scholarly journals A Study on Minimum Sigma Set SRUKF Based GPS/INS Tightly-Coupled System

2017 ◽  
Author(s):  
Maosong Wang ◽  
Xiaofeng He ◽  
Wenqi Wu ◽  
Zhenbo Liu
Keyword(s):  
Kalman Filter ◽  
Kalman Filters ◽  
Unscented Kalman Filter ◽  
Coupled System ◽  
The State ◽  
Computational Time ◽  
Square Root ◽  
Unscented Transformation ◽  
Tightly Coupled ◽  
The Stability

In this paper, firstly, some questionable formulas and conceptual oversights of previous reduced sigma set unscented transformation (UT) methods are revised through theoretical analysis. Then the revised UT methods based Kalman filters are used in a GPS/INS tightly-coupled system. The Kalman filter flows are the kind of square-root, since the square-root unscented Kalman filters (SRUKFs) can guarantee the stability of the system. By using the reduced sigma set SRUKFs (which contain simplex sigma set square-root unscented Kalman filter (S-SRUKF), spherical simplex sigma set square-root unscented Kalman filter (SS-SRUKF) and minimum sigma set square-root unscented Kalman filter (M-SRUKF)), the computation cost is greatly saved compared with the standard SRUKF, while the accuracy of the GPS/INS tightly-coupled system still maintained. The structure of the GPS/INS tightly-coupled system is in the form of error state, and the time updates of the state and the state covariance of SRUKFs are directly estimated without using UT, thus the computational time is also greatly saved. The pseudo-satellite is introduced to aid the system when the observation information is deficient, for example, when the GPS signal is deficient in the maneuver environment. By using the pseudo-satellite, the optimal performance of the system is guaranteed. Experiment of unmanned aerial vehicle (UAV) showed that the pseudo-satellite aided mechanism worked well.

Minimum Sigma Set SR-UKF for Quadrifocal Tensor-based Binocular Stereo Vision-IMU Tightly-coupled System

2018 ◽  
Vol 71 (6) ◽  
pp. 1329-1343 ◽  
Author(s):  
Maosong Wang ◽  
Wenqi Wu ◽  
Naser El-Sheimy ◽  
Zhiwen Xian
Keyword(s):  
Kalman Filter ◽  
Open Source ◽  
Binocular Vision ◽  
Unscented Kalman Filter ◽  
Coupled System ◽  
The State ◽  
Measurement Unit ◽  
Square Root ◽  
Epipolar Constraint ◽  
Tightly Coupled

This paper presents a binocular vision-IMU (Inertial Measurement Unit) tightly-coupled structure based on a Minimum sigma set Square-Root Unscented Kalman Filter (M-SRUKF) for real time navigation applications. Though the M-SRUKF has only half the sigma points of the SRUKF, it has the same accuracy as the SRUKF when applied to the binocular vision-IMU tightly-coupled system. As the Kalman filter flow is a kind of square-root system, the stability of the system can be guaranteed. The measurement model and the outlier rejection model of this tightly-coupled system not only utilises the epipolar constraint and the trifocal tensor geometry constraint between the consecutive two image pairs, but also uses the quadrifocal tensor geometry among four views. The structure of the binocular vision-IMU tightly-coupled system is in the form of an error state, and the time updates of the state and the state covariance are directly estimated without using Unscented Transformation (UT). Experiments are carried out based on an outdoor land vehicle open source dataset and an indoor Micro Aerial Vehicle (MAV) open source dataset. Results clearly show the effectiveness of the proposed new mechanisation.

A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems

2013 ◽  
Vol 300-301 ◽  
pp. 623-626 ◽  
Author(s):  
Yong Zhou ◽  
Yu Feng Zhang ◽  
Ju Zhong Zhang
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Covariance Matrix ◽  
Unscented Kalman Filter ◽  
Square Root ◽  
Noise Covariance Matrix ◽  
Measurement Noise Covariance ◽  
Noise Covariance ◽  
The Stability ◽  
Stability And Accuracy

This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on Square-Root Unscented Kalman Filter (SRUKF), the traditional Maybeck’s estimator is modified and extended to the nonlinear systems, the estimation of square root of the process noise covariance matrix Q or measurement noise covariance matrix R is obtained straightforwardly. Then the positive semi-definiteness of Q or R is guaranteed, some shortcomings of traditional Maybeck’s algorithm are overcome, so the stability and accuracy of the filter is improved greatly.

The Unscented Kalman Filter Estimators for High Dynamic Doppler Shift Environments

2012 ◽  
Vol 532-533 ◽  
pp. 1487-1491
Author(s):  
Kun Zhao ◽  
Ke Gang Pan ◽  
Ai Jun Liu ◽  
Dao Xing Guo
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Doppler Shift ◽  
Unscented Kalman Filter ◽  
The State ◽  
Extend Kalman Filter ◽  
Unscented Transformation ◽  
High Dynamic ◽  
Simulation Results ◽  
Dynamic Trajectory

The Extend Kalman Filter (EKF) is widely used in the tracking of high dynamic Doppler shift trajectories, but it has some flows when it is used to estimate the state of nonlinear systems. In this paper, we apply the Unscented Transformation (UT) based Unscented Kalman Filter (UKF) to the state estimation in the high dynamic Doppler environments. Two versions of the UKF estimators, augmented UKF estimator and nonaugemented UKF estimator are designed. To compare the performance of them, they are applied to tracking a common high dynamic trajectory, and simulation results declare that given different conditions, the performance of the estimators will be different.

scholarly journals Square-Root Cubature Kalman Filter Based on H∞ Filter for Attitude Measurement of High-Spinning Aircraft

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ping-an Zhang ◽  
Wei Wang ◽  
Min Gao ◽  
Yi Wang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Euler Angle ◽  
Positive Semidefinite ◽  
Measurement Model ◽  
The State ◽  
Measurement Noise ◽  
Attitude Measurement ◽  
Square Root ◽  
Cubature Kalman Filter

A novel H∞ filter called square-root cubature H∞ Kalman filter is proposed for attitude measurement of high-spinning aircraft. In this method, a combined measurement model of three-axis geomagnetic sensor and gyroscope is used, and the Euler angle algorithm model is used to reduce the state dimension and linearize the state equation, which can reduce the amount of calculation. Simultaneously, the method can be applied to the case of measurement noise uncertainty. By continuously modifying the error limiting parameters to update the measurement noise estimation, the filtering accuracy and robustness can be improved. The square-root forms enjoy a consistently improved numerical stability because all the resulting covariance matrices by QR decomposition are guaranteed to stay positive semidefinite. The algorithm is applied to the simulation experiment of attitude measurement with the combination of geomagnetic sensor and gyroscope and compared with the results of Unscented Kalman filter, cubature Kalman filter, square root cubature Kalman filter, and singular value decomposition cubature Kalman filter, which proves the effectiveness and superiority of the algorithm.

scholarly journals A square root unscented Kalman filter for multiple view geometry based stereo cameras/inertial navigation

2016 ◽  
Vol 13 (5) ◽  
pp. 172988141666485 ◽  
Author(s):  
Zhiwen Xian ◽  
Junxiang Lian ◽  
Mao Shan ◽  
Lilian Zhang ◽  
Xiaofeng He ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Inertial Navigation ◽  
Square Root ◽  
Multiple View Geometry ◽  
Multiple View ◽  
Stereo Cameras

Model aided airborne integrated navigation system based on an improved square-root unscented H∞ filter

2018 ◽  
Vol 41 (5) ◽  
pp. 1290-1300
Author(s):  
Jieliang Shen ◽  
Yan Su ◽  
Qing Liang ◽  
Xinhua Zhu
Keyword(s):  
Kalman Filter ◽  
Navigation System ◽  
Unscented Kalman Filter ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Strong Nonlinearity ◽  
Square Root ◽  
Integrated Navigation ◽  
Fusion Algorithm ◽  
Integrated Navigation System

An inertial navigation system (INS) aided with an aircraft dynamic model (ADM) is developed as a novel airborne integrated navigation system, coping with the absence of a global navigation satellite system. To overcome the shortcomings of the conventional linear integration of INS/ADM based on an extended Kalman filter, a nonlinear integration method is proposed. Fast-update ADM makes it possible to utilize a direct filtering method, which employs nonlinear INS mechanics as system equations and a nonlinear ADM as observation equations, substituting the indirect filtering based on linear error equations. The strong nonlinearity generally calls for an unscented Kalman filter to accomplish the fusion process. Dealing with the model uncertainty, the inaccurate statistical characteristics of the noise and the potential nonpositive definiteness of the covariance matrix, an improved square-root unscented H∞ filter (ISRUHF) is derived in the paper, in which the robust factor [Formula: see text] is further expanded into a diagonal matrix [Formula: see text], to improve the accuracy and robustness of the integrated navigation system. Corresponding simulations as well as real flight tests based on a small-scale fixed-wing aircraft are operated and ISRUHF shows superiority compared with the commonly used fusion algorithm.

Spherical Simplex Unscented Kalman Filter-Based Jumping and Static Interacting Multiple Model

2017 ◽  
Vol 32 (04) ◽  
pp. 1850010
Author(s):  
Yi Pan ◽  
Hui Ye ◽  
Keke He
Keyword(s):  
Kalman Filter ◽  
Nonlinear Filtering ◽  
System Parameter ◽  
Unscented Kalman Filter ◽  
Continuous System ◽  
The State ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Real Time System ◽  
Spherical Simplex

A modified interacting multiple model (IMM) method called spherical simplex unscented Kalman filter-based jumping and static IMM (SSUKF-JSIMM) is proposed to solve the problem of nonlinear filtering with unknown continuous system parameter. SSUKF-JSIMM regards the continuous system parameter space as a union of disjoint regions, and each region is assigned to a model. For each model, under the assumption that the parameter belongs to the corresponding region, one sub-filter is used to estimate the parameter and the state when the parameter is presumed to be jumping, and another sub-filter is used to estimate the parameter and the state when the parameter is presumed to be static. Considering that spherical simplex unscented Kalman filter (SSUKF) is more suitable for a real-time system than the unscented Kalman filter (UKF), SSUKFs are adopted as the sub-filters of SSUKF-JSIMM. Results of the two SSUKFs are fused as the estimation output of the model. Experimental results show that SSUKF-JSIMM achieves higher performance than IMM, SIR, and UKF in bearings-only tracking problem.

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