Strong Tracking Cubature Kalman Filter Research Articles

Improved Strong Tracking Cubature Kalman Filter for UWB Positioning.

For the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate predictive dynamics model in wireless ultra-wideband (UWB) positioning systems, an improved strong tracking cubature Kalman filter (ISTCKF) positioning algorithm is proposed in this paper. The main idea of the algorithm is as follows. First, the observations are reconstructed based on the weighted positioning results obtained from the predictive dynamics model and the least squares algorithm. Second, the difference in statistical properties between the observation noise and the NLOS errors is utilized to identify the NLOS observations by the corresponding judgment statistics obtained from the operation between the original observations and the reconstructed observations. The main positioning error of the UWB positioning system at the current moment is then judged by the NLOS identification results, and the corresponding fading factors are calculated according to the judgment results. Finally, the corresponding ISTCKF is constructed based on the fading factors to mitigate the main positioning error and obtain accurate positioning result in the UWB positioning system. In this paper, the reconstructed observations mitigate the observation noise in the original observation, and then the ISTCKF mitigates the main errors in the UWB positioning system. The experimental results show that the ISTCKF algorithm reduces the positioning error by 55.2%, 32.3% and 28.9% compared with STCKF, ACKF and RSTCKF, respectively. The proposed ISTCKF algorithm significantly improves the positioning accuracy and stability of the UWB system.

Robust Adaptive Heading Tracking Fusion for Polarization Compass With Uncertain Dynamics and External Disturbances

For the polarization compass (PC), maintaining high-precision and high-robustness autonomous measurement of the heading information under conditions where the atmospheric polarized light is being blocked or disturbed represents a challenging problem. In this paper, the E-vector orientation algorithm, which provides high orientation accuracy and real-time performance in sunny weather, and the symmetric axis orientation algorithm, which offers a strong anti-interference ability in occluded environments, are integrated to solve this problem. Furthermore, an improved state error model is established to increase the accuracy of the heading estimation. To track the system state rapidly and circumvent the uncertainties caused by measurement noise variance, an improved variational Bayesian strong tracking cubature Kalman filter (VBSTCKF) is proposed to estimate both the state and the time-varying measurement noise variance accurately. In addition, a multi-frequency data fusion algorithm based on residual compensation is proposed to overcome the inconsistent sampling operation frequency problems of the two orientation algorithms. The outstanding feature is that the proposed multi-frequency VBSTCKF (MF-VBSTCKF) can improve the orientation precision and robustness while also ensuring the high-frequency output performance. Finally, experimental results acquired in occluded environments verify the superiority of the proposed method.

Multilayer Model-Aided INS Based on Real-Time Corrected Vehicle Dynamics Model

Vehicle dynamics model-aided inertial navigation system (INS) is an effective approach for autonomous navigation when the Global Navigation Satellite System fails, However, the accuracy of the vehicle dynamics model (VDM) will decrease, or even diverge, in low-speed and high-dynamic situations, which leads to the performance degradation of the whole system. The traditional VDM-aided INS uses the velocity information from VDM to estimate and correct INS errors, but most previous research ignored that the acceleration and angular velocity from INS are more accurate than VDM. To reach the full potential of INS and VDM, this paper proposed a three-layer structure for the VDM-aided INS. In the proposed method, the navigation information is divided into the sensor layer, system layer I, and system layer II. In the sensor layer, VDM is corrected by INS through the strong tracking cubature Kalman filter, and the chi-square test is adopted to avoid redundant computation. In the system layer I, INS is aided by the corrected velocity information from VDM. In the system layer II, the position is updated with the velocity and attitude that are corrected in the system layer I. As the result, VDM and INS can be corrected in different layers simultaneously, and the accuracy and robustness of the whole system can be improved. The simulation experiment proved that, with the sensor layer filter, the velocity errors of VDM can be reduced by 35% in low-speed and high-dynamic situations, and reduced by 20% in the normal situation. Then, a 31-minute field test shows that the maximum horizontal position error of the proposed method is 241.8 m, while those of two traditional VDM-aided INS methods are more than 500 m.

Adaptive Markov IMM Based Multiple Fading Factors Strong Tracking CKF for Maneuvering Hypersonic-Target Tracking

Hypersonic targets have complex motion states and high maneuverability. The traditional interactive multi-model (IMM) has low tracking accuracy and a slow convergence speed. Therefore, this paper proposes a strong tracking cubature Kalman filter (CKF) adaptive interactive multi-model (AIMM) based on multiple fading factors. Firstly, this paper analyzes the structure of the CKF algorithm, introduces the fading factor of the strong tracking algorithm into the covariance matrix of the time update and measurement update, and adjusts the filter gain online and in real time, which can reduce the decline infilter accuracy caused by model mismatch. Secondly, Singer model, “current” statistical (CS) model, and Jerk model are selected in the model set of IMM and introduced singular value decomposition (SVD) decomposition to solve the problem that Cholesky decomposition cannot be performed in the CKF due to the model dimension expansion. Last, an adaptive algorithm for the Markov matrix in the IMM is proposed. The transition probability was adaptively modified by the value of the model likelihood function to enhance the proportion of matching models. The simulation results show that the proposed algorithm enhanced the proportion of matching models in the IMM and improved the tracking accuracy by 16.51% and the convergence speed by 37.5%.

Charging Diagnosis of Power Battery Based on Adaptive STCKF and BLS for Electric Vehicles

This article proposes a BLS-STCKF estimation and diagnosis scheme of state of charge (SOC) and RUL prediction for power batteries in electric vehicles (EVs). First, the process of SOC estimation is considered as a time series problem. The walk-forward validation method has been applied in BLS (Broad Learning System) estimator training and validation. Then, a sliding window with variable width is used to help the time series SOC estimation improve. Meanwhile, STCKF (Strong Tracking Cubature Kalman Filter) is combined with BLS to help search for an optimal hyperparameter for BLS. Then, this article takes the SOC diagnosis as a problem of diagnosing abnormal time segments and uses HOT SAX(Heuristically Ordered Time series using Symbolic Aggregate ApproXimation) to detect SOC anomalies. Moreover, a prediction method of RUL (Remain Useful Life) has been designed by BLS-STCK. In light of result of RUL, the capacity degradation is considered to improve SOC estimation, and capacity retention coefficient is posed to adjust BLS-STCKF when battery aged. Finally, the proposed methods has also been evaluated by real driving data of EVs. Based on those critical experiments, rational analysis and conclusion have been illustrated that the proposed method has competitive accuracy.

A new fuzzy strong tracking cubature Kalman filter for INS/GNSS

A new fuzzy strong tracking cubature Kalman filter for INS/GNSS

A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot.

The motion state of a quadruped robot in operation changes constantly. Due to the drift caused by the accumulative error, the function of the inertial measurement unit (IMU) will be limited. Even though multi-sensor fusion technology is adopted, the quadruped robot will lose its ability to respond to state changes after a while because the gain tends to be constant. To solve this problem, this paper proposes a strong tracking mixed-degree cubature Kalman filter (STMCKF) method. According to system characteristics of the quadruped robot, this method makes fusion estimation of forward kinematics and IMU track. The combination mode of traditional strong tracking cubature Kalman filter (TSTCKF) and strong tracking is improved through demonstration. A new method for calculating fading factor matrix is proposed, which reduces sampling times from three to one, saving significantly calculation time. At the same time, the state estimation accuracy is improved from the third-degree accuracy of Taylor series expansion to fifth-degree accuracy. The proposed algorithm can automatically switch the working mode according to real-time supervision of the motion state and greatly improve the state estimation performance of quadruped robot system, exhibiting strong robustness and excellent real-time performance. Finally, a comparative study of STMCKF and the extended Kalman filter (EKF) that is commonly used in quadruped robot system is carried out. Results show that the method of STMCKF has high estimation accuracy and reliable ability to cope with sudden changes, without significantly increasing the calculation time, indicating the correctness of the algorithm and its great application value in quadruped robot system.

Vehicle path tracking Based on Strong Tracking Cubature Kalman Filter While Encountering An Emergency Collision Avoidance

Considering the high speed emergency avoidance situations, the vehicle path tracking was studied in this paper. The three degrees of freedom nonlinear vehicle model and the cubature Kalman filter are applied to tracking vehicle emergency avoidance path. For the degradation of adaptive tracking performance in the vehicle emergency avoidance, an improved strong tracking cubature Kalman filter algorithm is proposed by introducing the fading factor into filtering process which is learnt from strong tracking filter. The algorithm has a simple implementation, high estimation accuracy and good robustness. Different target paths are selected and the cubature Kalman filter is applied to simulate path tracking in the vehicle emergency avoidance. The simulation results show that the proposed path tracking method can control the vehicle tracking the ideal collision avoidance path rapidly without collisions.

A novel strong tracking cubature Kalman filter and its application in maneuvering target tracking

The fading factor exerts a significant role in the strong tracking idea. However, traditional fading factor introduction method hinders the accuracy and robustness advantages of current strong-tracking-based nonlinear filtering algorithms such as Cubature Kalman Filter (CKF) since traditional fading factor introduction method only considers the first-order Taylor expansion. To this end, a new fading factor idea is suggested and introduced into the strong tracking CKF method. The new fading factor introduction method expanded the number of fading factors from one to two with reselected introduction positions. The relationship between the two fading factors as well as the general calculation method can be derived based on Taylor expansion. Obvious superiority of the newly suggested fading factor introduction method is demonstrated according to different nonlinearity of the measurement function. Equivalent calculation method can also be established while applied to CKF. Theoretical analysis shows that the strong tracking CKF can extract the third-order term information from the residual and thus realize second-order accuracy. After optimizing the strong tracking algorithm process, a Fast Strong Tracking CKF (FSTCKF) is finally established. Two simulation examples show that the novel FSTCKF improves the robustness of traditional CKF while minimizing the algorithm time complexity under various conditions.

Consensus Based Strong Tracking Adaptive Cubature Kalman Filtering for Nonlinear System Distributed Estimation

The distributed cubature Kalman filter is widely used in the field of target tracking, however, the presence of model uncertainties will undermine its tracking stability and effectiveness for tracking maneuvering target. In order to eliminate this effect on maneuvering target tracking, this paper develops a distributed consensus based strong tracking cubature Kalman filter scheme. First, each node obtains its local estimation with the usage of local observations via strong tracking cubature Kalman filter, where the suboptimal fading factor and adaptive factor are introduced for adaptively modifying the filter gain. Then, the designed filter gain is used for updating the local state estimation. Second, after all, nodes have achieved its local estimation, each node exchanges its local estimation to its neighbors and updates its local estimation according to the consensus communication protocol. It can be further proved that the distributed interaction between neighbors will contribute to enhancing the tracking stability. The detailed proof for stochastic boundedness of the estimation error is analyzed by introducing a stochastic process. Simulation results demonstrate that the proposed algorithm can achieve higher tracking accuracy than the existing methods for tracking a maneuvering target.

A Novel Fifth-Degree Strong Tracking Cubature Kalman Filter for Two-Dimensional Maneuvering Target Tracking

A novel fifth-degree strong tracking cubature Kalman filter is put forward to improve the two-dimensional maneuvering target tracking accuracy. First, a new fifth-degree cubature rule, with only one point more than the theoretical lower bound, is used to approximate the intractable nonlinear Gaussian weighted integral in the nonlinear Kalman filtering framework, and a novel fifth-degree cubature Kalman filter is proposed. Then, the suboptimal fading factor is designed for the filter to adjust the filtering gain matrix online and force the residual sequences mutually orthogonal, thus improving the ability of the filter to track the mutation state, and the fifth-degree strong tracking cubature Kalman filter is derived. The suboptimal fading factor is calculated in a new method, which reduces the number of calculations for the cubature points from three times to twice without calculating the Jacobian matrix. The simulation results indicate that the proposed filter has the ability to track the maneuvering target and achieve higher target tracking accuracy and thus verifies the effectiveness of the proposed filter.

An Improved Strong Tracking Cubature Kalman Filter for GPS/INS Integrated Navigation Systems.

The cubature Kalman filter (CKF) is widely used in the application of GPS/INS integrated navigation systems. However, its performance may decline in accuracy and even diverge in the presence of process uncertainties. To solve the problem, a new algorithm named improved strong tracking seventh-degree spherical simplex-radial cubature Kalman filter (IST-7thSSRCKF) is proposed in this paper. In the proposed algorithm, the effect of process uncertainty is mitigated by using the improved strong tracking Kalman filter technique, in which the hypothesis testing method is adopted to identify the process uncertainty and the prior state estimate covariance in the CKF is further modified online according to the change in vehicle dynamics. In addition, a new seventh-degree spherical simplex-radial rule is employed to further improve the estimation accuracy of the strong tracking cubature Kalman filter. In this way, the proposed comprehensive algorithm integrates the advantage of 7thSSRCKF’s high accuracy and strong tracking filter’s strong robustness against process uncertainties. The GPS/INS integrated navigation problem with significant dynamic model errors is utilized to validate the performance of proposed IST-7thSSRCKF. Results demonstrate that the improved strong tracking cubature Kalman filter can achieve higher accuracy than the existing CKF and ST-CKF, and is more robust for the GPS/INS integrated navigation system.

多终端五阶强跟踪容积卡尔曼滤波实时定轨

多终端五阶强跟踪容积卡尔曼滤波实时定轨

A robust strong tracking cubature Kalman filter for spacecraft attitude estimation with quaternion constraint

This paper considers a robust strong tracking nonlinear filtering problem in the case there are model uncertainties including the model mismatch, unknown disturbance and status mutation in the spacecraft attitude estimation system with quaternion constraint. Two multiple fading factor matrices are employed to regulate the prediction error covariance matrix, which guarantees its symmetry. The spherical-radial cubature rule is developed to deal with the multi-dimensional integrals. The quaternion constraint is maintained by utilizing the gain correction method. Therefore a robust strong tracking cubature Kalman filter (RSTCKF) is formed for the spacecraft attitude estimation with quaternion constraint. Unlike adopting a single fading factor in the traditional strong tracking filter, the presented filter uses two multiple fading factor matrices to make different channels have respective filter adjustment capability, which improves the tracking performance of this algorithm. Simulation results show the effectiveness of the proposed RSTCKF.

A New Method for State of Charge Estimation of Lithium-Ion Battery Based on Strong Tracking Cubature Kalman Filter

The estimation of state of charge (SOC) is a crucial evaluation index in a battery management system (BMS). The value of SOC indicates the remaining capacity of a battery, which provides a good guarantee of safety and reliability of battery operation. It is difficult to get an accurate value of the SOC, being one of the inner states. In this paper, a strong tracking cubature Kalman filter (STCKF) based on the cubature Kalman filter is presented to perform accurate and reliable SOC estimation. The STCKF algorithm can adjust gain matrix online by introducing fading factor to the state estimation covariance matrix. The typical second-order resistor-capacitor model is used as the battery’s equivalent circuit model to dynamically simulate characteristics of the battery. The exponential-function fitting method accomplishes the task of relevant parameters identification. Then, the developed STCKF algorithm has been introduced in detail and verified under different operation current profiles such as Dynamic Stress Test (DST) and New European Driving Cycle (NEDC). Making a comparison with extended Kalman filter (EKF) and CKF algorithm, the experimental results show the merits of the STCKF algorithm in SOC estimation accuracy and robustness.

A Strong Tracking Cubature Kalman Filter for Nonlinear Estimation

In this paper, a novel method based on cubature Kalman filter (CKF) and strong tracking filter (STF) has been proposed for nonlinear state estimation problem. The proposed method is named as strong tracking cubature Kalman filter (STCKF). In the STCKF, a scaling factor derived from STF is added and it can be tuned online to adjust the filtering gain accordingly. Simulation results indicate STCKF outperforms over EKF and CKF in state estimation accuracy.