Kalman Filter Research Articles

A position-free control strategy in the full speed domain based on an electro-hydraulic pump

The electric plunger hydraulic pump plays a crucial role in hydraulic transmission technology by integrating an electric motor and a hydraulic pump. The main objectives in designing such devices are to improve efficiency, achieve miniaturization, and promote environmental sustainability. This paper introduces a speed control strategy for an electric hydraulic pump that operates across its entire speed range without relying on position sensor feedback. We begin by establishing the overall model of the electric hydraulic pump and motor characteristics under different operating conditions. Next, we employ a high-frequency injection control method to enable the electric hydraulic pump to start at zero-speed or low-speed states. Additionally, the optimized extended Kalman filtering control method enhances the robustness and tracking performance of the electric hydraulic pump in the medium to high-speed range. Finally, considering the motor characteristics under different operating conditions, we achieve sensorless control of the electric hydraulic pump across the full speed range. Our proposed control strategy provides a promising solution for the control of electric plunger hydraulic pumps, with widespread industrial applications.

Assimilation of ground-based GNSS data using a local ensemble Kalman filter

Tropical cyclones become increasingly nonlinear and dynamically unstable in high-resolution models. The initial conditions are typically sub-optimal, leaving scope to improve the accuracy of forecasts with improved data assimilation. Simultaneously, the lack of real ground-based GNSS observations over the ocean poses significant challenges when evaluating the assimilation results in oceanic regions. In this study, an Observation System Simulation Experiment is carried out based on a tropical cyclone case. Assimilation experiments using the WRF-PDAF framework are conducted. Conventional and GNSS observation operators are implemented. A diverse array of synthetic observations, encompassing temperature (T), wind components (U and V), precipitable water (PW), and zenith total delay (ZTD), are assimilated utilizing the Local Error-Subspace Transform Kalman filter (LESTKF). The findings highlight the improvement in forecast accuracy achieved through the assimilation process over the ocean. Multiple observation types further improve the forecast accuracy. The study underscores the crucial role of GNSS data assimilation techniques. The assimilation of GNSS data presents potential for advancing weather forecasting capabilities. Thus, the construction of ground-based GNSS observation stations over the ocean is promising.

Consensus SE(3)-Constrained Extended Kalman Filter for Close Proximity Orbital Relative Pose Estimation

In this paper, a recently proposed SE(3)-constrained extended Kalman filter (EKF) is extended to formulate a strategy for relative orbit estimation in a space-based sensor network. The resulting consensus SE(3)-constrained EKF utilizes space-based sensor fusion and is applied to the problem of spacecraft proximity operations and formation flying. The proposed filter allows for the state (i.e., pose and velocities) estimation of the deputy satellite while accounting for measurement error statistics using the rotation matrix to represent attitude. Via a comparison with a conventional filter in the literature, it is shown that the use of the proposed consensus SE(3)-constrained EKF can improve the convergence performance of the existing filter for satellite formation flying. Moreover, the benefits of faster convergence and consensus speed by using communication networks with more connections are illustrated to show the significance of the proposed sensor fusion strategy in spacecraft proximity operations.

SimpleTrackV2: Rethinking the Timing Characteristics for Multi-Object Tracking.

Multi-object tracking tasks aim to assign unique trajectory codes to targets in video frames. Most detection-based tracking methods use Kalman filtering algorithms for trajectory prediction, directly utilizing associated target features for trajectory updates. However, this approach often fails, with camera jitter and transient target loss in real-world scenarios. This paper rethinks state prediction and fusion based on target temporal features to address these issues and proposes the SimpleTrackV2 algorithm, building on the previously designed SimpleTrack. Firstly, to address the poor prediction performance of linear motion models in complex scenes, we designed a target state prediction algorithm called LSTM-MP, based on long short-term memory (LSTM). This algorithm encodes the target's historical motion information using LSTM and decodes it with a multilayer perceptron (MLP) to achieve target state prediction. Secondly, to mitigate the effect of occlusion on target state saliency, we designed a spatiotemporal attention-based target appearance feature fusion (TSA-FF) target state fusion algorithm based on the attention mechanism. TSA-FF calculates adaptive fusion coefficients to enhance target state fusion, thereby improving the accuracy of subsequent data association. To demonstrate the effectiveness of the proposed method, we compared SimpleTrackV2 with the baseline model SimpleTrack on the MOT17 dataset. We also conducted ablation experiments on TSA-FF and LSTM-MP for SimpleTrackV2, exploring the optimal number of fusion frames and the impact of different loss functions on model performance. The experimental results show that SimpleTrackV2 handles camera jitter and target occlusion better, achieving improvements of 1.6%, 3.2%, and 6.1% in MOTA, IDF1, and HOTA, respectively, compared to the SimpleTrack algorithm.

A 6 month-long real-time time scale steered to NIM-Sr1 optical lattice clock

Abstract NIM-Sr1 optical lattice clock has been operated intermittently for seven consecutive months with an operation uptime around 13.8%, which serves as the reference to steer a hydrogen maser for generating a real-time time scale TS(Sr1). The peak-to-peak time difference of TS(Sr1) compared to UTC is 1.8 ns within 180 days and is less than 0.5 ns within the last month, after correcting the time error induced by a time transfer link abnormality. A dedicated automation system with hardware and software is developed to monitor the operation status of NIM-Sr1, process the measurement data, and periodically predict the hydrogen maser frequency. According to the simulation results, a composite algorithm based on both Kalman filtering (KF) and weighted least squares fitting (WLSF) is utilized for generating TS(Sr1). The KF is utilized when the unavailability of NIM-Sr1 is shorter than one day, and the WLSF with fitting interval T fit=30 d is utilized in other conditions leveraging the long-term predictability of the hydrogen maser. In addition, it is demonstrated by simulation and the post-processing of earlier experimental data that, a time scale with smaller time error can be achieved by shortening the WLSF interval from 30 days to about 5 days under the condition of sufficient measurement data points for reducing the statistical error.

Discrete adaptive sliding mode controller design for overhead cranes considering measurement noise and external disturbances

AbstractResearch on the motion control of overhead cranes, constrained by underactuated characteristics, helps improve the efficiency of payload transportation. Most studies require all system state variables (trolley displacement, payload swing angle, and their velocities). In practice, sensors measure and transmit these variables, but noise affects their accuracy, reducing control performance. Additionally, uncertainties in crane parameters, unmodeled friction, and unknown disturbances threaten the system's stability. Traditional methods struggle to address these issues effectively. To address these challenges, this article proposes an adaptive discrete sliding mode control (DSMC) method with a Kalman filter. By extending the state system and considering disturbances as new variables, the Kalman filter effectively eliminates signal noise, accurately estimates disturbances, and estimates system states simultaneously. The proposed method incorporates disturbance compensators into the adaptive DSMC, utilizing exponential terms to suppress oscillations caused by excessively high or low control gains, thus increasing control speed. Experimental comparisons demonstrate the superiority and robustness of the proposed control method under various disturbance conditions.

Research on LSTM-Based Maneuvering Motion Prediction for USVs

Maneuvering motion prediction is central to the control and operation of ships, and the application of machine learning algorithms in this field is increasingly prevalent. However, challenges such as extensive training time, complex parameter tuning processes, and heavy reliance on mathematical models pose substantial obstacles to their application. To address these challenges, this paper proposes an LSTM-based modeling algorithm. First, a maneuvering motion model based on a real USV model was constructed, and typical operating conditions were simulated to obtain data. The Ornstein–Uhlenbeck process and the Hidden Markov Model were applied to the simulation data to generate noise and random data loss, respectively, thereby constructing a sample set that reflects real experiment characteristics. The sample data were then pre-processed for training, employing the MaxAbsScaler strategy for data normalization, Kalman filtering and RRF for data smoothing and noise reduction, and Lagrange interpolation for data resampling to enhance the robustness of the training data. Subsequently, based on the USV maneuvering motion model, an LSTM-based black-box motion prediction model was established. An in-depth comparative analysis and discussion of the model’s network structure and parameters were conducted, followed by the training of the ship maneuvering motion model using the optimized LSTM model. Generalization tests were then performed on a generalization set under Zigzag and turning conditions to validate the accuracy and generalization performance of the prediction model.

Comprehensive battery aging dataset: capacity and impedance fade measurements of a lithium-ion NMC/C-SiO cell

Battery degradation is critical to the cost-effectiveness and usability of battery-powered products. Aging studies help to better understand and model degradation and to optimize the operating strategy. Nevertheless, there are only a few comprehensive and freely available aging datasets for these applications. To our knowledge, the dataset1 presented in the following is one of the largest published to date. It contains over 3 billion data points from 228 commercial NMC/C+SiO lithium-ion cells aged for more than a year under a wide range of operating conditions. We investigate calendar and cyclic aging and also apply different driving cycles to cells. The dataset1 includes result data (such as the remaining usable capacity or impedance measured in check-ups) and raw data (i.e., measurement logs with two-second resolution). The data can be used in a wide range of applications, for example, to model battery degradation, gain insight into lithium plating, optimize operating strategies, or test battery impedance or state estimation algorithms using machine learning or Kalman filtering.

Radar-Based Target Tracking Using Deep Learning Approaches with Unscented Kalman Filter

Machine learning, a rapidly growing field, has attracted numerous researchers for its ability to automatically learn from and make predictions based on data. This manuscript presents an innovative approach to estimating the covariance matrix of noise in radar measurements for target tracking, resulting from collaborative efforts. Traditionally, researchers have assumed that the covariance matrix of noise in sonar measurements is present in the vast majority of literature related to target tracking. On the other hand, this research aims to estimate it by employing deep learning algorithms with noisy measurements in range, bearing, and elevation from radar sensors. This collaborative approach, involving multiple disciplines, provides a more precise and accurate covariance matrix estimate. Additionally, the unscented Kalman filter was combined with the gated recurrent unit, multilayer perceptron, convolutional neural network, and long short-term memory to accomplish the task of 3D target tracking in an airborne environment. The quantification of the results was achieved through the use of Monte Carlo simulations, which demonstrated that the convolutional neural network performed better than any other approach. The system was simulated using a Python program, and the proposed method offers higher accuracy and faster convergence time than conventional target tracking methods. This is a demonstration of the potential that collaboration can have in research.

A deep learning deviation-based scheme to defend against false data injection attacks in power distribution systems

Defending against false data injection attacks (FDIAs) in cyber-physical power systems is crucial. Detection in power distribution systems is complex due to load variations, uncertainties, and fewer meters. Defense strategies include model-driven and data-driven approaches, but model-based methods can trigger false alarms due to threshold setting issues. The current research proposes a novel data-driven method to address threshold setting issues in detecting and localizing FDIAs in power distribution systems. First, a dataset is created by recording estimated measurement values using an unscented Kalman filter and weighted least squares across various attack scenarios. These estimated measurements are then fed into a deep artificial neural network (ANN) for binary classification to detect attacks. The output, along with the estimated measurements, is used by another ANN to localize the corrupted meter zone. This deep learning-based approach improves threshold setting over the common chi-square method. Results show that the proposed deep learning method for FDIA detection and localization outperforms a recently proposed ensemble of shallow models. The area under the curve value increases by about 5% with lower training time. The approach is also effective against previously unseen attack strategies and different feeder topologies.

A Novel Estimating Algorithm of Critical Driving Parameters for Dual-Motor Electric Drive Tracked Vehicles Based on a Nonlinear Observer and an Adaptive Kalman Filter

High-speed dual-motor electric drive tracked vehicles (DDTVs) have emerged as a research hotspot in the field of tracked vehicles in recent years due to their advantages in fuel economy and the scalability of electrical equipment. The emergency braking of a DDTV at high speed can lead to slipping or even yawing (which is caused by a large deviation of forces at each track directly), posing significant challenges to the vehicle’s stability and safety. Therefore, the accurate real-time acquisition of critical driving parameters, such as the longitudinal force and vehicle speed, is crucial for the stability control of a DDTV. This paper developed a novel estimating algorithm of critical driving parameters for DDTVs equipped with conventional sensors such as rotary transformers at PMSMs and onboard accelerometers on the basis of their dynamics models. The algorithm includes a sensor signal preprocessing module, a longitudinal force estimation method based on a nonlinear observer, and a speed estimation method based on an adaptive Kalman filter. Through hardware-in-loop experiments based on a Speedgoat real-time target machine, the proposed algorithm is proven to estimate the longitudinal force of the track and vehicle speed accurately, whether the vehicle has stability control functions or not, providing a foundation for the further development of vehicle stability control algorithms.

Real-time monitoring and optimization of machine learning intelligent control system in power data modeling technology

In response to the problems of insufficient model accuracy and poor real-time performance in real-time monitoring and optimization of data models in traditional power systems, this paper explored them based on machine learning. It used methods such as box plots and Kalman filters to preprocess power data and used Fourier transform and long short-term memory (LSTM) network to extract data features. Based on long-term and short-term memory networks, this paper constructed a deep neural network model to process data. Recursive feature elimination method can be used for feature selection in the model, and multi-model integration method can be used for feature fusion. The experiment trained and tested the model on two datasets, IEEE 39-Bus and Pecan Street. The experimental results show that the accuracy of the paper's model in both the training and testing sets is higher than that of the convolutional neural network, decision tree, and support vector machine models in the comparative experiments, reaching 93 % and 94 %, respectively. The average response times in three different testing methods were 139.8 ms, 151 ms, and 140.6 ms, respectively. The lowest daily failure rate for 30 consecutive days of work was 0 %, which reflects the stability of the model; in the satisfaction survey of practitioners, the proportion of high recognition answers to each question was higher than 80 %. The experimental results show that the machine learning intelligent control system has achieved good application in power data modeling technology, providing a reference for similar research in the future.

Unstructured environment navigation and trajectory calibration technology based on multi-data fusion

In order to effectively improve the accuracy and efficiency of unstructured environment navigation and trajectory calibration, a multi data fusion based unstructured environment navigation and trajectory calibration method was studied. Described the basic principles of the Strapdown Inertial Navigation System and Doppler Log. After introducing DVL velocity information and relative position information of underwater robots into SINS, the Kalman filter fusion algorithm was used to obtain the system's state equation and measurement equation. The navigation parameter error and device error parameters of the system were selected as the state variables. The difference between SINS output speed and DVL measurement speed, as well as the difference between SINS output position and relative position, are used as the speed and position measurements of the measurement system. Error estimation is obtained through indirect filtering, and the accuracy of navigation and positioning is improved through output correction. The experimental results show that the proposed method has a good calibration effect and can effectively improve the accuracy and efficiency of trajectory calibration in unstructured environments.

Microbubble tracking based on partial smoothing-based adaptive generalized labelled Multi-Bernoulli filter for super-resolution imaging

Super-resolution ultrasound (SRUS) can image the vasculature at microscopic resolution according to microbubble (MB) localization, with velocity vector maps obtained based on MB tracking information. High MB concentrations can reduce the acquisition time of SRUS imaging, however adjacent and intersecting vessels are difficult to distinguish, thus decreasing resolution. Low acquisition frame rates affect the precision of flow velocity estimation. This study proposes a partial smoothing-based adaptive generalized labeled multi-Bernoulli filter (SAGLMB) to precisely track the MB motion at different flow velocities. SAGLMB employs a generalized labelled multi-Bernoulli filter (GLMB) for MB trajectory allocation to separate adjacent and intersecting vessels. Furthermore, the nonlinear motion of MB was predicted by an unscented Kalman filter, and a cardinalized probability hypothesis density filter was applied to suppress clutter interference. Finally, the trajectories were smoothed by unscented Rauch-Tung-Striebel to improve the resolution of the SRUS image. The simulation results demonstrate that SAGLMB outperforms the conventional bipartite graph-based tracking at high MB concentrations, achieving at least an 8.55 % improvement in the correctly paired precision, with 3 times increase in the structural similarity index measure. Moreover, SAGLMB can obtain more precise flow velocity estimations with a 4 times improvement than the conventional method. The SRUS results of rabbit kidney show that the proposed method significantly improves resolution of adjacent and intersecting vessels at higher MB concentrations and maintains this performance as the acquisition frame rate decreases. Furthermore, the rat brain microvascular network was reconstructed with 9.21 μm (λ/11.1) resolution. Therefore, SAGLMB can achieve robust SRUS imaging at high concentrations and low acquisition frame rates.

A Robust Tri-Electromagnet-Based 6-DoF Pose Tracking System Using an Error-State Kalman Filter.

Magnetic pose tracking is a non-contact, accurate, and occlusion-free method that has been increasingly employed to track intra-corporeal medical devices such as endoscopes in computer-assisted medical interventions. In magnetic pose-tracking systems, a nonlinear estimation algorithm is needed to recover the pose information from magnetic measurements. In existing pose estimation algorithms such as the extended Kalman filter (EKF), the 3-DoF orientation in the S3 manifold is normally parametrized as unit quaternions and simply treated as a vector in the Euclidean space, which causes a violation of the unity constraint of quaternions and reduces pose tracking accuracy. In this paper, a pose estimation algorithm based on the error-state Kalman filter (ESKF) is proposed to improve the accuracy and robustness of electromagnetic tracking systems. The proposed system consists of three electromagnetic coils for magnetic field generation and a tri-axial magnetic sensor attached to the target object for field measurement. A strategy of sequential coil excitation is developed to separate the magnetic fields from different coils and reject magnetic disturbances. Simulation and experiments are conducted to evaluate the pose tracking performance of the proposed ESKF algorithm, which is also compared with standard EKF and constrained EKF. It is shown that the ESKF can effectively maintain the quaternion unity and thus achieve a better tracking accuracy, i.e., a Euclidean position error of 2.23 mm and an average orientation angle error of 0.45°. The disturbance rejection performance of the electromagnetic tracking system is also experimentally validated.

A measurement modified centered error entropy cubature Kalman filter for integrated INS/GNSS

Due to unpredictable environmental factors, the measurement noise in INS/GNSS integration can be affected by outliers or exhibit statistical uncertainty. A single adaptive or robust filter may not be suitable for all noise scenarios. To address this issue, a new approach called the measurement noise covariance matrix (MNCM) ’R’ modified centered error entropy cubature Kalman filter (RMCEECKF) is proposed in this study. In this method, the MNCM is adjusted based on the innovation sequence, and outliers are detected using the Mahalanobis distance. If outliers are identified, the CEE criterion with strong robustness is applied for the posterior update. Simulation results on INS/GNSS integration demonstrate that the RMCEECKF offers higher estimation accuracy compared to existing methods in scenarios involving outliers, uncertain noise covariance, and outliers under uncertain noise covariance. The inclusion of outlier detection also enhances the computational efficiency of RMCEECKF when compared to the CEECKF.

An enhanced stochastic error modeling using multi-Gauss–Markov processes for GNSS/INS integration system

Angular random walk (ARW), rate random walk (RRW), and bias instability (BI) are the main noise types in inertial measurement units (IMUs) and thus determine the navigation performance of IMUs. BI is the flicker noise, which determines the noise level of an inertial sensor. The traditional error modeling approach involves modeling the ARW and BI processes as RRW or Gauss–Markov (GM) processes, and this approach is applied as a suboptimal filter in the global navigation satellite system (GNSS)/inertial navigation system (INS) extended Kalman filter (EKF). In this paper, the random error identification processes for white noise and colored noise for inertial sensors are separated using the Allan variance and power spectral density methods and the equivalence of the stochastic process differential equations of bias instability and a combination of multiple first-order GM processes are derived. A colored noise compensation method is proposed based on the enhanced EKF model. Experimental results demonstrate that, compared to traditional error models, our proposed model reduces positional drift error in dynamic testing from 195 to 49 m, enhancing positional accuracy by 40.2%. These findings confirm the potential and superiority of our method in complex navigation environments.

The Zero-Velocity Correction Method for Pipe Jacking Automatic Guidance System Based on Fiber Optic Gyroscope.

The pipe jacking guidance system based on a fiber optic gyroscope (FOG) has gained extensive attention due to its high degree of safety and autonomy. However, all inertial guidance systems have accumulative errors over time. The zero-velocity update (ZUPT) algorithm is an effective error compensation method, but accurately distinguishing between moving and stationary states in slow pipe jacking operations is a major challenge. To address this challenge, a "MV + ARE + SHOE" three-conditional zero-velocity detection (TCZVD) algorithm for the fiber optic gyroscope inertial navigation system (FOG-INS) is designed. Firstly, a Kalman filter model based on ZUPT is established. Secondly, the TCZVD algorithm, which combines the moving variance of acceleration (MV), angular rate energy (ARE), and stance hypothesis optimal estimation (SHOE), is proposed. Finally, experiments are conducted, and the results indicate that the proposed algorithm achieves a zero-velocity detection accuracy of 99.18% and can reduce positioning error to less than 2% of the total distance. Furthermore, the applicability of the proposed algorithm in the practical working environment is confirmed through on-site experiments. The results demonstrate that this method can effectively suppress the accumulated error of the inertial guidance system and improve the positioning accuracy of pipe jacking. It provides a robust and reliable solution for practical engineering challenges. Therefore, this study will contribute to the development of pipe jacking automatic guidance technology.

Study of Global Navigation Satellite System Receivers' Accuracy for Unmanned Vehicles.

The development of unmanned ground vehicles and unmanned aerial vehicles requires high-precision navigation due to the autonomous motion and higher traffic intensity. The existing L1 band GNSS receivers are a good and cheap decision for smartphones, vehicle navigation, fleet management systems, etc., but their accuracy is not good enough for many civilian purposes. At the same time, real-time kinematic (RTK) navigation allows for position precision in a sub-centimeter range, but the system cost significantly narrows this navigation to a very limited area of applications, such as geodesy. A practical solution includes the integration of dual-band GNSS receivers and inertial sensors to solve high-precision navigation tasks, but GNSS position accuracy may significantly affect IMU performance due to having a great impact on Kalman filter performance in unmanned vehicles. The estimation of dilution-of-precision (DOP) parameters is essential for the filter performance as the optimality of the estimation in the filter is closely connected to the quality of a priori information about the noise covariance matrix and measurement noise covariance. In this regard, the current paper analyzes the DOP parameters of the latest generation dual-band GNSS receivers and compares the results with the L1 ones. The study was accomplished using two types of antennas-L1/L5 band patch and wideband helix antennas, which were designed and assembled by the authors. In addition, the study is extended with a comparison of GNSS receivers from different generations but sold on the market by one of the world's leading GNSS manufacturers. The analyses of dilution-of-precision (DOP) parameters show that the introduction of dual-band receivers may significantly increase the navigation precision in a sub-meter range, in addition to multi-constellation signal reception. The fast advances in the performance of the integrated CPU in GNSS receivers allow the number of correlations and tracking satellites to be increased from 8-10 to 24-30, which also significantly improves the position accuracy even of L1-band receivers.

Maximum Correntropy Polynomial Chaos Kalman Filter for Underwater Navigation

This paper develops an underwater navigation solution that utilizes a strapdown inertial navigation system (SINS) and fuses a set of auxiliary sensors such as an acoustic positioning system, Doppler velocity log, depth meter, and magnetometer to accurately estimate an underwater vessel's position and orientation. The conventional integrated navigation system assumes Gaussian measurement noise, while in reality, the noises are non-Gaussian, particularly contaminated by heavy-tailed impulsive noises. To address this issue, and to fuse the system model with the acquired sensor measurements efficiently, we develop a square root polynomial chaos Kalman filter based on maximum correntropy criteria. The proposed method uses Hermite polynomial chaos expansion to tackle the nonlinearity, and it has the potential to estimate the states in a more accurate way in presence of a non-Gaussian measurement noise. The filter is initialized using acoustic beaconing to accurately locate the initial position of the vehicle. The computational complexity of the proposed filter is calculated in terms of flops count. The proposed method is compared with the existing maximum correntropy sigma point filters in terms of estimation accuracy and computational complexity. It is found from the simulation results that the proposed method is more accurate compared to the conventional deterministic sample point filters and Huber's M-estimator.