Adaptive Square-root Cubature Kalman Filter Research Articles

Impact of Trade Protectionism on Economic Growth Based on Bayesian Networks and Fuzzy Logic

A government policy known as trade protectionism limits international trade in order to support home industries. Since the global financial crisis, the country's economy has seen a slowdown in trade growth. The data is taken from the China Census Bureau (CCB) and after the data is fed in to data processing technique our proposed is Adaptive Square Root Cubature Kalman Filter (ASRCKF). The preprocessed data is fed into the Bayesian Networks (BN) decision making activities in different influencing factors to foreign trade protectionism and uses fuzzy logic (FL) analyze the China’s foreign trade Protectionism. Set of data is-processing-decision making activities in which actual data using Bayesian networks and fuzzy logic are combined in the Trade Protectionism. The proposed model is implemented in MATLAB/ Simulink platform and the accuracy is compared to various existing approaches such as Particle Optimization Algorithm (POA) Radial Basis Function (RBF) and Support vector neural network (SVNN) method our proposed method obtains 98% of accuracy.

Development of a GNSS/INS-based automatic navigation land levelling system

In this study, an automatic navigation land levelling system based on the global navigation satellite system (GNSS) and an inertial navigation system (INS) was developed to improve the efficiency and accuracy of land levelling. The developed system platform was composed of an integrated positioning unit, steering and lifting controller, and vehicle control terminal. Automatic navigation land levelling vehicle terminal software was designed to realize data communication, processing and storage, and display. Through the cooperation of the platform and software, the system completed the automatic navigation terrain survey, automatic planning/design and automatic navigation land levelling functions. In addition, a GNSS/INS integrated positioning method based on an adaptive square root cubature Kalman filter (ASRCKF) was designed, which obtained the correction positioning points of the tractor and scraper and adaptively predicted the state and measurement noise of the SRCKF. An automatic steering and lifting control method was designed to realize synchronous automatic navigation land levelling control, which was combined with the positioning method. Field experiments were carried out to validate the path tracking effect of the dynamic filtering navigation and a comparison of the manual and automatic land levelling operation performance. The navigation experimental results showed that the average root mean square error (RMSE) of the tractor and the scraper were 2.94 cm and 3.15 cm in tracking a straight path and 8.61 cm and 9.83 cm in tracking a curved path, respectively. The average RMSE of the path tracking based on the ASRCKF positioning method was reduced by 75.2% and 67.4% for the tractor and the scraper, respectively. The land levelling experimental results showed that the elevation distribution around the datum elevation of the automatic navigation land levelling increased by 8.7% compared to the manual operation. The GNSS/INS-based automatic navigation land levelling system can notably reduce the lateral position deviations, improve the control accuracy and land levelling efficiency, and meet the control accuracy requirements of unmanned tractor-scraper land levelling operations.

Joint estimation of SOC and SOH of lithium battery based on multi-time scale EKF-ASRCKF algorithm

To address the low accuracy of battery charged of state (SOC) estimation due to fixed model parameters and capacity, a joint multi-time scale estimation algorithm (EKF-ASRCKF) is proposed in this paper, which consists of the adaptive square root cubature Kalman filter (ASRCKF) algorithm and the extended Kalman filter (EKF) algorithm. Firstly, the model parameters and capacity on the macroscopic time scale are identified by the EKF algorithm; meanwhile, the battery capacity estimation results characterize the battery health of state (SOH). Then the ASRCKF algorithm estimates the SOC on the microscopic time scale. Finally, the experimental validation is carried out under the BBDST condition. The validation result indicates that the EKF-ASRCKF algorithm provides a good estimation of the model parameters and capacity, which further improves the estimation precision of the battery SOC.

State-of-charge estimation of lithium-ion batteries based on fractional-order modeling and adaptive square-root cubature Kalman filter

This paper mainly studies the state of charge (SOC) estimation of lithium batteries based on a fractional-order adaptive square-root cubature Kalman filter (FO-ASRCKF). Firstly, a fractional-order model (FOM) of lithium battery is established by using fractional-order derivative theory. In order to meet the identification accuracy, an improved adaptive genetic algorithm is applied to the process of multi-parameter model identification. Then, the FO-ASRCKF algorithm based on FOM and adaptive rules is proposed, and a comparative experiment with Fractional-order adaptive iterative extended Kalman filter (FO-AIEKF) and Integer-order adaptive square-root cubature Kalman filter (IO-ASRCKF) is carried out. The experimental results show that the proposed FO-ASRCKF can work normally under various working conditions, and it has higher SOC estimation accuracy, with the mean absolute error (MAE) being less than 0.5%. Moreover, it can also overcome the divergence caused by noise and wrong initial values, indicating a better robustness.

Estimation of Longitudinal Force, Sideslip Angle and Yaw Rate for Four-Wheel Independent Actuated Autonomous Vehicles Based on PWA Tire Model.

This article introduces an efficient and high-precision estimation framework for four-wheel independently actuated (FWIA) autonomous vehicles based on a novel tire model and adaptive square-root cubature Kalman filter (SCKF) estimation strategy. Firstly, a reliable and concise tire model that considers the tire’s nonlinear mechanics characteristics under combined conditions through the piecewise affine (PWA) identification method is established to improve the accuracy of the lateral dynamics model of FWIA autonomous vehicles. On this basis, the longitudinal relaxation length of each tire is integrated into the lateral dynamics modeling of FWIA autonomous vehicle. A novel nonlinear state function, including the PWA tire model, is proposed in this paper. To reduce the impact of the uncertainty of noise statistics on the estimation accuracy, an adaptive SCKF estimation algorithm based on the maximum a posteriori (MAP) criterion is proposed in the estimation framework. Finally, the estimation accuracy and stability of the adaptive SCKF algorithm are verified by the co-simulation of CarSim and Simulink. The simulation results show that when the statistical characteristics of noise are unknown and the target state changes suddenly under critical maneuvers, the estimation framework proposed in this paper still maintains high accuracy and stability.

Longitudinal-lateral-cooperative estimation algorithm for vehicle dynamics states based on adaptive-square-root-cubature-Kalman-filter and similarity-principle

It is infeasible to measure vehicle dynamics states (VDS) directly without expensive measurement instruments, especially for the tire-road peak adhesion coefficient (μmax). However, four-wheel-independent-drive-electric-vehicle (4WIDEV) provides convenience for the observation of these dynamic states, because the rotation rate and torque of the in-wheel motor can be acquired directly. Vehicle nonlinear longitudinal-lateral dynamics, the single estimation method for all VDS and the time-varying measurement noise of sensors cause difficulties for the observation. Common the extended-Kalman-filter (EKF) is unsuitable to estimate VDS in strong nonlinear region. This paper propose a longitudinal-lateral cooperative estimation algorithm based on adaptive-square-root-cubature-Kalman-filter (ASRCKF) and partitioned similarity-principle (SP) to estimate the vehicle states and the tire-road peak adhesion coefficient sequentially for 4WIDEV. Firstly, a nonlinear 7-degree-of-freedom (7DOF) vehicle model and magic-formula (MF) tire model are built as the base of the successive estimation scheme. Then, recursive-least-squares (RLS) is adopted to estimate the tire longitudinal force. With the estimated tire longitudinal force, an ASRCKF which can be adjusted adaptively by the feedback dynamics states, is designed for the estimation of vehicle states. Next, the SP algorithm combined with the characteristic of longitudinal-lateral dynamics, which is benefit for μmax estimation when tire dynamics enters the nonlinear region, is proposed. Finally, experiment and simulation results show that excellent performance can be achieved with the proposed estimation method in varying driving conditions.

High Dynamic Weak Signal Tracking Algorithm of a Beidou Vector Receiver Based on an Adaptive Square Root Cubature Kalman Filter.

Compared with a scalar tracking receiver, the Beidou vector tracking receiver has the advantages of smaller tracking errors, fast loss-of-lock reacquisition, and high stability. However, in extremely challenging conditions, such as highly dynamic and weak signals, the loop will exhibit a high degree of nonlinearity, and observations with gross errors and large deviations will reduce the positioning accuracy and stability. In view of this situation, based on the concepts of cubature Kalman filtering and square root filtering, a square root cubature Kalman filtering (SRCKF) algorithm is given. Then, combining this algorithm with the concept of covariance matching based on an innovation sequence, an adaptive square root cubature Kalman filter (ASRCKF) algorithm is proposed. The algorithm was verified, and the tracking performance of the vector locking loop (VLL) realized by the algorithm was compared with the SRCKF VLL and the ASRCKF scalar locking loop (SLL). The simulation results show that, regardless of whether in a highly dynamic weak signal environment or in a general situation where the signal-to-noise ratio is higher than the tracking threshold, the tracking accuracy and stability of the ASRCKF VLL are higher than those of the SRCKF VLL and the ASRCKF SLL, the three-dimensional position error of the ASRCKF VLL does not exceed 36 m, and the three-dimensional velocity error does not exceed 3.5 m/s.

Correction adaptive square-root cubature Kalman filter with application to autonomous vehicle target tracking

For a state estimation problem of nonlinear system, the square-root cubature Kalman filter (SCKF) is an effective method when the noise statistical characteristics are known. However, the performance of SCKF often degrade significantly in the face of uncertain noises interference, particularly in case of measurement or system failure. In this paper, we focus on improving the accuracy and robustness of SCKF under irregular noise. First, a weighted adaptive SCKF (WASCKF) algorithm is presented with moving window method. The WASCKF can improve the accuracy of SCKF by adaptively adjusting the covariances of measurement noise and process noise. Next, in order to further improve the robustness of WASCKF against the abrupt abnormal noise, a correction adaptive SCKF (CASCKF) algorithm based on fault detection mechanism is proposed. The CASCKF algorithm can detect whether there is a fault according to a statistical function of Chi-square distribution, and can judge and carry out the necessary correction processing by using an isolate rule. Finally, the performance of CASCKF is verified by numerical experiments of autonomous vehicle target tracking problem. The results show that the proposed CASCKF algorithm has good accuracy and robustness even with sudden abnormal noise interference.

Robust SCKF Filtering Method for MINS/GPS In-Motion Alignment.

This paper presents a novel multiple strong tracking adaptive square-root cubature Kalman filter (MSTASCKF) based on the frame of the Sage–Husa filter, employing the multi-fading factor which could automatically adjust the Q value according to the rapidly changing noise in the flight process. This filter can estimate the system noise in real-time during the filtering process and adjust the system noise variance matrix Q so that the filtering accuracy is not significantly reduced with the noise. At the same time, the residual error in the filtering process is used as a measure of the filtering effect, and a multiple fading factor is introduced to adjust the posterior error variance matrix in the filtering process, so that the residual error is always orthogonal and the stability of the filtering is maintained. Finally, a vibration test is designed which simulates the random noise of the short-range guided weapon in flight through the shaking table and adds the noise to the present simulation trajectory for semi-physical simulation. The simulation results show that the proposed filter can significantly reduce the attitude estimation error caused by random vibration.

State estimation based on improved cubature Kalman filter algorithm

During the recursive calculate process of the cubature Kalman filter (CKF), the covariance matrix tends to lose positive definiteness and noise statistical characteristics are inaccurate, which results in inaccurate filtering or even filter divergence. This study presents an improved algorithm based on the CKF. The algorithm combines the square root filter algorithm and the Sage–Husa maximum a posterior noise estimator, which can ensure the non-negative determination and symmetry of the covariance matrix and has the ability to deal with unknown and time-varying noise statistical characteristics in the filtering process adaptively. In the multi-dimension system, the noise covariance matrix may dissatisfy non-negative definiteness and result in filter divergence, and then the noise covariance matrix estimator is improved. The analysis is verified by state estimation example of the non-linear system, compared with the standard CKF, the accuracy of the adaptive square root CKF (ASRCKF) state estimation is increased by 63.13, 63.88, and 42.71%, respectively. Finally, the effectiveness of the ASRCKF is verified by the state estimation of the permanent magnet linear synchronous motor.

Application of adaptive square root cubature Kalman filter in turbofan engine gas path performance monitoring

Kalman filters are very popular in turbofan engine community for health monitoring purposes. In this study, in order to get better performance in terms of filtering accuracy and noise adaptability, an Adaptive Square Root Cubature Kalman Filter (ASRCKF) was proposed to estimate health parameters of the turbofan engine gas path components. In the ASRCKF algorithm, the mean value and covariance of the engine nonlinear function were calculated by cubature rule-based numerical integration method and used as a substitute for nonlinear model in nonlinear Kalman filter. The latest information of measurement parameters in the recursion and filtering process was used to estimate and self-adjust the noises cross-covariance by removable window method to get higher filtering accuracy. Compared with the Extended Kalman Filter (EKF) and Square Root Cubature Kalman Filter (SRCKF), the simulation results in the gradual and rapid deterioration process of turbofan engine gas path components indicate that the higher accuracy and faster convergence can be obtained through ASRUKF, which can be used in health parameters estimation and condition monitoring of turbofan engine gas path.1

Adaptive Cubature Kalman Filter Based on the Expectation-Maximization Algorithm

A cubature Kalman filter is considered to be one of the most useful methods for nonlinear systems. However, when the statistical characteristics of noise are unknown, the estimation accuracy is degraded. Therefore, an adaptive square-root cubature Kalman filter (ASCKF) is designed to handle the unknown noise. The maximum likelihood criterion and expectation-maximization algorithm are employed to adaptively estimate the parameters of unknown noise, thus restraining the disturbance resulting from unknown noise and improving the estimation accuracy. The stability of the proposed algorithm is theoretically analyzed. Finally, simulations are carried out to illustrate that the performance of the ASCKF algorithm is much more reliable than that of a standard square-root cubature Kalman filter.

Fusion Algorithm Design Based on Adaptive SCKF and Integral Correction for Side-Slip Angle Observation

Vehicle side-slip angle is crucial for various vehicle active safety applications, but measuring it directly needs expensive measurement instruments and the vehicle nonlinear dynamics, parameters uncertainty, and sensor noise cause difficulties in its observation. Therefore, the accurate, affordable side-slip angle estimator is essential. Thus, a novel adaptive square-root cubature Kalman filter (ASCKF)-based estimator with the integral correction fusion is proposed. First, the square-root cubature Kalman filter (SCKF) parameters can be adjusted adaptively based on the vehicle dynamics states. Then, considering the unknown colored noises of sensors, the integral estimation is corrected by the damping item and zero-point-reset method and the integral value can compensate the estimation error caused by the vehicle nonlinear dynamics. Therefore, the accurate side-slip angle can be estimated by the adaptive fusion of the estimation and integral values. The simulation results and real-vehicle tests show that the proposed ASCKF-based fusion algorithm has better performance than both the traditional SCKF and ASCKF.

Low-cost adaptive square-root cubature Kalman filter for systems with process model uncertainty

A novel low-cost adaptive square-root cubature Kalman filter (LCASCKF) is proposed to enhance the robustness of process models while only increasing the computational load slightly. It is well-known that the Kalman filter cannot handle uncertainties in a process model, such as initial state estimation errors, parameter mismatch and abrupt state changes. These uncertainties severely affect filter performance and may even provoke divergence. A strong tracking filter (STF), which utilizes a suboptimal fading factor, is an adaptive approach that is commonly adopted to solve this problem. However, if the strong tracking SCKF (STSCKF) uses the same method as the extended Kalman filter (EKF) to introduce the suboptimal fading factor, it greatly increases the computational load. To avoid this problem, a low-cost introductory method is proposed and a hypothesis testing theory is applied to detect uncertainties. The computational load analysis is performed by counting the total number of floating-point operations and it is found that the computational load of LCASCKF is close to that of SCKF. Experimental results prove that the LCASCKF performs as well as STSCKF, while the increase in computational load is much lower than STSCKF.

The Application of Adaptive Square Root Cubature Particle Filtering Algorithm in Initial Alignment of Large Azimuth Misalignment in SINS

The error model of Strap-down Inertial Navigation System (SINS) initial alignment is nonlinear under large azimuth misalignment angle condition, and it could be processed by the Particle Filter (PF) algorithm. Because the importance density function of the standard particle filter algorithm is difficult to select, a new algorithm of the Cubature Particle Filter (CPF) is proposed in this paper. In the new algorithm, the importance density function of standard particle filter is obtained by Adaptive Square root Cubature Kalman Filter (ASCKF), square root decomposition is chosen to enhance the numerical robustness and ensure that the state covariance matrix is positive definite. To meet the realtime requirement, the adaptive factor is introduced to control system model error. As the computer simulation results are shown that this algorithm could reduce the effect of inaccurate noise statistical model and it is a very effective nonlinear filtering algorithm.

Multi-sensor hybrid fusion algorithm based on adaptive square-root cubature Kalman filter

In the normal operation condition, a conventional square-root cubature Kalman filter (SRCKF) gives sufficiently good estimation results. However, if the measurements are not reliable, the SRCKF may give inaccurate results and diverges by time. This study introduces an adaptive SRCKF algorithm with the filter gain correction for the case of measurement malfunctions. By proposing a switching criterion, an optimal filter is selected from the adaptive and conventional SRCKF according to the measurement quality. A subsystem soft fault detection algorithm is built with the filter residual. Utilizing a clear subsystem fault coefficient, the faulty subsystem is isolated as a result of the system reconstruction. In order to improve the performance of the multi-sensor system, a hybrid fusion algorithm is presented based on the adaptive SRCKF. The state and error covariance matrix are also predicted by the priori fusion estimates, and are updated by the predicted and estimated information of subsystems. The proposed algorithms were applied to the vessel dynamic positioning system simulation. They were compared with normal SRCKF and local estimation weighted fusion algorithm. The simulation results show that the presented adaptive SRCKF improves the robustness of subsystem filtering, and the hybrid fusion algorithm has the better performance. The simulation verifies the effectiveness of the proposed algorithms.