scholarly journals A New Variance-Covariance Matrix for Improving Positioning Accuracy in High-Speed GPS Receivers

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7324
Author(s):  
Narjes Rahemi ◽  
Mohammad Reza Mosavi ◽  
Diego Martín
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
High Speed ◽  
Dynamic Models ◽  
Unscented Kalman Filter ◽  
Statistical Characteristics ◽  
Spatial Correlations ◽  
Positioning Accuracy ◽  
High Speeds ◽  
Variance Covariance Matrix

One of the main challenges in using GPS is reducing the positioning accuracy in high-speed conditions. In this contribution, by considering the effect of spatial correlation between observations in estimating the covariances, we propose a model for determining the variance–covariance matrix (VCM) that improves the positioning accuracy without increasing the computational load. In addition, we compare the performance of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) combined with different dynamic models, along with the proposed VCM in GPS positioning at high speeds. To review and test the methods, we used six motion scenarios with different speeds from medium to high and examined the positioning accuracy of the methods and some of their statistical characteristics. The simulation results demonstrate that the EKF algorithm based on the Gauss–Markov model, along with the proposed VCM (based on the sinusoidal function and considering spatial correlations), performs better and provides at least 30% improvement in the positioning, compared to the other methods.

scholarly journals A High-Precision, Real-Time, and Robust Indoor Visible Light Positioning Method Based on Mean Shift Algorithm and Unscented Kalman Filter

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1094 ◽  
Author(s):  
Zekun Xie ◽  
Weipeng Guan ◽  
Jieheng Zheng ◽  
Xinjie Zhang ◽  
Shihuan Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Visible Light ◽  
Real Time ◽  
High Speed ◽  
Unscented Kalman Filter ◽  
Light Emitting Diode ◽  
Mean Shift ◽  
Indoor Navigation ◽  
Positioning Accuracy ◽  
Mean Shift Algorithm

Visible light positioning (VLP) is a promising technology for indoor navigation. However, most studies of VLP systems nowadays only focus on positioning accuracy, whereas robustness and real-time ability are often overlooked, which are all indispensable in actual VLP situations. Thus, we propose a novel VLP method based on mean shift (MS) algorithm and unscented Kalman filter (UKF) using image sensors as the positioning terminal and a Light Emitting Diode (LED) as the transmitting terminal. The main part of our VLP method is the MS algorithm, realizing high positioning accuracy with good robustness. Besides, UKF equips the mean shift algorithm with the capacity to track high-speed targets and improves the positioning accuracy when the LED is shielded. Moreover, a LED-ID (the identification of the LED) recognition algorithm proposed in our previous work was utilized to locate the LED in the initial frame, which also initialized MS and UKF. Furthermore, experiments showed that the positioning accuracy of our VLP algorithm was 0.42 cm, and the average processing time per frame was 24.93 ms. Also, even when half of the LED was shielded, the accuracy was maintained at 1.41 cm. All these data demonstrate that our proposed algorithm has excellent accuracy, strong robustness, and good real-time ability.

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.

scholarly journals Orbit Propagation and Determination of Low Earth Orbit Satellites

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ho-Nien Shou
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Nonlinear Problems ◽  
Low Earth Orbit ◽  
Earth Orbit ◽  
Positioning Accuracy ◽  
Orbit Propagation

This paper represents orbit propagation and determination of low Earth orbit (LEO) satellites. Satellite global positioning system (GPS) configured receiver provides position and velocity measures by navigating filter to get the coordinates of the orbit propagation (OP). The main contradictions in real-time orbit which is determined by the problem are orbit positioning accuracy and the amount of calculating two indicators. This paper is dedicated to solving the problem of tradeoffs. To plan to use a nonlinear filtering method for immediate orbit tasks requires more precise satellite orbit state parameters in a short time. Although the traditional extended Kalman filter (EKF) method is widely used, its linear approximation of the drawbacks in dealing with nonlinear problems was especially evident, without compromising Kalman filter (unscented Kalman Filter, UKF). As a new nonlinear estimation method, it is measured at the estimated measurements on more and more applications. This paper will be the first study on UKF microsatellites in LEO orbit in real time, trying to explore the real-time precision orbit determination techniques. Through the preliminary simulation results, they show that, based on orbit mission requirements and conditions using UKF, they can satisfy the positioning accuracy and compute two indicators.

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 Improving the Stochastic Model for VRS Network-Based GNSS Surveying

2019 ◽  
Vol 54 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Thanate Jongrujinan ◽  
Chalermchon Satirapod
Keyword(s):  
Stochastic Model ◽  
Covariance Matrix ◽  
Ambiguity Resolution ◽  
Reference Station ◽  
Double Difference ◽  
Atmospheric Effects ◽  
Equal Weight ◽  
Virtual Reference ◽  
Positioning Accuracy ◽  
Variance Covariance Matrix

Abstract The VRS network-based technique has become the main precise GNSS surveying method especially for medium-range baselines (approximately 20-70 km). The key concept of this approach is to use the observables of multiple reference stations to generate the network correction in the form of a virtual reference station for mitigating distance-dependent errors including atmospheric effects and orbital uncertainty at the user’s location. Numerous GNSS data processing strategies have been adopted in the functional model in order to improve both the positioning accuracy and the success of ambiguity resolution. However, it is impossible to completely model the aforementioned errors. As a result, the unmodelled residuals still remain in the virtual reference station observables when the least squares estimation is employed. An alternative approach to deal with these residuals is to construct a more realistic stochastic model whereby the variance-covariance matrix is assumed to be homoscedastic. This research aims to investigate a suitable stochastic model used for the VRS technique. The rigorous statistical method, MINQUE has been applied to estimate the variance-covariance matrix of the double-difference observables for a virtual reference station to rover baseline determination. The findings of the comparison to the equal-weight model and the satellite elevation-based model indicated that the MINQUE procedure could enhance the positioning accuracy. In addition, the reliability of ambiguity resolution is also improved.

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.

scholarly journals Modeling of Dual-Spinning Projectile with Canard and Trajectory Filtering

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Guan ◽  
Wenjun Yi
Keyword(s):  
Kalman Filter ◽  
High Speed ◽  
Unscented Kalman Filter ◽  
Measurement Data ◽  
Degree Of Freedom ◽  
Guidance System ◽  
Measurement Information ◽  
Reliable Measurement ◽  
Kalman Filter Algorithm ◽  
Spinning Projectile

The article establishes a seven-degree-of-freedom projectile trajectory model for a new type of spinning projectile. Based on this model, a numerical analysis is performed on the ballistic characteristics of the projectile, and the trajectory of the dual-spinning projectile is filtered with the unscented Kalman filter algorithm, so that the measurement information of projectile onboard equipment is more accurate and more reliable measurement data are provided for the guidance system. The numerical simulation indicates that the dual-spinning projectile is mainly different from the traditional spinning projectile in that a degree of freedom is added in the direction of the axis of the projectile, the forebody of the projectile spins at a low speed or even holds still to improve the control precision of the projectile control system, while the afterbody spins at a high speed maintaining the gyroscopic stability of the projectile. The trajectory filtering performed according to the unscented Kalman filter algorithm can improve the accuracy of measurement data and eliminate the measurement error effectively, so as to obtain more accurate and reliable measurement data.

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