Guobin Chang

Bio: Guobin Chang is an academic researcher from China University of Mining and Technology. The author has contributed to research in topics: GNSS applications & Kalman filter. The author has an hindex of 18, co-authored 92 publications receiving 1115 citations. Previous affiliations of Guobin Chang include Naval University of Engineering & Chinese Academy of Sciences.

Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion

Abstract: 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.

Huber-based novel robust unscented Kalman filter

Abstract: 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.

Multiple Outliers Suppression Derivative-Free Filter Based on Unscented Transformation

Abstract: D UE to its familiarity and computational feasibility, the Kalman filter (KF) has found numerous applications in automatic control, navigation, and communications since its introduction [1–3]. Many nonlinear Kalman type filters (KTFs) have been introduced to extend the KF to nonlinear dynamic and measurement models by forming a Gaussian approximation to the posterior state distribution. Among these nonlinear KTFs, the unscented Kalman filter (UKF) is most celebrated due to its easy implementation, appropriate performance and computational feasibility [4]. However, it is well documented that when the state or measurement noises are contaminated by outliers, theKTF’s performance can severely degrade, because they rely on weighted least-squares (WLS) criteria which is susceptible to outliers [5]. To handle these outliers, several algorithms based on the concept of robust statistics have been proposed. By minimizing the worst-case estimation error averaged over all samples, theH1 basedKF can be used to treat process noises, measurement noises, and model uncertainties [6]. However, it breaks down in the presence of randomly occurring outliers since the design matrices of the H1 filter cannot accommodate well the outliers induced by the thick tails of a noise distribution [7]. Other approaches are robust to either state or measurement outliers and they can not cope with both types of outliers jointly [8–10]. Therefore, they may yield unreliable results when state andmeasurement outliers occur simultaneously. Converting the classical recursive approach into a batch-mode regression form and solving it iteratively, Gandhi proposed a generalized maximum likelihood (GM) type KF which is robust to both the state and measurement outliers [7]. Through auxiliary unknown variables that are jointly estimated along with the state based on the least-squares criterion regularized with the l1 norm, both the state and measurement outliers can also be handled in [11]. However, these methods of [7,11] are both limited to the linear case. Although Gandhi has extended his method to the nonlinear case making use of the extended Kalman filter (EKF) [12], the crude approximation and the cumbersome derivation and evaluation of Jacobian matrices in the EKF may degrade its performance. References [13–16] have combined the derivative-free filters with the M estimator mainly to handle the measurement outliers. Although the structure proposed in [13–16] can be used to handle the state outliers with many iterations, unfortunately, only one iteration is suggested in [13–16], which is not enough to suppress the state outliers. Moreover, in [13–16] the nonlinear measurement functions are also statistically linearized and haven’t been used directly. To the best knowledge of the authors, robust derivative-free filters without linear or statistically linear approximation that addresses both the state and measurement outliers haven’t been studied before. This Note will focus on the robust state estimation problem with outliers using the UKF framework. Based on the GM perspective on the KF, the quadratic cost function in the KF framework is modified by the robust cost function [9,13], to robustify the KF. In this respect, the robust cost function is virtually used to reformulate the predicted state covariance and the measurement noise covariance. Then the reformulated covariance is propagated through the UKF. To handle the state outliers, the measurement update of the UKF should be iterated, which is accomplished by a modification of the iterated UKF [17]. The rest of this Note is organized as follows. Section II presents a GM perspective on the KF and points out how the robustM estimate methodology can be embedded into the UKF framework without linear or statistically linear approximation. Section III is devoted to derive the robust derivative-free filter called the outlier robust unscented Kalman filter (ORUKF) algorithm. Some discussions of the proposed algorithm and comparisonswith existing algorithms are the subject of Sec. IV. Simulation results and comparisons are presented in Sec. V. Finally, conclusions are drawn in Sec. VI.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

Abstract: Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

「Earth,Planets and Space」のオープンアクセス出版

Abstract: ▶ Gathers original articles on topics in earth and planetary sciences ▶ Coverage includes geomagnetism, aeronomy, space science, seismology, volcanology, geodesy and planetary science ▶ Official journal of the Society of Geomagnetism and Earth, Planetary and Space Sciences, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan, and The Japanese Society for Planetary Sciences

The Global Positioning System

Abstract: This research study explores the Global Positioning System (GPS), its history, and the process of discovery needed to create the most accurate GPS possible, as well as the contemporary applications of GPS technology. Starting with the first satellite in space, GPS has been a work in progress. Originally pursued by the military for improvements to military tactics, GPS has become integrated into the everyday lives of millions of people around the world. How GPS determines location is a dichotomy, with simplistic theory and complex application. Many factors go into GPS to provide a consistent, accurate location. The orbital planes the satellites are placed in provide 24/7 coverage globally, the L-band frequencies used were chosen specifically for the characteristics they possess, and the multiple atomic clocks installed on each satellite provide incredible accuracy down to the nanoseconds, which is quintessential in GPS accuracy. The applications in GPS are far reaching and more applications are continually being discovered. With as far as GPS technology has progressed, there are still several factors that degrade the signal and are a challenge to overcome. Many of these challenges can be corrected efficiently, however, others, such as scintillation and total electron content variability in the ionosphere, create major hurdles to overcome. Luckily, there are many programs that aid in the correction process of these hurdles. The History of GPS According to R. Saunders’ article ​A Short History of GPS Development,​ The Global Positioning System (GPS) has a long history of trial and error and refinement and improvement. It’s purpose has shifted from being a military strategic asset to commonplace among the general public with its use in traveling, farming, and even banking. The beginning of GPS, introduced with a simple idea, can be traced back to the Soviet Union in the late 1950’s. In 1957, the Soviet Union made history with successfully launching the first satellite in space. To track the satellite Sputnik, Physicists and Scientists at John Hopkins University’s Applied Physics Laboratory listened to the beeps Sputnik’s signals produced. They noticed that the beeps had a Doppler Effect or Doppler Shift as the satellite passed by. Much like the sound a siren makes as a fire truck approaches, then as it passes, the sound of the siren seems different. The change in timing between the beeps let the scientist know Sputnik’s location. This led to the idea of reversing that process, to give a location on the Earth. Using radio frequencies to determine location in a two dimensional plane had been around since WWII, but using satellites would push this technology into the three dimensional realm. The United States Navy, Army, and Air Force all began developing their own GPS satellites in the 1960’s, but this was no small task. In the early 1960’s, the Navy launched its first Transit Satellite. The failure of this satellite, however, was due to