Tianjin Institute of Hydrographic Surveying and Charting

Tianjin, China

Tianjin Institute of Hydrographic Surveying and Charting

Tianjin, China
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Chang L.,Wuhan Naval University of Engineering | Hu B.,Wuhan Naval University of Engineering | Chang G.,Tianjin Institute of Hydrographic Surveying and Charting | Li A.,Wuhan Naval University of Engineering
IET Science, Measurement and Technology | Year: 2012

This study concerns the unscented Kalman filter (UKF) for the non-linear dynamic systems with error statistics following non-Gaussian probability distributions. A novel robust unscented Kalman filter (NRUKF) is proposed. In the NRUKF the measurement information (measurements or measurements noise) is reformulated using Huber cost function, then the standard unscented transformation (UT) is applied to exact non-linear measurement equation. Compared with the conventional Huber-based unscented Kalman filter (HUKF) which is derived by applying the Huber technique to modify the measurement update equations of the standard UKF, the NRUKF, without linear (statistical linear) approximation, has much-improved performance and versatility with maintaining the robustness. Then the NRUKF is applied to the target tracking problem. The validity of the algorithm is demonstrated through numerical simulation study. © 2012 The Institution of Engineering and Technology.


Chang G.,Tianjin Institute of Hydrographic Surveying and Charting
Journal of Process Control | Year: 2014

Adaptive and robust methods are two opposite strategies to be adopted in the Kalman filter when the difference between the predictive observation and the actual observation, i.e. the innovation vector is abnormally large. The actual observation is more weighted in the former one, and is less weighted in the later one. This article addresses the subject of making a choice between the adaptive and robust methods when abnormal innovation occurs. An adaptive method with fading memory and a robust method with enhancing memory is proposed in the Kalman filter based on the chi-square distribution of the square of the Mahalanobis distance of the innovation. A heuristic method of recursively choosing among the adaptive, the robust, and the standard Kalman filter approaches in the occurrence of abnormal innovations is proposed through incorporating the observations at the next instance. The proposed method is both adaptive and robust, i.e. having the ability of strongly tracking the variation of the state and being insensitive to gross errors in observation. Numerical simulations of a simple illustrating example validate the efficacy of the proposed method. © 2014 Elsevier Ltd. All rights reserved.


Chang G.,Tianjin Institute of Hydrographic Surveying and Charting
Automatica | Year: 2014

This note points out that the framework proposed in (Wang et al.; 2012) is equivalent to the conventional de-coupling framework introduced in some textbooks; see e.g. (Bar-Shalom et al.; 2001). © 2013 Elsevier Ltd. All rights reserved.


Chang L.,Wuhan Naval University of Engineering | Hu B.,Wuhan Naval University of Engineering | Chang G.,Tianjin Institute of Hydrographic Surveying and Charting
Journal of Guidance, Control, and Dynamics | Year: 2014

The USQUE has been approved to be very attractive for the attitude estimation and has been extended to the integrated GPS and inertial navigation application. Actually, the USQUE can be used in any applications with quaternion such as the in-motion alignment. To calculate the propagated sigma points of the GRP in the USQUE the propagated sigma points of the error quaternion should be first determined, which is achieved by multiplying the propagated sigma points of the quaternion with a reference quaternion. In the USQUE the propagated sigma point of the quaternion in the center is selected as the reference quaternion. The intrinsic-gradient descent algorithm uses the fact that quaternion algebra provides a unique definition of the distance between two attitudes. The intrinsic-gradient-descent algorithm is an iterative method, and the number of iterations is usually very small.


Chang L.,Wuhan Naval University of Engineering | Hu B.,Wuhan Naval University of Engineering | Chang G.,Wuhan Naval University of Engineering | Chang G.,Tianjin Institute of Hydrographic Surveying and Charting | Li A.,Wuhan Naval University of Engineering
Journal of Guidance, Control, and Dynamics | Year: 2012

A robust derivative-free algorithm named outliers robust unscented Kalman filter (ORUKF) is proposed to handle both the state and measurement outliers. Based on the generalized maximum likelihood perspective on the Kalman filter, the state is first augmented with the measurement noise, then the covariance of the augmented state is reformulated by the M estimate methodology and embedded into a modified version of the iterated unscented Kalman filter (UKF) to detect and suppress the outliers. Attractive features of the novel robust derivative-free algorithm include ability to handle multiple outliers, ability to exhibit the accuracy and flexibility of the UKF for the nonlinear problems, and high statistical efficiency under nominal conditions and flexibility to encompass maximum likelihood estimate.


Chang G.,Tianjin Institute of Hydrographic Surveying and Charting
Journal of Navigation | Year: 2014

A loosely coupled Inertial Navigation System (INS) and Global Positioning System (GPS) are studied, particularly considering the constant lever arm effect. A five-element vector, comprising a craft's horizontal velocities in the navigation frame and its position in the earth-centred and earth-fixed frame, is observed by GPS, and in the presence of lever arm effect, the nonlinear observation equation from the state vector to the observation vector is established and addressed by the correction stage of an unscented Kalman filter (UKF). The conditionally linear substructure in the nonlinear observation equation is exploited, and a computationally efficient refinement of the UKF called marginalized UKF (MUKF) is investigated to incorporate this substructure where fewer sigma points are needed, and the computational expense is cut down while the high accuracy and good applicability of the UKF are retained. A performance comparison between UKF and MUKF demonstrates that the MUKF can achieve, if not better, at least a comparable performance to the UKF, but at a lower computational expense. Copyright © The Royal Institute of Navigation 2013 Â.


Chang G.,Tianjin Institute of Hydrographic Surveying and Charting | Chang G.,Wuhan Naval University of Engineering
Journal of Geodesy | Year: 2014

A robust Kalman filter scheme is proposed to resist the influence of the outliers in the observations. Two kinds of observation error are studied, i.e., the outliers in the actual observations and the heavy-tailed distribution of the observation noise. Either of the two kinds of errors can seriously degrade the performance of the standard Kalman filter. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. By assuming that the observation is Gaussian distributed with the mean and covariance being the observation prediction and its associate covariance, the judging index should be Chi-square distributed with the dimension of the observation vector as the degree of freedom. Hypothesis test is performed to the actual observation by treating the above Gaussian distribution as the null hypothesis and the judging index as the test statistic. If the null hypothesis should be rejected, it is concluded that outliers exist in the observations. In the presence of outliers scaling factors can be introduced to rescale the covariance of the observation noise or of the innovation vector, both resulting in a decreased filter gain. And the scaling factors can be solved using the Newton's iterative method or in an analytical manner. The harmful influence of either of the two kinds of errors can be effectively resisted in the proposed method, so robustness can be achieved. Moreover, as the number of iterations needed in the iterative method may be rather large, the analytically calculated scaling factor should be preferred. © 2014 Springer-Verlag Berlin Heidelberg.


Chang G.,Tianjin Institute of Hydrographic Surveying and Charting
Journal of Geodesy | Year: 2014

The Kalman filter for linear systems with colored measurement noises is revisited. Besides two well-known approaches, i.e., Bryson’s and Petovello’s, another measurement time difference-based approach is introduced. This approach is easy to be implemented and generalized to nonlinear system, and can provide filtering solutions directly. A unified view on these approaches is provided, and the equivalence between any two of the three is proved. In the case study part it is validated that, compared to the approach that neglects the time correlations, the approaches that take them into account not only avoid overly optimistically evaluating the estimate, but also improve the transient accuracy of the estimate. © 2014, Springer-Verlag Berlin Heidelberg.


Chang G.,Tianjin Institute of Hydrographic Surveying and Charting | Chang G.,Xian Research Institute Of Surveying And Mapping
Journal of Geodesy | Year: 2015

In this note, the 3D similarity datum transformation problem with Gauss–Helmert model, also known as the 3D symmetric Helmert transformation, is studied. The closed-form least-squares solution, i.e., without iteration, to this problem is derived. It is found that the rotation parameters in this solution are the same to that for the transformation with Gauss–Markov model, while the scale and translation parameters differ from each other. © 2015, Springer-Verlag Berlin Heidelberg.


Chang L.,Wuhan Naval University of Engineering | Hu B.,Wuhan Naval University of Engineering | Chang G.,Wuhan Naval University of Engineering | Chang G.,Tianjin Institute of Hydrographic Surveying and Charting | Li A.,Wuhan Naval University of Engineering
Journal of Process Control | Year: 2013

In this study, a discrete-time robust nonlinear filtering algorithm is proposed to deal with the contaminated Gaussian noise in the measurement, which is based on a robust modification of the derivative-free Kalman filter. By interpreting the Kalman type filter (KTF) as the recursive Bayesian approximation, the innovation is reformulated capitalizing on the Huber's M-estimation methodology. The proposed algorithm achieves not only the robustness of the M-estimation but also the accuracy and flexibility of the derivative-free Kalman filter for the nonlinear problems. The reliability and accuracy of the proposed algorithm are tested in the Univariate Nonstationary Growth Model. © 2013 Elsevier Ltd.

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