A variational Bayesian method for inverse problems with impulsive noise

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.Comment: 20 pages, to appear in J. Comput. Phy

Real-time flutter identification

The techniques and a FORTRAN 77 MOdal Parameter IDentification (MOPID) computer program developed for identification of the frequencies and damping ratios of multiple flutter modes in real time are documented. Physically meaningful model parameterization was combined with state of the art recursive identification techniques and applied to the problem of real time flutter mode monitoring. The performance of the algorithm in terms of convergence speed and parameter estimation error is demonstrated for several simulated data cases, and the results of actual flight data analysis from two different vehicles are presented. It is indicated that the algorithm is capable of real time monitoring of aircraft flutter characteristics with a high degree of reliability

Pulsar data analysis with PSRCHIVE

PSRCHIVE is an open-source, object-oriented, scientific data analysis software library and application suite for pulsar astronomy. It implements an extensive range of general-purpose algorithms for use in data calibration and integration, statistical analysis and modeling, and visualisation. These are utilised by a variety of applications specialised for tasks such as pulsar timing, polarimetry, radio frequency interference mitigation, and pulse variability studies. This paper presents a general overview of PSRCHIVE functionality with some focus on the integrated interfaces developed for the core applications.Comment: 21 pages, 5 figures; tutorial presented at IPTA 2010 meeting in Leiden merged with talk presented at 2011 pulsar conference in Beijing; includes further research and development on algorithms for RFI mitigation and TOA bias correctio

Robust Andrew's sine estimate adaptive filtering

The Andrew's sine function is a robust estimator, which has been used in outlier rejection and robust statistics. However, the performance of such estimator does not receive attention in the field of adaptive filtering techniques. Two Andrew's sine estimator (ASE)-based robust adaptive filtering algorithms are proposed in this brief. Specifically, to achieve improved performance and reduced computational complexity, the iterative Wiener filter (IWF) is an attractive choice. A novel IWF based on ASE (IWF-ASE) is proposed for impulsive noises. To further reduce the computational complexity, the leading dichotomous coordinate descent (DCD) algorithm is combined with the ASE, developing DCD-ASE algorithm. Simulations on system identification demonstrate that the proposed algorithms can achieve smaller misalignment as compared to the conventional IWF, recursive maximum correntropy criterion (RMCC), and DCD-RMCC algorithms in impulsive noise. Furthermore, the proposed algorithms exhibit improved performance in partial discharge (PD) denoising.Comment: 5 pages, 5 figure

A new algorithm of tracking time-varying channels in impulsive noise environment using a robust Kalman filter

2005 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS 2005), Hong Kong, 13-16 December 2005This paper proposes a new algorithm for tracking time-varying channels in impulsive noise environment using a robust Kalman filter. It employs a simple dynamical model of the channel, where the changes in the impulse response coefficients are due entirely to the innovations of the Kalman filter. This reduces the arithmetic complexity, while offering reasonable good performance. The robust Kalman filter is used to restrain the adverse effect of impulsive noise and provide estimates of the covariance matrices of the state and measurement noises. The noisy channel estimates from the Kalman filter can be used to estimate the parameters of the channel coefficients when they are assumed to follow an AR model. Finally, the two processes can be coupled together to further improve the performance. Simulation results show that the new algorithm gives more stable performance than the conventional methods under impulsive noise environment. © 2005 IEEE.published_or_final_versio

A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms that improve the convergence performance of the conventional algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and extends the stability bound on the step size. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyzes and simulation results. We show the extended stability bound of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin