Developing Computationally Efficient Nonlinear Cubature Kalman Filtering for Visual Inertial Odometry

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Trung Nguyen ◽  
George K. I. Mann ◽  
Andrew Vardy ◽  
Raymond G. Gosine
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
High Speed ◽  
Three Dimensional ◽  
Measurement Model ◽  
Estimation Accuracy ◽  
Computationally Efficient ◽  
Fusion Algorithm ◽  
Deterministic Sampling ◽  
Cubature Kalman Filter

This paper presents a computationally efficient sensor-fusion algorithm for visual inertial odometry (VIO). The paper utilizes trifocal tensor geometry (TTG) for visual measurement model and a nonlinear deterministic-sampling-based filter known as cubature Kalman filter (CKF) to handle the system nonlinearity. The TTG-based approach is developed to replace the computationally expensive three-dimensional-feature-point reconstruction in the conventional VIO system. This replacement has simplified the system architecture and reduced the processing time significantly. The CKF is formulated for the VIO problem, which helps to achieve a better estimation accuracy and robust performance than the conventional extended Kalman filter (EKF). This paper also addresses the computationally efficient issue associated with Kalman filtering structure using cubature information filter (CIF), the CKF version on information domain. The CIF execution avoids the inverse computation of the high-dimensional innovation covariance matrix, which in turn further improves the computational efficiency of the VIO system. Several experiments use the publicly available datasets for validation and comparing against many other VIO algorithms available in the recent literature. Overall, this proposed algorithm can be implemented as a fast VIO solution for high-speed autonomous robotic systems.

scholarly journals Double-Layer Cubature Kalman Filter for Nonlinear Estimation

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 986 ◽  
Author(s):  
Feng Yang ◽  
Yujuan Luo ◽  
Litao Zheng
Keyword(s):  
Kalman Filter ◽  
Computational Complexity ◽  
Double Layer ◽  
Poor Performance ◽  
The State ◽  
Estimation Accuracy ◽  
Sampling Point ◽  
Stochastic Sampling ◽  
Deterministic Sampling ◽  
Cubature Kalman Filter

The cubature Kalman filter (CKF) has poor performance in strongly nonlinear systems while the cubature particle filter has high computational complexity induced by stochastic sampling. To address these problems, a novel CKF named double-Layer cubature Kalman filter (DLCKF) is proposed. In the proposed DLCKF, the prior distribution is represented by a set of weighted deterministic sampling points, and each deterministic sampling point is updated by the inner CKF. Finally, the update mechanism of the outer CKF is used to obtain the state estimations. Simulation results show that the proposed algorithm has not only high estimation accuracy but also low computational complexity, compared with the state-of-the-art filtering algorithms.

scholarly journals A Federated Derivative Cubature Kalman Filter for IMU-UWB Indoor Positioning

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3514 ◽  
Author(s):  
Chengyang He ◽  
Chao Tang ◽  
Chengpu Yu
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Unscented Kalman Filter ◽  
Wide Band ◽  
Linear Measurement ◽  
Indoor Positioning ◽  
State Equation ◽  
Estimation Accuracy ◽  
Measurement Unit ◽  
Cubature Kalman Filter

The inertial measurement unit and ultra-wide band signal (IMU-UWB) combined indoor positioning system has a nonlinear state equation and a linear measurement equation. In order to improve the computational efficiency and the localization performance in terms of the estimation accuracy, the federated derivative cubature Kalman filtering (FDCKF) method is proposed by combining the traditional Kalman filtering and the cubature Kalman filtering. By implementing the proposed FDCKF method, the observations of the UWB and the IMU can be effectively fused; particularly, the IMU can be continuously calibrated by UWB so that it does not generate cumulative errors. Finally, the effectiveness of the proposed algorithm is demonstrated through numerical simulations, in which FDCKF was compared with the federated cubature Kalman filter (FCKF) and the federated unscented Kalman filter (FUKF), respectively.

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

Sensors ◽  
2021 ◽  
Vol 21 (20) ◽  
pp. 6707
Author(s):  
Na Li ◽  
Shufang Zhang ◽  
Yi Jiang
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Signal To Noise Ratio ◽  
Three Dimensional ◽  
General Situation ◽  
Weak Signal ◽  
Square Root ◽  
Tracking Accuracy ◽  
Cubature Kalman Filter ◽  
Accuracy And Stability

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.

A Strong Tracking Cubature Kalman Filter for Nonlinear Estimation

2013 ◽  
Vol 313-314 ◽  
pp. 1115-1119
Author(s):  
Yong Qi Wang ◽  
Feng Yang ◽  
Yan Liang ◽  
Quan Pan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Scaling Factor ◽  
Estimation Accuracy ◽  
Nonlinear State Estimation ◽  
Cubature Kalman Filter ◽  
Novel Method ◽  
Simulation Results ◽  
Tracking Filter ◽  
Nonlinear State

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.

scholarly journals Novel MARG-Sensor Orientation Estimation Algorithm Using Fast Kalman Filter

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Siwen Guo ◽  
Jin Wu ◽  
Zuocai Wang ◽  
Jide Qian
Keyword(s):  
Kalman Filter ◽  
Process Model ◽  
Attitude Determination ◽  
Angular Rate ◽  
Estimation Algorithm ◽  
Measurement Model ◽  
Estimation Accuracy ◽  
Orientation Estimation ◽  
Kinematic Equation ◽  
Sensor Orientation

Orientation estimation from magnetic, angular rate, and gravity (MARG) sensor array is a key problem in mechatronic-related applications. This paper proposes a new method in which a quaternion-based Kalman filter scheme is designed. The quaternion kinematic equation is employed as the process model. With our previous contributions, we establish the measurement model of attitude quaternion from accelerometer and magnetometer, which is later proved to be the fastest (computationally) one among representative attitude determination algorithms of such sensor combination. Variance analysis is later given enabling the optimal updating of the proposed filter. The algorithm is implemented on real-world hardware where experiments are carried out to reveal the advantages of the proposed method with respect to conventional ones. The proposed approach is also validated on an unmanned aerial vehicle during a real flight. Results show that the proposed one is faster than any other Kalman-based ones and even faster than some complementary ones while the attitude estimation accuracy is maintained.

scholarly journals An Integrated Adaptive Kalman Filter for High-Speed UAVs

2019 ◽  
Vol 9 (9) ◽  
pp. 1916 ◽  
Author(s):  
Tiantian Huang ◽  
Hui Jiang ◽  
Zhuoyang Zou ◽  
Lingyun Ye ◽  
Kaichen Song
Keyword(s):  
Kalman Filter ◽  
High Speed ◽  
Sensor Data ◽  
Adaptive Kalman Filter ◽  
Fusion Algorithm ◽  
Multi Sensor Data Fusion ◽  
Aerial Vehicle ◽  
Robust Adaptive ◽  
Tracking Filter ◽  
Filter Algorithms

In order to solve the problems of filtering divergence and low accuracy in Kalman filter (KF) applications in a high-speed unmanned aerial vehicle (UAV), this paper proposed a new method of integrated robust adaptive Kalman filter: strong adaptive Kalman filter (SAKF). The simulation of two high-dynamic conditions and a practical experiment were designed to verify the new multi-sensor data fusion algorithm. Then the performance of the Sage–Husa adaptive Kalman filter (SHAKF), strong tracking filter (STF), H∞ filter and SAKF were compared. The results of the simulation and practical experiments show that the SAKF can automatically select its filtering process under different conditions, according to an anomaly criterion. SAKF combines the advantages of SHAKF, H∞ filter and STF, and has the characteristics of high accuracy, robustness and good tracking skill. The research has proved that SAKF is more appropriate in high-speed UAV navigation than single filter algorithms.

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

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2251 ◽  
Author(s):  
Jikai Liu ◽  
Pengfei Wang ◽  
Fusheng Zha ◽  
Wei Guo ◽  
Zhenyu Jiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Real Time ◽  
Quadruped Robot ◽  
The State ◽  
Estimation Accuracy ◽  
Robot System ◽  
Calculation Time ◽  
Motion State ◽  
Cubature Kalman Filter

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.

Iterated Cubature Kalman Filter for State Estimation of Maneuver Reentry Vehicle

2012 ◽  
Vol 466-467 ◽  
pp. 1329-1333
Author(s):  
Jing Mu ◽  
Chang Yuan Wang
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Unscented Kalman Filter ◽  
High Accuracy ◽  
Estimation Accuracy ◽  
Reentry Vehicle ◽  
Vehicle Simulation ◽  
Cubature Kalman Filter ◽  
Simulation Results ◽  
Iterate Process

We present the new filters named iterated cubature Kalman filter (ICKF). The ICKF is implemented easily and involves the iterate process for fully exploiting the latest measurement in the measurement update so as to achieve the high accuracy of state estimation We apply the ICKF to state estimation for maneuver reentry vehicle. Simulation results indicate ICKF outperforms over the unscented Kalman filter and square root cubature Kalman filter in state estimation accuracy.

Nonlinear Kalman Filtering With Expensive Forward Models Via Measure Change

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Brian J. Burrows ◽  
Douglas Allaire
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
High Speed ◽  
Unscented Kalman Filter ◽  
Computational Cost ◽  
Test Problems ◽  
Model Approximation ◽  
Forward Models ◽  
Estimation Scheme ◽  
Increase In Accuracy

Abstract Filtering is a subset of a more general probabilistic estimation scheme for estimating the unobserved parameters from the observed measurements. For nonlinear, high speed applications, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are common estimators; however, expensive and strongly nonlinear forward models remain a challenge. In this paper, a novel Kalman filtering algorithm for nonlinear systems is developed, where the numerical approximation is achieved via a change of measure. The accuracy is identical in the linear case and superior in two nonlinear test problems: a challenging 1D benchmarking problem and a 4D structural health monitoring problem. This increase in accuracy is achieved without the need for tuning parameters, rather relying on a more complete approximation of the underlying distributions than the Unscented Transform. In addition, when expensive forward models are used, we achieve a significant reduction in computational cost without resorting to model approximation.

scholarly journals State of Charge Estimation for Lithium-Ion Battery by Using Dual Square Root Cubature Kalman Filter

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Luping Chen ◽  
Liangjun Xu ◽  
Ruoyu Wang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Lithium Ion ◽  
State Of Charge ◽  
Estimation Accuracy ◽  
Square Root ◽  
Battery Management ◽  
Balance Performance ◽  
Soc Estimation ◽  
Cubature Kalman Filter

The state of charge (SOC) plays an important role in battery management systems (BMS). However, SOC cannot be measured directly and an accurate state estimation is difficult to obtain due to the nonlinear battery characteristics. In this paper, a method of SOC estimation with parameter updating by using the dual square root cubature Kalman filter (DSRCKF) is proposed. The proposed method has been validated experimentally and the results are compared with dual extended Kalman filter (DEKF) and dual square root unscented Kalman filter (DSRUKF) methods. Experimental results have shown that the proposed method has the most balance performance among them in terms of the SOC estimation accuracy, execution time, and convergence rate.

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