping practitioners with an effective tool to optimize energy management, this study addresses a critical aspect of building performance. The practical case studies demonstrate the versatility and applicability of this approach in real-world scenarios. In a world increasingly prioritizing energy efficiency and sustainability, this research empowers professionals to make informed decisions, enhance building performance, and contribute to a greener and more sustainable future, all within a concise and actionable framework.

Novel Unscented Kalman Filter-based method to assess the thermal behavior of carbon brake discs for high-performance motorcycles

In the past few decades, braking systems with carbon discs have become the dominant technology for many racing applications, such as in the MotoGP class. Indeed, they provide higher friction coefficients. Moreover, thanks to their lightweight materials (with respect to conventional steel brakes), the unsprung masses and the gyroscopic effects can be reduced. Therefore, the motorcycle dynamic performance can be significantly improved. The usage of carbon brakes requires a very accurate assessment of their thermal behavior. In fact, although their operating temperature in real racing conditions may cover a wide range, their optimal braking performance can be achieved only within a relatively narrow temperature range. This work focuses on the development of the Unscented Kalman Filter (UKF) algorithm as a suitable mathematical tool for assessing the temperature gradient of the carbon disc mounted on the motorcycles competing in the MotoGP™ world championship. A one-dimensional (1D) finite element (FE) model of the disc is developed to provide the a priori state estimate that the filter will combine with the information measured by the temperature sensor available on board to compute the optimal posterior temperature estimation. Besides estimating temperature, the UKF is also exploited to identify the convection heat transfer coefficient (h) of the disc, which is a fundamental parameter for a proper model calibration.

State of charge estimation for lithium-ion battery based on improved online parameters identification and adaptive square root unscented Kalman filter

Accurate state of charge estimation is crucial for the safe and efficient operation of lithium-ion batteries. The Kalman filtering algorithm has been widely used in state-of-charge (SOC) estimation. To solve the problem of filter divergence and sensitivity to noise, the joint SOC estimation method is proposed to achieve accurate and robust estimation of SOC, which is composed of improved variable forgetting factor recursive least square (VFFRLS) and adaptive square root unscented Kalman filter (ASRUKF). The improved VFFRLS method uses the mean square value of the multi-step voltage residual instead of the traditional one-step voltage residual to correct the forgetting factor, and the ASRUKF improves the accuracy and stability of estimation by introducing the square root method and the adaptive method. Estimations under three typical working conditions are quantitatively studied, the experimental results show that the proposed method has good accuracy and stability. The maximum mean absolute error (MAE) is 0.0061, and the corresponding root mean square error (RMSE) is 0.0090. Furthermore, the experimental verification after adding offset errors to measured data shows that the proposed method can still track the reference SOC with satisfactory accuracy in the range of voltage offset error less than ±0.5 % and current offset error less than ±3 %, both for the constant offset error and the random error, and the SOC error is less than 2.5 %.

Equivalent circuit modeling and state-of-charge estimation of lithium titanate battery under low ambient pressure

The low ambient pressure during the flight of aircraft has a significant impact on the performance and safety of the onboard power battery. In order to ensure the safe operation of the battery system, it is very important to accurately estimate and manage the state-of-charge (SOC) of the battery. In this work, the equivalent circuit modeling (ECM) of lithium titanate battery (LTB) is studied in detail, and the influence of analog circuit model parameters in low ambient pressures is discussed for the first time. The forgetting factor recursive least square algorithm is introduced to accurately identify the ECM parameters of the LTB under different pressures online. The particle swarm optimization algorithm is innovatively proposed to optimize the covariance matrix of the Kalman filter algorithm. The verification shows that the root mean square error of the ECM of LTB under different ambient pressures is less than 0.025. In the SOC estimation process, the noise covariance matrixes of the extended Kalman filter and the unscented Kalman filter are optimized by the particle swarm algorithm. The optimized SOC estimation absolute error is less than 3 %, especially at 96 kPa and 30 kPa, where the absolute error is less than 2 %.

Co-estimation of maximum available capacity and state-of-charge for lithium-ion batteries in multi-operating mode with temperature and degradation state adaptivity

Accurate state of charge (SOC) estimation is critical for battery management systems (BMS). A new SOC estimation framework is developed, containing four modules: battery modeling, parameter identification, SOC estimation, and capacity estimation. It mainly makes three improvements to improve the adaptability. In the parameter identification module, an improved forgetting factor parameters identification method is proposed to obtain model parameters with high precision. For SOC estimation, considering the impact of noise on SOC estimation, an adaptive square root unscented Kalman filter is proposed, which can solve the divergence issue caused by inappropriate noise matrix iteration. Moreover, a weighted recursive least squares algorithm is developed to estimate the maximum available capacity and feed the result back into the SOC estimation module to improve the estimation accuracy. The experimental results show that the proposed framework can obtain high-precision SOC estimation results under different temperatures and aging conditions.

Wi-Fi throughput estimation and forecasting for vehicle-to-infrastructure communication

Vehicles increasingly need to connect to external networking infrastructure, to support applications such as over-the-air updates, edge computing, and even autonomous driving. The ubiquity of IEEE 802.11 Wi-Fi makes it ideal for opportunistic vehicular access. However, that ubiquity also creates a problem of choice. In a heterogeneous Wi-Fi environment, where different networks coexist, it becomes important for vehicles to be able to pick the best-performing one. Focusing on delay-insensitive traffic, we equate network performance with throughput. To inform network selection we aim to first estimate current throughput, and then forecast its evolution through time. In order to avoid introducing load onto the network, we estimate throughput using only passively observable variables such as signal strength. We used Symbolic Regression (SR) and an Unscented Kalman Filter (UKF) to develop a computationally inexpensive estimation model — UKF-SR. We trained and tested this model using experimental data featuring 802.11n, ac, and ad networks. UKF-SR proved competitive against more expensive models such as shallow neural networks. To predict future throughput, we explored both general time-series forecasting models such as Autoregressive Integrated Moving Average (ARIMA), and domain-specific ones based on mobility information. The latter clusters historical throughput according to attributes such as vehicle position and direction of movement, using the cluster’s average as the forecast. An evaluation using experimental data showed the mobility-based models to meaningfully outperform general forecasting.

Adaptive Truck Platooning with Drones: A Decentralized Approach for Highway Monitoring

The increasing demand for efficient and safe transportation systems has led to the development of autonomous vehicles and vehicle platooning. Truck platooning, in particular, offers numerous benefits, such as reduced fuel consumption, enhanced traffic flow, and increased safety. In this paper, we present a drone-based decentralized framework for truck platooning in highway monitoring scenarios. Our approach employs multiple drones, which communicate with the trucks and make real-time decisions on whether to form a platoon or not, leveraging Model Predictive Control (MPC) and Unscented Kalman Filter (UKF) for drone formation control. The proposed framework integrates a simple truck model in the existing drone-based simulation, addressing the truck dynamics and constraints for practical applicability. Simulation results demonstrate the effectiveness of our approach in maintaining the desired platoon formations while ensuring collision avoidance and adhering to the vehicle constraints. This innovative drone-based truck platooning system has the potential to significantly improve highway monitoring efficiency, traffic management, and safety. Our drone-based truck platooning system is primarily designed for implementation in highway monitoring and management scenarios, where its enhanced communication and real-time decision-making capabilities can significantly contribute to traffic efficiency and safety. Future work may focus on field trials to validate the system in real-world conditions and further refine the algorithms based on practical feedback and evolving vehicular technologies.