non-Gaussian Outliers Research Articles

Iterated rational quadratic kernel - High-order unscented Kalman filtering algorithm for spacecraft tracking

The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods. However, reentry flight is accompanied by complex flight environments, which brings to the uncertain, complex, and strongly coupled non-Gaussian detection noise. As a result, there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application. To address these issues, a new iterated rational quadratic (RQ) kernel high-order unscented Kalman filtering (IRQ-HUKF) algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed. Firstly, the characteristic analysis of the RQ kernel is investigated in detail, which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing high-order moments of the RQ kernel. Subsequently, the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion, termed the iterated RQ kernel-UKF (RQ-UKF) algorithm by derived analytically, which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing high-order moments and heavy-tailed characteristics. Meanwhile, to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems, the high-order Sigma Points (SP) as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF. Finally, to further improve the flexibility of the IRQ-HUKF algorithm in practical application, an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence (KLD) method and parametric sensitivity analysis of the RQ kernel. The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.

Underwater Vehicle Positioning by Correntropy-Based Fuzzy Multi-Sensor Fusion.

The ability of the underwater vehicle to determine its precise position is vital to completing a mission successfully. Multi-sensor fusion methods for underwater vehicle positioning are commonly based on Kalman filtering, which requires the knowledge of process and measurement noise covariance. As the underwater conditions are continuously changing, incorrect process and measurement noise covariance affect the accuracy of position estimation and sometimes cause divergence. Furthermore, the underwater multi-path effect and nonlinearity cause outliers that have a significant impact on positional accuracy. These non-Gaussian outliers are difficult to handle with conventional Kalman-based methods and their fuzzy variants. To address these issues, this paper presents a new and improved adaptive multi-sensor fusion method by using information-theoretic, learning-based fuzzy rules for Kalman filter covariance adaptation in the presence of outliers. Two novel metrics are proposed by utilizing correntropy Gaussian and Versoria kernels for matching theoretical and actual covariance. Using correntropy-based metrics and fuzzy logic together makes the algorithm robust against outliers in nonlinear dynamic underwater conditions. The performance of the proposed sensor fusion technique is compared and evaluated using Monte-Carlo simulations, and substantial improvements in underwater position estimation are obtained.

Direct Least Absolute Deviation Fitting of Ellipses

Scattered data from edge detection usually involve undesired noise which seriously affects the accuracy of ellipse fitting. In order to alleviate this kind of degradation, a method of direct least absolute deviation ellipse fitting by minimizing the ℓ1 algebraic distance is presented. Unlike the conventional ℓ2 estimators which tend to produce a satisfied performance on ideal and Gaussian noise data, while do a poor job for non-Gaussian outliers, the proposed method shows very competitive results for non-Gaussian noise. In addition, an efficient numerical algorithm based on the split Bregman iteration is developed to solve the resulting ℓ1 optimization problem, according to which the computational burden is significantly reduced. Furthermore, two classes of ℓ2 solutions are introduced as the initial guess, and the selection of algorithm parameters is studied in detail; thus, it does not suffer from the convergence issues due to poor initialization which is a common drawback existing in iterative-based approaches. Numerical experiments reveal that the proposed method is superior to its ℓ2 counterpart and outperforms some of the state-of-the-art algorithms for both Gaussian and non-Gaussian artifacts.

Sparse linear regression models of high dimensional covariates with non-Gaussian outliers and Berkson error-in-variable under heteroscedasticity

The use of penalized least squares based estimations in high dimensional linear regression has been received a great deal of attention during past decades and applied to variable selections under sparsity scenarios. However, it remains unclear that complex data with multiple uncertainties in measurements, such as outliers, error-in-variables and heteroscedasticity, to what extent, can influence these approaches. This paper, here, demonstrates the behaviors of least-squares based approaches in complex data problems, and suggests an alternative approach, Wald-type estimator, relying on theoretical perspectives. Numerical experiments and real data analysis are also presented to illustrate the performance of the different estimation strategies.

Image Denoising via Improved Dictionary Learning with Global Structure and Local Similarity Preservations

We proposed a new efficient image denoising scheme, which leads to four important contributions. The first is to integrate both reconstruction and learning based approaches into a single model so that we are able to benefit advantages from both approaches simultaneously. The second is to handle both multiplicative and additive noise removal problems. The third is that the proposed approach introduces a sparse term to reduce non-Gaussian outliers from multiplicative noise and uses a Laplacian Schatten norm to capture the global structure information. In addition, the image is represented by preserving the intrinsic local similarity via a sparse coding method, which allows our model to incorporate both global and local information from the image. Finally, we propose a new method that combines Method of Optimal Directions (MOD) with Approximate K-SVD (AK-SVD) for dictionary learning. Extensive experimental results show that the proposed scheme is competitive against some of the state-of-the-art denoising algorithms.

Robust Jacobian matrix estimation for image-based visual servoing

A method for local estimation through training of the feature Jacobian for uncalibrated closed-loop robot manipulator control is presented, which can handle non-Gaussian outliers due to illumination changes. This is achieved through the employment of a robust estimator. The method is experimentally validated through a sunroof fitting robot in a closed-loop control scheme.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K -means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54–71 and 59–73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications.

Linear inverse problems in viscoelastic continua and a minimax method for Fredholm equations of the first kind

A new theory based on an extensively modified version of the minimax method is proposed to estimate the cause from the result, that is, the characteristic functions of viscoelastic media from experimentally obtained material functions through the solution of Fredholm integral equations of the first kind. The method takes into account the non-Gaussian outliers, and does not require the assumption of a priori error bounds as in other smoothing techniques which may lead to instability or to a stable solution not representative of the true solution. The algorithm is applied to several hypothetical test problems to show the excellent performance of the method in extreme severe conditions. The shortcomings of the Tikhonov's regularization and other smoothing techniques are discussed. It is shown that the solution via these methods may not represent the real solution in any norm. The new method is applied to linear viscoelasticity to obtain the relaxation spectrum from experimental material functions. The relaxation spectra of some materials obtained via the proposed adaptive-robust minimax algorithm and experiments run in a rotary viscometer are presented.

Accurate atomic mass measurements from Penning trap mass comparisons of individual ions

We report measurements of mass ratios of 20 pairs of molecular ions with a single ion Penning trap mass spectrometer having an accuracy exceeding one part in 1010. The dominant source of error is random magnetic field fluctuations which cause a 2.6 × 10−10 rms scatter in measurements of the cyclotron frequency. Robust statistical analysis of the data ensures that nongaussian outliers are weighted less heavily in a smooth and consistent manner. Systematic errors are estimated to be 2 × 10−11 or below for doublet mass comparisons. The ratios form an overdetermined set, such that the atomic masses of nine isotopes can be derived from at least two independent groups of ion mass ratios, providing many consistency checks for systematic errors at the 10−10 level. At this level of precision, certain mass measurements have important implications in fundamental metrology. Results presented here are essential for defining a practical atomic standard of mass, for calibrating γ-ray wavelengths and for determining the molar Planck constant and the fine structure constant.