Sage-Husa Adaptive Kalman Filter Research Articles

GNSS/5G Joint Position Based on Weighted Robust Iterative Kalman Filter

The Global Navigation Satellite System (GNSS) is widely used for its high accuracy, wide coverage, and strong real-time performance. However, limited by the navigation signal mechanism, satellite signals in urban canyons, bridges, tunnels, and other environments are seriously affected by non-line-of-sight and multipath effects, which greatly reduce positioning accuracy and positioning continuity. In order to meet the positioning requirements of human and vehicle navigation in complex environments, it was necessary to carry out this research on the integration of multiple signal sources. The Fifth Generation (5G) signal possesses key attributes, such as low latency, high bandwidth, and substantial capacity. Simultaneously, 5G Base Stations (BSs), serving as a fundamental mobile communication infrastructure, extend their coverage into areas traditionally challenging for GNSS technology, including indoor environments, tunnels, and urban canyons. Based on the actual needs, this paper proposes a system algorithm based on 5G and GNSS joint positioning, aiming at the situation that the User Equipment (UE) only establishes the connection with the 5G base station with the strongest signal. Considering the inherent nonlinear problem of user position and angle measurements in 5G observation, an angle cosine solution is proposed. Furthermore, enhancements to the Sage–Husa Adaptive Kalman Filter (SHAKF) algorithm are introduced to tackle issues related to observation weight distribution and adaptive updates of observation noise in multi-system joint positioning, particularly when there is a lack of prior information. This paper also introduces dual gross error detection adaptive correction of the forgetting factor based on innovation in the iterative Kalman filter to enhance accuracy and robustness. Finally, a series of simulation experiments and semi-physical experiments were conducted. The numerical results show that compared with the traditional method, the angle cosine method reduces the average number of iterations from 9.17 to 3 with higher accuracy, which greatly improves the efficiency of the algorithm. Meanwhile, compared with the standard Extended Kalman Filter (EKF), the proposed algorithm improved 48.66%, 35.17%, and 38.23% at 1σ/2σ/3σ, respectively.

A meticulous covariance adaptive Kalman filter for satellite attitude estimation

Aiming at the problems of model errors, non-Gaussian noise and measurement anomaly in the spacecraft attitude estimation system, this article proposes an improved adaptive filtering method based on covariance matching, which solves the problems of simultaneous dynamics model error and measurement model error in the attitude estimation system, and at the same time, effectively reduces the effects of non-Gaussian noise and large outlier situations occurring in the vector measurement sensor. Firstly, an adaptive filtering algorithm based on the innovation sequence estimation covariance is investigated under the framework of multiplicative extended Kalman filter (MEKF), which is used to correct process noise covariance, then the Sage–Husa adaptive Kalman filtering (SHAKF) method is combined to correct the measurement noise covariance, and finally the meticulous covariance adaptive multiplicative extended Kalman filter is designed. The proposed algorithm uses both innovation and SHAKF methods to correct the two covariance matrices simultaneously. Several attitude estimation simulation scenarios are set up to simulate the proposed algorithm in the presence of model errors, non-Gaussian noise, and large outlier. The simulation results demonstrate that the proposed algorithm outperforms the conventional algorithms in terms of estimation accuracy and robustness.

Energy-Optimal Adaptive Control Based on Model Predictive Control.

Energy-optimal adaptive cruise control (EACC) is becoming increasingly popular due to its ability to save energy. Considering the negative impacts of system noise on the EACC, an improved modified model predictive control (MPC) is proposed, which combines the Sage-Husaadaptive Kalman filter (SHAKF), the cubature Kalman filter (CKF), and the back-propagation neural network (BPNN). The proposed MPC improves safety and tracking performance while further reducing energy consumption. The final simulation results show that the proposed algorithm has a stronger energy-saving capability compared to previous studies and always maintains an appropriate relative distance and relative speed to the vehicle in front, verifying the effectiveness of the proposed algorithm.

A novel adaptive nonlinear Kalman filter scheme for DVL-aided SINS alignment in underwater vehicles

The rapid and accurate initial alignment of a strapdown inertial navigation system (SINS) aided by a Doppler velocity logger (DVL) still poses a significant challenge in unmanned underwater vehicle navigation. In this study, a novel adaptive nonlinear filtering alignment scheme is developed for a SINS with a large misalignment angle. In previous studies, the frame-inconsistency problem of the nonlinear SINS error model was neglected. Thus, a modified nonlinear error model of a SINS is derived here rigorously as the process model of the nonlinear Kalman filter. In addition, the noise amplification of applying Sage-Husa adaptive Kalman filter (SHAKF) in alignment is analyzed, and a novel arctangent fading memorial factor is introduced to dynamically adjust the weight of current measurements. Simulations and field experiments indicate that the proposed algorithm is efficient in underwater DVL/SINS in-motion alignment. The alignment accuracy and convergence rate of the modified model are significantly improved compared to those of the traditional model. The arctangent fading memorial SHAKF can reliably estimate the measurement noise and improve the performance of alignment.

An integrated adaptive Kalman filter for improving the reliability of navigation systems

Abstract Integrated GPS/INS using Kalman filter is the best technique for improving navigation accuracy. Assuming that the covariance matrices are known and constant, a conventional Kalman filter (CKF) is usually used, however, when they are unknown and time-varying, several adaptive estimation approaches have to be developed to estimate the statistical information of the measurement (R), process (Q), and state (P) covariance matrices. In many situations, blunders/faults in the measurement model and/or sudden changes in the dynamic model may occur during the navigation period. Therefore, the CKF, as well as the adaptive Kalman filter (AKF) will exhibit abnormal behavior and may lead the filter to be suboptimal or even diverge. In this study, the Sage-Husa adaptive Kalman filter (SHAKF) and innovation-based adaptive Kalman filter (IAKF) approaches are employed for adapting the measurement covariance matrix(R). In the case of abrupt changes in the dynamic model, the state covariance matrix (P) is adapted using the strong tracking filter (STF). The performance of these adaptive approaches is evaluated before and after simulating a fault of different sizes in the measurement and dynamic models. The results show that with a large window width, the SHAKF outperforms the CKF and IAKF. However, when the system encounters any fault either in the measurement or dynamic model, the SHAKF loses its optimality and diverges. The sensitivity of the SHAKF to the fault is because the R matrix accumulates with the propagation of the recursive noise estimator. On the other hand, the IAKF and STF provide better performance than both the CKF and SHAKF because the gain matrix is adaptively adjusted to mitigate the influence of the fault, and therefore, they behave normally when a fault of any size occurs in the measurement and/or dynamic model.

Novel pedestrian navigation system based on zero velocity update procedure technology and improved Sage‐Husa adaptive Kalman filter with index fading memory factor

AbstractTo acquire an accurate location on the occasions, such as in an indoor, tunnel, and valley, where satellite navigation signals fail. The paper designs a pedestrian navigation system by using the zero velocity update procedure technology (ZUPT) and Kalman filter to reduce the location error. The measurement noise characteristic (mean and variance) of the micro electro mechanical systems gyros is unknown and time variant, but in traditional studies, it is usually thought and calculated as a constant. So the optimality of the error estimation of the Kalman filter cannot be reached. To address this question, this paper proposes the improved Sage–Husa Adaptive Kalman Filter (SHAKF) based on the index fading memory factor to realise the state estimation of the Kalman filter and navigation error correction. The advantage of improved SHAKF is it can accurately estimate the state vector when the measurement noise is unknown and time variant. To verify the validity of novel navigation methods, walking experiments under outdoor environments and indoor environments are carried out. The results of actual walking experiments demonstrate that the proposed method can effectively reduce the pedestrian location error compared with the traditional ZUPT method. The mean location error is reduced by more than 10%, and the variance of the location error is reduced by more than 5%.

A modified adaptive Kalman filtering method for maneuvering target tracking of unmanned surface vehicles

The filtering methods are crucial for an unmanned surface vehicle (USV) to realize target tracking. Due to the poor observation caused by the strong vibration during the navigation of the USV, the target tracking accuracy of the traditional filtering method has been significantly degraded. A modified strong tracking-based expended Sage-Husa adaptive robust Kalman filter (MST-ESHARKF) algorithm is proposed to overcome this problem in this paper. In the proposed algorithm, a modified fading factor for the strong tracking Kalman filter is introduced to eliminate disturbance-induced filter divergence. In addition, the adaptive factor of robust Kalman filtering is designed to balance the predicted and observed states dedicated to improving the robustness of the algorithm. Finally, the biased and unbiased estimators for measurement and process noise covariances are merged, and the measurement noise covariance matrix’s interval is constrained, resulting in a simultaneous evaluation of measurement and process noise covariance matrices with improved dependability of the proposed algorithm. The simulation and experiment results show that the proposed MST-ESHARKF outperforms the existing filters in target tracking.

Slope Estimation Method of Electric Vehicles Based on Improved Sage–Husa Adaptive Kalman Filter

In order to deal with many influence factors of electric vehicles in driving under complex conditions, this paper establishes the system state equation based on the longitudinal dynamics equation of vehicle. Combined with the improved Sage–Husa adaptive Kalman filter algorithm, the road slope estimation model is established. After the driving speed and rough slope observation are input into the slope estimation model, the accurate road slope estimation at the current time can be obtained. The road slope estimation method is compared with the original Sage–Husa adaptive Kalman filter road slope estimation method through three groups of road tests in different slope ranges, and the accuracy and stability advantages of the proposed algorithm in road conditions with large slopes are verified.

Neural network dynamic surface position control of n‐joint robot driven by PMSM with unknown load observer

To solve the problems of low accuracy and poor stability due to modeling error, external disturbance and unknown load, which exist in the position servo control of permanent magnet synchronous motor (PMSM) driven joint robot, this article is to propose the radial basis function (RBF) neural networks dynamic surface control strategy with the Sage-Husa adaptive Kalman filter load torque observer. For the unknown load torque of the robot, the PMSM load torque observer is established by using the Sage-Huga adaptive Kalman filter. The RBF neural network dynamic surface controller is designed using the online approximation capability of the neural network, which is used to approximate the modeling error, external interference and filtering error generated by the dynamic surface control of the joint robot online. Combining the above strategies, the n-joint robot position controller is designed. The stability of this control strategy is demonstrated by stability analysis. Simulations and experiments on the two-joint robot show that the control strategy ensures the accuracy and stability of the joint robot position control.

Hammerstein-Wiener nonlinear system identification by using honey badger algorithm hybridized Sage-Husa adaptive Kalman filter with real-time applications

This paper introduces a hybrid Sage-Husa adaptive Kalman filter (SHAKF) with a metaheuristic algorithm to estimate the parameters of the Hammerstein-Wiener (H-W) model. The initial state parameters of the SHAKF must be appropriately tuned based on the estimation problem; otherwise, it would lead to divergence. To get the global optimal tuned SHAKF parameters for modelling the H-W system, this proposed work has formulated an objective function based on the identification problem optimised with a recently introduced metaheuristic technique called the Honey Badger algorithm (HBA). Finally, the unknown parameters of the H-W system are identified by using the basic SHAKF technique by considering the achieved optimised SHAKF parameters as the initial state inputs. The efficiency of the proposed technique is verified on numerical problems, and its practical feasibility is tested on mechanical systems, namely arm robots and ball-and-beam system identification based on real data sets. The experimental results warrant that the proposed technique possesses high robustness to additive noise, quick convergence speed and low steady-state error compared to the other recently reported methods. For comparison study, different metaheuristic algorithms, namely, comprehensive learning particle swarm optimiser (CLPSO), an ensemble of mutation strategies and control parameters with the differential evolution (EPSDE) and colliding bodies optimisation (CBO), are incorporated into SHAKF to estimate the H-W systems and the obtained results for various standard metrics show the superiority of the proposed HBA-aided SHAKF method over others.

Radar Target Tracking for Unmanned Surface Vehicle Based on Square Root Sage-Husa Adaptive Robust Kalman Filter.

Dynamic information such as the position and velocity of the target detected by marine radar is frequently susceptible to external measurement white noise generated by the oscillations of an unmanned surface vehicle (USV) and target. Although the Sage–Husa adaptive Kalman filter (SHAKF) has been applied to the target tracking field, the precision and stability of SHAKF remain to be improved. In this paper, a square root Sage–Husa adaptive robust Kalman filter (SR-SHARKF) algorithm together with the constant jerk model is proposed, which can not only solve the problem of filtering divergence triggered by numerical rounding errors, inaccurate system mathematics, and noise statistical models, but also improve the filtering accuracy. First, a novel square root decomposition method is proposed in the SR-SHARKF algorithm for decomposing the covariance matrix of SHAKF to assure its non-negative definiteness. After that, a three-segment approach is adopted to balance the observed and predicted states by evaluating the adaptive scale factor. Finally, the unbiased and the biased noise estimators are integrated while the interval scope of the measurement noise is constrained to jointly evaluate the measurement and observation noise for better adaptability and reliability. Simulation and experimental results demonstrate the effectiveness of the proposed algorithm in eliminating white noise triggered by the USV and target oscillations.

A modified Sage-Husa adaptive Kalman filter for state estimation of electric vehicle servo control system

Kalman filter algorithm is widely used in state estimation of electric vehicles (EV) servo system as dynamic estimation of power system. In order to improve the estimation effect of noise interference in engineering practice, a scheme of Modified Sage-Husa adaptive Kalman filter (MSHAKF) combined with fuzzy clustering algorithm is proposed. The scheme processes the experimental data in a robust and adaptive way through the combination of constantly changing fuzzy clustering and MSHAKF, so as to better represent the dynamic characteristics of EV. The simulation results show that this method has higher estimation accuracy than the traditional method on the premise of unknown disturbance and noise characteristics in the system, and is more in line with the practical application of EV.

Needle Tip Tracking in 2D Ultrasound Based on Improved Compressive Tracking and Adaptive Kalman Filter

Ultrasound (US) is commonly used in percutaneous needle procedures for real-time guidance. Accurate and robust automatic needle tracking is highly desirable to address the influence of noise and artifacts in US images. This letter presents a tracking approach which combines an improved compressive tracking (ICT) algorithm and a modified Sage-Husa adaptive Kalman filter (SHAKF) to achieve real-time needle tip tracking under 2D US. Estimated needle insertion velocity is used to improve the tracking performance while the high US pixel intensity of the needle tip is used to correct drift. A simplified SHAKF is then implemented to adaptively estimate the statistical characteristics of the noise in the compressive tracking results. An innovation threshold is proposed to improve the response speed of the filter while a normalized cross correlation based method is used to improve the tracking robustness. The proposed tracking approach has been evaluated in in-plane and out-of-plane motions under different insertion speeds and angles in both phantom and tissue experiments. Compared with the original compressive tracking, ICT+Kalman filter, and the template matching algorithm, our proposed approach demonstrates highly accurate tracking performance and high robustness in all cases.

Roll Angular Rate Measurement for High Spinning Projectiles Based on Redundant Gyroscope System.

Precision-guided projectiles, which can significantly improve the accuracy and efficiency of fire strikes, are on the rise in current military engagements. The accurate measurement of roll angular rate is critical to guide a gun-launched projectile. However, Micro-Electro-Mechanical System (MEMS) gyroscope with low cost and large range cannot meet the requirement of high precision roll angular rate measurement due to the limitation by the current technology level. Aiming at the problem, the optimization-based angular rate estimation (OBARS) method specific for projectiles is proposed in this study. First, the output angular rate model of redundant gyroscope system based on the autoregressive integrated moving average (ARIMA) model is established, and then the conventional random error model is improved with the ARIMA model. After that, a Sage-Husa Adaptive Kalman Filter (SHAKF) algorithm that can suppress the time-varying process and measurement noise under the flight condition of the high dynamic of the projectile is designed for the fusion of dynamic data. Finally, simulations and experiments have been carried out to validate the performance of the method. The results demonstrate the proposed method can effectively improve the angular rate accuracy more than the related traditional methods for high spinning projectiles.

The Application of the Modified Sage-Husa Adaptive Kalman Filter in the Excitation Force Identification of Under-Chassis Active Equipment for Railway Vehicles

Abstract Excitation force of under-chassis active equipment of railway vehicles has a significant impact on the floor vibration of the car body. In order to improve the accuracy of the excitation force identification of active equipment in engineering practice, a new excitation force identification method was proposed by applying modified Sage-Husa adaptive Kalman filter (MSHAKF). First, the advantages of the MSHAKF over conventional Kalman filter (CKF) are introduced. Simulation shows that the MSHAKF has excellent exactness and robustness for active equipment excitation force identification. Finally, a test device for identifying excitation force was established. The infinite impulse response (IIR) low-pass filter is designed by using the bilinear transformation method to eliminate the identification error caused by the frequency multiplication components in the response signal. The experimental result shows that the proposed method is very effective in engineering practice without mastering the noise characteristics of the system.

An EL-SHAKF-Based Integration Scheme for Gyro Thermal-Magnetic Coupling Heading- Effect Drift Compensation in INS

Inertial navigation system (INS) is widely equipped in various vehicles for overcoming GPS-challenging environments. The thermal-magnetic coupling heading-effect drift (thermal-magnetic drift) of INS is a multi-physics coupling error related to carrier maneuver, which cannot be compensated well by traditional methods. In this paper, the source of gyro thermal-magnetic drift are analyzed and an Ensemble Learning (EL) and Sage-Husa adaptive Kalman filter (SHAKF) based integration scheme for the thermal-magnetic drift compensation in high-grade INS is established. In the integrated system, the geomagnetic field strength calculated by International Geomagnetic Reference Field (IGRF) model and temperature information measured by sensors are selected as input of the thermal-magnetic drift prediction model. The gyro biases estimated by exponential fading SHAKF are taken as target in training phase. The EL algorithms, LSBoost and Bagging, are used for training when GPS data is available. The gyro thermal-magnetic drift is predicted and compensated by the trained model during GPS outages. Land and sea tests show its effectiveness on compensate the gyro thermal-magnetic drift of the proposed method.

An Improved Adaptive Kalman Filter for Underwater SINS/DVL System

The main challenge of Strap-down Inertial Navigation System (SINS)/Doppler velocity log (DVL) navigation system is the external measurement noise. Although the Sage–Husa adaptive Kalman filter (SHAKF) has been introduced in the integrated navigation field, the precision and stability of the SHAKF are still the tricky problems to be overcome. The primary aim of this paper is to improve the precision and stability of underwater SINS/DVL system. To attain this, a SINS/DVL tightly integrated model is established, where beam measurements are used without transforming them to 3D velocity. The proposed improved SHAKF algorithm is based on variable sliding window estimation and fading filter. The simulations and vehicle test results demonstrate the effectiveness of the proposed underwater SINS/DVL tightly integrated navigation method based on the improved SHAKF. In addition, the position accuracy of the designed method outperforms that of the SHAKF method.

Physical-layer authentication based on adaptive Kalman filter for V2X communication

Security and authentication are an important guarantee for vehicle to everything (V2X). At present, V2X security schemes in most countries are based on public key infrastructure (PKI). These schemes require additional digital signatures when sending basic safety messages (BSMs), which means security requires additional overhead. Consequently, V2X communication efficiency will be affected in the case of traffic congestion. To solve this problem, we propose a physical-layer authentication model based on channel characteristics in the V2X environment. The model uses the Sage-Husa adaptive Kalman filter, which can dynamically adjust statistical properties of the noises according to observation. Furthermore, we select CSI and RSSI to design a physical-layer authentication scheme based on this model, which can replace the digital signature. Finally, we analyze the impact of the filter algorithm and the factors affecting the authentication threshold, and compare our work with similar schemes. As a result, the proposed scheme makes minor changes to the PKI-based V2X security and effectively reduces the overhead of security. Due to the time-varying channel characteristics, this scheme can prevent impersonation by malicious attackers, thereby improving the security of communication.

MEMS-Based IMU Drift Minimization: Sage Husa Adaptive Robust Kalman Filtering

The Attitude Heading Reference System (AHRS) has been widely used to provide the position and orientation of a rigid body. A low cost MEMS based inertial sensor measurement unit (IMU) is a core device in AHRS. To improve the AHRS system performance, there is a need to develop (i) stochastic IMU error models and (ii) random noise minimization techniques. In this paper, we modify the Sage-Husa Adaptive Kalman Filter (SHAKF) to incorporate time-varying noise estimator and robustifier, termed as Modified Sage-Husa Adaptive Robust Kalman Filter (MSHARKF). In the proposed algorithm, a three segment approach is used to evaluate the adaptive scale factor followed by the learning statistics. The scale factor is iteratively updated in the MSHARKF equations. In addition, angle random walk (ARW) and bias instability (BI) errors are represented by state-space models. The proposed algorithm is applied to restrain the drift error and random noise in the MEMS IMUs signals. The performance of this algorithm is analyzed using Allan variance (AV) analysis for static signals whereas the Root Mean Square Error (RMSE) values are evaluated for dynamic signals. Experimental results demonstrate the effectiveness of MSHARKF in reducing the drift and random noise in static and dynamic conditions as compared with other existing algorithms. Finally, we present sufficient conditions for convergence proof of the MSHARKF algorithm.

Application of Updated Sage–Husa Adaptive Kalman Filter in the Navigation of a Translational Sprinkler Irrigation Machine

Autonomous navigation for agricultural machinery has broad and promising development prospects. Kalman filter technology, which can improve positioning accuracy, is widely used in navigation systems in different fields. However, there has not been much research performed into navigation for sprinkler irrigation machines (SIMs). In this paper, firstly, a self-developed SIM is introduced. Secondly, the kinematics model is established on the platform of the self-developed SIM, and the updated Sage–Husa adaptive Kalman filter, which is an accurate and real-time self-adaptive filtering algorithm, is applied in the navigation of the SIM with the aim of improving the positioning accuracy. Finally, experiment verifications were carried out, and the results show that the self-developed SIM has good navigation performance. Besides this, the influence of abnormal observations on the positioning accuracy of the system can be restrained by using the updated Sage–Husa adaptive Kalman filter. After using the updated Sage–Husa adaptive Kalman filter for the SIM, the maximum deviation between the SIM and the predetermined path is 0.18 m, and the average deviation is 0.08 m; these deviations are within a reasonable range. This proves that the updated Sage–Husa adaptive Kalman filter is applicable for the navigation of sprinkler irrigation machines.