Kalman Fusion Research Articles

Application of RBF Neural Network in Navigation Filtering Algorithm

As a high-precision and widely used navigation method, satellite navigation can provide users with all-weather and all-time services. In recent years, with the improvement of satellite positioning accuracy requirements, using conventional Kalman filter algorithm to solve the problem can not meet the requirements of high accuracy and low cost of satellite navigation. To solve these problems, this paper proposes the RBF Kalman fusion filtering algorithm. The original data without processing is compared with the results of traditional model and RBF Kalman fusion filtering model through the simulation experiment.The results show that the algorithm can better improve the positioning accuracy.

Object tracking on event cameras with offline–online learning

Compared with conventional image sensors, event cameras have been attracting attention thanks to their potential in environments under fast motion and high dynamic range (HDR). To tackle the lost-track issue due to fast illumination changes under HDR scene such as tunnels, an object tracking framework has been presented based on event count images from an event camera. The framework contains an offline-trained detector and an online-trained tracker which complement each other: The detector benefits from pre-labelled data during training, but may have false or missing detections; the tracker provides persistent results for each initialised object but may suffer from drifting issues or even failures. Besides, process and measurement equations have been modelled, and a Kalman fusion scheme has been proposed to incorporate measurements from the detector and the tracker. Self-initialisation and track maintenance in the fusion scheme ensure autonomous real-time tracking without user intervene. With self-collected event data in urban driving scenarios, experiments have been conducted to show the performance of the proposed framework and the fusion scheme.

High Precision Positioning with Multi-Camera Setups: Adaptive Kalman Fusion Algorithm for Fiducial Markers.

The paper addresses the problem of fusing the measurements from multiple cameras in order to estimate the position of fiducial markers. The objectives are to increase the precision and to extend the working area of the system. The proposed fusion method employs an adaptive Kalman algorithm which is used for calibrating the setup of cameras as well as for estimating the pose of the marker. Special measures are taken in order to mitigate the effect of the measurement noise. The proposed method is further tested in different scenarios using a Monte Carlo simulation, whose qualitative precision results are determined and compared. The solution is designed for specific positioning and alignment tasks in physics experiments, but also, has a degree of generality that makes it suitable for a wider range of applications.

High-precision Positioning and Deformation Monitoring Analysis of BD/GPS Based on Improved Kalman Filter Fusion

Abstract The real time kinematic of global positioning system (GPS-RTK) provides precise positioning for bridge deformation monitoring and monitoring bridge health status. In order to solve the problem that the satellite signal is vulnerable to the influence of the positioning environment when monitoring bridges in the valleys and urban buildings[1], and the problem that Kalman fusion algorithm is difficult to detect the divergence caused by interruption or wrong data[2]. This paper proposes an improved Kalman filter fusion position method based on the BD/GPS fusion positioning. This improved algorithm introduces the environmental information. The confidence level is calculated with membership function by defining the confidence region of sensor, so as to the fusion weight coefficient is determined. This paper analyzes the performance of BD/GPS positioning in bridge monitoring through comparing the traditional fusion method with the improved fusion method. Experiments show that the improved algorithm eliminates the problem of error divergence; the average number of visible satellites in BD/GPS fusion positioning is increased by 7 compared with that of GPS single system positioning, the GDOP value is reduced by 21.83%, and the positioning error is reduced by 2.51 cm. The feasibility of all-weather monitoring in the mountains, buildings and other areas is verified, and millimeter accuracy is provided, which greatly improves the performance of bridge deformation monitoring.

Multi-joint Cooperative Control of Athletes under High Intensity Training

The control structure and performance of high intensity sports training on the trunk joint of athletes is analyzed to improve the quality of sports training, a multi-joint cooperative control model for athletes under high intensity sports training is proposed based on attitude sensor fusion tracking compensation. The multi-joint kinematics model of the athletes’ torso under high intensity sports training is constructed, and the constraint parameters of the multi-joint linkage and cooperative control of the athletes are analyzed combined with the identification method of the parameters of the state space model. The mechanical control model of the action of high intensity sports training on athletes’ torso is established by using the coupling method of driving branch chain inertia, and the characteristics of multi-joint linkage coupling of athletes are analyzed. The collaborative filtering Kalman fusion method is used to realize the parameter fusion and adaptive parameter identification of athletes’ multi-joint linkage. According to the results of parameter recognition, athletes’ multi-joint linkage collaborative control is realized. The simulation results show that the high intensity sports training method has good stability and low error of attitude parameter adjustment for athletes’ multi-joint linkage and coordination control, which improves the effect of sports training.

Distributed Dimensionality Reduction Fusion Estimation for Cyber-Physical Systems Under DoS Attacks

This paper studies the distributed dimensionality reduction fusion estimation problem for a class of cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. The problem is modeled under the resource constraints (i.e., bandwidth or energy) for the defender and attacker. Based on a new attack and compensation model, a recursive distributed Kalman fusion estimator (DKFE) is designed for the addressed CPSs. Though the optimization objects of the defender and attacker are opposite, the corresponding optimization problems are established based on different available information. In this case, an explicit form of suboptimal dimensionality reduction is given against DoS attacks, while an effective attack strategy is proposed for the attacker. A stability condition is derived such that the mean square error of the designed DKFE is bounded. Two illustrative examples are given to show the effectiveness of the proposed methods.

Distributed Federated Tobit Kalman Filter Fusion Over a Packet-Delaying Network: A Probabilistic Perspective

This paper investigates the distributed federated Tobit Kalman filter fusion problem for a class of discrete-time systems subject to measurement censoring and packet delays. The censored measurement is characterized by the Tobit measurement model and the packet delay obeys the Poisson distribution. At the input terminal of each local estimator, a censoring detection device and a buffer with finite length are exploited to tackle the censored/delayed measurements. The filtering fusion is carried out in two steps: in the first step, every sensor in the network collects and sends its measurements to the corresponding local estimator via an unreliable network with probabilistic packet delays and, in the second step, the estimates from local estimators are further collected by the fusion center to form a fused estimate. The local estimator runs a modified Tobit Kalman filtering algorithm, which is designed based on the modified Tobit regression model, while the fusion center performs a distributed federated modified Tobit Kalman filtering algorithm, which is devised on the basis of the federated Kalman fusion rule. Given the buffer length, the prescribed bound on the estimation error covariance and the probability distribution of the packet delay, the stability performance of the proposed filtering fusion algorithm is evaluated via a probabilistic approach. Simulation results are provided to show the feasibility of the proposed filter.

Precision landing using an adaptive fuzzy multi-sensor data fusion architecture

The positional inaccuracies associated with the GPS/INS measurements make the terminal phase of the normal GPS/INS landing system imprecise. To solve this problem, an adaptive fuzzy data fusion algorithm is developed to obtain more accurate state estimates while the vehicle approaches the landing surface. This algorithm takes the translational displacements in x and y from the mounted Optical Flow (OF) sensor and fuses them with the INS attitude measurements and the altimeter measurements. This low cost adaptive algorithm can be used for vertical landings in areas where GPS outages might happen or in GPS denied areas. The adaptation is governed by imposing appropriate assumptions under which the filter measurement noise matrix R is predicted. The R matrix is continuously adjusted through a fuzzy inference system (FIS) based on the Kalman innovative sequence and the applied covariance-matching technique. This adaptive fuzzy Kalman fusion algorithm (AFKF) is used to estimate the vehicle’s states while landing is being commanded. AFKF results are compared with these obtained using a classical Kalman estimation technique. The AFKF algorithm shows better states estimates than its conventional counterpart does. Compared to prior landing systems, the proposed low cost AFKF has achieved a precision landing with less than 10 cm maximum estimated position error. Real precision landing flights were conducted to demonstrate the validity of the proposed intelligent estimation method.

Monocular Visual Odometry Based on Trifocal Tensor Constraint

For the problem of real-time precise localization in the urban street, a monocular visual odometry based on Extend Kalman fusion of optical-flow tracking and trifocal tensor constraint is proposed. To diminish the influence of moving object, such as pedestrian, we estimate the motion of the camera by extracting the features on the ground, which improves the robustness of the system. The observation equation based on trifocal tensor constraint is derived, which can form the Kalman filter alone with the state transition equation. An Extend Kalman filter is employed to cope with the nonlinear system. Experimental results demonstrate that, compares with Yu’s 2-step EKF method, the algorithm is more accurate which meets the needs of real-time accurate localization in cities.

Relative entropy-based Kalman filter for seamless indoor/outdoor multi-source fusion positioning with INS/TC-OFDM/GNSS

The current single data source positioning navigation systems cannot meet the high precision and high reliability required for indoor/outdoor positioning service. In this study, based on an inertial navigation system, time-and-code division-orthogonal frequency division multiplexing ranging technology and a global navigation satellite system, a relative entropy-based Kalman multi-source fusion positioning model is developed. First, multi-source numerical observation data are filtered, and the outliers are processed in data layers to improve data source reliability and to extract stable observation data. Next, the degree of the multi-source data coupling is quantified in an information layer to analyze the multi-source information coupling degree and to develop a coupling degree factor and a Kalman fusion positioning model for multi-source heterogeneous information. Tests show that this method significantly improves system positioning, navigation stability and positioning precision.

Walking Ability Assessment System for Parkinson's Patients Based on Inertial Sensor

In order to evaluate the ability of Parkinson's patients to walk comprehensively, a system based on MEMS to aid clinical quantification of ability in Parkinson's is established. The inertial units are respectively fixed on the back and the waist of subject to be measured. The Kalman fusion algorithm is used to extract the characteristic parameters of accelerometer and gyroscope data. SVM classifier is designed to train and test the classifier by the feature. The results show that the system possesses a high recognition rate for Parkinson's patients and normal subjects and for the classification of the walking ability of patients with Parkinson's disease. So, this system can aid doctors to give more object diagnostic conclusion.

Bio-Inspired Real-Time Prediction of Human Locomotion for Exoskeletal Robot Control

Human motion detection is of fundamental importance for control of human–robot coupled systems such as exoskeletal robots. Inertial measurement units have been widely used for this purpose, although delay is a major challenge for inertial measurement unit-based motion capture systems. In this paper, we use previous and current inertial measurement unit readings to predict human locomotion based on their kinematic properties. Human locomotion is a synergetic process of the musculoskeletal system characterized by smoothness, high nonlinearity, and quasi-periodicity. Takens’ reconstruction method can well characterize quasi-periodicity and nonlinear systems. With Takens’ reconstruction framework, we developed improving methods, including Gaussian coefficient weighting and offset correction (which is based on the smoothness of human locomotion), Kalman fusion with complementary joint data prediction and united source of historical embedding generation (which is synergy-inspired), and Kalman fusion with the Newton-based method with a velocity and acceleration high-gain observer (also based on smoothness). After thorough analysis of the parameters and the effect of these improving techniques, we propose a novel prediction method that possesses the combined advantages of parameter robustness, high accuracy, trajectory smoothness, zero dead time, and adaptability to irregularities. The proposed methods were tested and validated by experiments, and the real-time applicability in a human locomotion capture system was also validated.

Secure Fusion Estimation for Bandwidth Constrained Cyber-Physical Systems Under Replay Attacks

State estimation plays an essential role in the monitoring and supervision of cyber-physical systems (CPSs), and its importance has made the security and estimation performance a major concern. In this case, multisensor information fusion estimation (MIFE) provides an attractive alternative to study secure estimation problems because MIFE can potentially improve estimation accuracy and enhance reliability and robustness against attacks. From the perspective of the defender, the secure distributed Kalman fusion estimation problem is investigated in this paper for a class of CPSs under replay attacks, where each local estimate obtained by the sink node is transmitted to a remote fusion center through bandwidth constrained communication channels. A new mathematical model with compensation strategy is proposed to characterize the replay attacks and bandwidth constrains, and then a recursive distributed Kalman fusion estimator (DKFE) is designed in the linear minimum variance sense. According to different communication frameworks, two classes of data compression and compensation algorithms are developed such that the DKFEs can achieve the desired performance. Several attack-dependent and bandwidth-dependent conditions are derived such that the DKFEs are secure under replay attacks. An illustrative example is given to demonstrate the effectiveness of the proposed methods.

Networked Fusion Estimation under Denial-of-Service Attacks

This paper studies the fusion estimation problem for a class of networked multi-sensor fusion systems (NMFSs) under bandwidth constraints and denial-of-service (DoS) attacks. The dimensionality reduction strategy is used to satisfy the finite bandwidth, while the prediction compensation strategy is used to reduce the information loss caused by attacks. Based on dimensionality reduction and DoS attack model, a recursive distributed Kalman fusion estimator (DKFE) is designed for the addressed NMFSs. An explicit form of the dimensionality reduction is given against DoS attacks, while an effective attack strategy is proposed for the attacker. An illustrative example is given to show the effectiveness of the proposed methods.

A compressive tracking based on time-space Kalman fusion model

The compressive tracking (CT) method is a simple yet efficient algorithm which compresses the high-dimensional features into a low-dimensional space while preserving most of the salient information. This paper proposes a compressive time-space Kalman fusion tracking algorithm to extend the CT method to the case of multi-sensor fusion tracking. Existing fusion trackers deal with multi-sensor features individually and without time-space adaptability. Besides, significant information cumulated in the updating process has not been fully exploited, which calls for a necessity for temporal information extraction. Unlike previous algorithms, the proposed fusion model is completed in both space and time domains. Also, extended Kalman filter is introduced to formulate an updating method for fusion coefficient optimization. The accuracy and robustness of the proposed fusion tracking algorithm are demonstrated by several experimental results.

Covariance Intersection Fusion Kalman Estimator for Multi-Sensor System with Measurements Delays

To handle the state estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computation complexity of cross-covariances, for a multi-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained, and then using the covariance intersection (CI) fusion method, the covariance intersection fusion steady-state Kalman estimator is presented. It is proved that its accuracy is higher than that of each local estimator, and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relations, hence it has good performances.

Parallel Covariance Intersection Fusion Optimal Kalman Filter

For multisensor network systems with unknown cross-covariances, a novel multi-level parallel covariance intersection (PCI) fusion Kalman filter is presented in this paper, which is realized by the multi-level parallel two-sensor covariance intersection (CI) fusers, so it only requires to solve the optimization problems of several one-dimensional nonlinear cost functions in parallel with loss computation burden. It can significantly reduce the computation time and increase data processing rate when the number of sensors is very large. It is proved that the PCI fuser is consistent, and its accuracy is higher than that of each local filter and is lower than that of the optimal Kalman fuser weighted by matrices. The geometric interpretation of accuracy relations based on the covariance ellipses is given. A simulation example for tracking systems verifies the accuracy relations.

Covariance Intersection Kalman Fuser for Two-Sensor System with Time-Delayed Measurements

To handle the estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computed burden and computational complexity of cross-covariances, for a two-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained and then using the Covariance Intersection (CI) fusion method, the covariance intersection steady-state Kalman fuser is presented. It is proved that its accuracy is higher than that of each local estimator and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relation and indicates that its actual accuracy is close to that of the Kalman fuser weighted by matrices, hence it has good performances.

Covariance Intersection Kalman Fuser for Two-sensor System with Time-delayed Measurements

For a two-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained and then using the Covariance Intersection (CI) fusion method, the covariance intersection steady-state Kalman fuser is presented. It can handle the estimation fusion problem between local estimation errors for the system with unknown cross-covariances and avoid a large computed burden and computational complexity of cross-covariances. It is proved that its accuracy is higher than that of each local estimator and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relation and indicates that its actual accuracy is close to that of the Kalman fuser weighted by matrices, hence it has good performances.

Cubature information filters with correlated noises and their applications in decentralized fusion

Data fusion for nonlinear systems is one of the challenging topics in state estimation and target tracking recently. We study decentralized cubature Kalman fusion in this paper. Cubature Kalman filter (CKF) is a more effective method than the conventional nonlinear filters, such as extended Kalman filter (EKF) and unscented Kalman filter (UKF). For most of the practical cases, there are correlative between process and measurement noises (Correlation I) and among measurement noises (Correlation II). So, it is more attractive to design fusion algorithms based on the CKF for the systems with complex correlated noises. Firstly, a cubature Kalman filter with correlation I (CKF-CN) is derived. Secondly, by introducing the EKF with correlated noises (EKF-CN) and its information filter EIF-CN, the CKF-CN is embedded in the EIF-CN framework to get a cubature information filter with correlated noises (CIF-CN). Consequently, a square-root cubature Kalman filter with noise correlation I (SCKF-CN) and the associated information filter SCIF-CN are presented to improve computational performance. Finally, based on the proposed SCIF-CN and matrix diagonalization, a decentralized nonlinear fusion algorithm is proposed for the multisensor system with Correlation I and Correlation II. Simulation examples are demonstrated to validate the proposed filters and fusion algorithms.