Presence Of Large Outliers Research Articles

2D and 3D Angles-Only Target Tracking Based on Maximum Correntropy Kalman Filters.

In this paper, angles-only target tracking (AoT) problem is investigated in the non Gaussian environment. Since the conventional minimum mean square error criterion based estimators tend to give poor accuracy in the presence of large outliers or impulsive noises in measurement, a maximum correntropy criterion (MCC) based framework is presented. Accordingly, three new estimation algorithms are developed for AoT problems based on the conventional sigma point filters, termed as MC-UKF-CK, MC-NSKF-GK and MC-NSKF-CK. Here MC-NSKF-GK represents the maximum correntropy new sigma point Kalman filter realized using Gaussian kernel and MC-NSKF-CK represents realization using Cauchy kernel. Similarly, based on the unscented Kalman filter, MC-UKF-CK has been developed. The performance of all these estimators is evaluated in terms of root-mean-square error (RMSE) in position and % track loss. The simulations were carried out for 2D as well as 3D AoT scenarios and it was inferred that, the developed algorithms performed with improved estimation accuracy than the conventional ones, in the presence of non Gaussian measurement noise.

Distributed non‐linear robust consensus‐based sensor calibration for networked control systems

In this study a new algorithm is proposed for distributed blind sensor macro-calibration in networked control systems robust to noise. The proposed distributed algorithm for estimation of gain and offset correction parameters is of stochastic approximation type, with local non-linear transformations of residuals. Convergence of the algorithm in mean-square and with probability one to consensus is proved for a large class of non-linear transformations, network properties and communication and measurement noise characteristics. The choice of the introduced non-linear transformations in accordance with the theory of robust statistics leads to the proposal of new calibration algorithms robustified w.r.t. noise. It is demonstrated by Monte Carlo simulation that the proposed algorithms are very efficient in the presence of large outliers from the point of view of both achievement of high convergence rate and adequate values of convergence points, outperforming the existing linear algorithms.

Maximum Total Correntropy Diffusion Adaptation Over Networks With Noisy Links

Distributed estimation over networks draws much attraction in recent years. In many situations, due to imperfect information communication among nodes, the performance of traditional diffusion adaptive algorithms such as the diffusion LMS (DLMS) may degrade. To deal with this problem, several modified DLMS algorithms have been proposed. However, these DLMS based algorithms still suffer from biased estimation and are not robust to impulsive link noise. In this paper, we focus on improving the performance of diffusion adaptation with noisy links from two aspects: accuracy and robustness. A new algorithm called diffusion maximum total correntropy (DMTC) is proposed. The new algorithm is theoretically unbiased in Gaussian noise, and can efficiently handle the link noises in the presence of large outliers. The adaptive combination rule is applied to further improve the performance. The stability analysis of the proposed algorithm is given. Simulation results show that the DMTC algorithm can achieve good performance in both Gaussian and non-Gaussian noise environments.

Multikernel Adaptive Filters Under the Minimum Cauchy Kernel Loss Criterion

The Cauchy loss has been successfully applied in robust learning algorithms in the presence of large outliers, but it may suffer from performance degradation in complex nonlinear tasks. To address this issue, by transforming the original data into the reproducing kernel Hilbert spaces (RKHS) with the kernel trick, a novel Cauchy kernel loss is developed in such a kernel space. Based on the minimum Cauchy kernel loss criterion, the multikernel minimum Cauchy kernel loss (MKMCKL) algorithm is proposed by mapping the input data into the multiple RKHS. The proposed MKMCKL algorithm can provide the performance improvement of the kernel adaptive filter (KAF) based on a single kernel, and also improve the stability of the multikernel adaptive filter based on the quadratic loss in impulsive noises, efficiently. To further curb the growth of network of MKMCKL, a novel sparsification method is presented to prune redundant data, thus reducing its computational and storage burdens. Simulations on different nonlinear applications illustrate the performance superiorities of the proposed algorithms in impulsive noises.

Maximum correntropy adaptation approach for robust compressive sensing reconstruction

Robust compressive sensing (CS) aims to recover the sparse signals from noisy measurements perturbed by non-Gaussian (i.e., heavy-tailed) noises, where traditional CS reconstruction algorithms may perform poorly owing to utilizing the l2 error norm in optimization. In this paper, we propose a novel maximum correntropy adaptation approach for robust CS reconstruction. The task is formulated as a l0 regularized maximum correntropy criterion (l0-MCC) optimization problem and is solved by adaptive filtering approach. The proposed l0-MCC algorithm has a simple algorithm structure and can adaptively estimate the sparsity. It can efficiently alleviate the negative impact of noise in the presence of large outliers. Moreover, a novel theoretical analysis on convergence of l0-MCC is also performed. Furthermore, a mini-batch-based l0-MCC (MB-l0-MCC) algorithm is developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed methods can achieve better performance than existing state-of-the-art algorithms.

Power law scaling and “Dragon-Kings” in distributions of intraday financial drawdowns

We investigate the distributions of ∊-drawdowns and ∊-drawups of the most liquid futures financial contracts of the world at time scales of 30s. The ∊-drawdowns (resp. ∊-drawups) generalize the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of ∊-drawdowns and ∊-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (Dragon-Kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.

Photogrammetric DSM denoising

Abstract. Image matching techniques can nowadays provide very dense point clouds and they are often considered a valid alternative to LiDAR point cloud. However, photogrammetric point clouds are often characterized by a higher level of random noise compared to LiDAR data and by the presence of large outliers. These problems constitute a limitation in the practical use of photogrammetric data for many applications but an effective way to enhance the generated point cloud has still to be found. In this paper we concentrate on the restoration of Digital Surface Models (DSM), computed from dense image matching point clouds. A photogrammetric DSM, i.e. a 2.5D representation of the surface is still one of the major products derived from point clouds. Four different algorithms devoted to DSM denoising are presented: a standard median filter approach, a bilateral filter, a variational approach (TGV: Total Generalized Variation), as well as a newly developed algorithm, which is embedded into a Markov Random Field (MRF) framework and optimized through graph-cuts. The ability of each algorithm to recover the original DSM has been quantitatively evaluated. To do that, a synthetic DSM has been generated and different typologies of noise have been added to mimic the typical errors of photogrammetric DSMs. The evaluation reveals that standard filters like median and edge preserving smoothing through a bilateral filter approach cannot sufficiently remove typical errors occurring in a photogrammetric DSM. The TGV-based approach much better removes random noise, but large areas with outliers still remain. Our own method which explicitly models the degradation properties of those DSM outperforms the others in all aspects.

Power Law Scaling and "Dragon-Kings'' in Distributions of Intraday Financial Drawdown

We investigate the distributions of e-drawdowns and e-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The e-drawdowns (resp. e-drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of e-drawdowns and e-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (dragon-kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.

On a Time-Varying Parameter Adaptive Self-Organizing System in the Presence of Large Outliers in Observations

In the previous papers (Pupeikis, 2000; Genov et al., 2006; Atanasov and Pupeikis, 2009), a direct approach for estimating the parameters of a discrete-time linear time-invariant (LTI) dynamic system, acting in a closed-loop in the case of additive noise with contaminating outliers uniformly spread in it, is presented. It is assumed there that the parameters of the LQG (Linear Quadratic Gaussian) controller are unknown, as well as known beforehand, too. The aim of the given paper is development of a minimum variance control (MVC) approach for a closed-loop discrete-time linear dynamic system when slowly or suddenly time-varying coefficients of the transfer function of such a system as well as that of a minimum variance (MV) controller are not known and ought to be estimated. The recursive parametric identification of an open-loop system and determination of the coefficients of the MV controller are performed in each current operation by processing observations in the case of additive noise at the output with contaminating outliers uniformly spread in it. The robust recursive technique, based on the S-algorithm, with a version of Shweppe's GM-estimator and with discounting previous data, used in the estimation, by introducing a constant as well as time-varying forgetting factors in the abovementioned estimator, is applied here in the calculation of estimates of the parameters of a dynamic system. Then, the recursive parameter estimates are used in each current iteration to determine unknown parameters of the MV controller. Afterwards, the current value of the MV control signal is found in each operation, and it is used to generate the output of the system, too. The results of numerical simulation by computer are presented and discussed.

On a parameter adaptive self-organizing system in the presence of large outliers in observations

The aim of the given paper is development of a minimum variance control (MVC) approach for a closed-loopdiscrete-time linear time-invariant (LTI) system when the parameters of a dynamic system as well as that of a controller are not known and ought to be estimated by processing observations in the case of additive Gaussian noise on the output with contaminating outliers uniformly spread in it. Afterwards, the current value of the control signal is found in each operation, and it is used to generate the output of the system. The results of numerical simulation by computer are presented and discussed here, too.

Exploring the economic rationale of extremes in GARCH generated betas The case of U.S. banks

The estimation of time varying beta is an important and growing area of research. The Multivariate GARCH model has been used in the literature to generate estimates of time varying betas. A common feature of the time varying risk estimates generated by this approach, is that they exhibit large outliers. In this paper, we investigate the incidence of such extreme beta observations in order to establish whether they are a response by the market to the arrival of news or alternatively are a result of the model picking up noise from the mean. Using daily data for a sample of U.S. deposit taking institutions over the period 1976 to 1994, this paper uses a Multivariate GARCH model to generate conditional beta estimates. The presence of large outliers is established and investigated. Generally, the results of this study suggest that these extreme observations are economically induced.

Robust pilot spectrum estimation for the quality control of digital seismic data

Abstract For monitoring the quality of seismic data, it is desirable to have an estimate of the noise spectrum that can be made without having to remove earthquake signals. A suitable low-resolution spectrum can be made by filtering the original time series into separate frequency bands and finding the variance in each, using a statistical estimator that is robust in the presence of large outliers. For bandwidths spaced logarithmically in frequency, this estimate will be most resistant to outliers at high frequencies.