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The highly accurate state estimation of nonlinear systems is needed in many different application fields. In many existing nonlinear filters, the uncompensated nonlinear approximation error and widely used numerical sampling methods both seriously affect the estimation accuracy and numerical stability. In this paper, based on the variational Bayesian framework, a novel iterative nonlinear filter consisting of forward modeling and inverse estimation is proposed. In the forward modeling stage, a linear Gaussian regression process with distributed variational parameters (VPs) is designed to fit the whole nonlinear measurement likelihood. The distributed VPs consider both first and second moments information, so as to compensate for approximation error from the whole likelihood perspective, instead of only the nonlinear function approximation, which can further improve the accuracy of Bayesian posterior update. In the linear Gaussian regression process, the original nonlinear measurement function (NMF) is just viewed as a prior and no longer directly participates in the modeling of the measurement likelihood. Hence, in the inverse estimation stage, when maximizing the evidence lower bound to update the posteriors of the state and VPs, we can obtain closed‐form solutions without numerical sampling methods to approximate the integral of NMF required in many existing methods, which can guarantee numerical stability. Moreover, to avoid the random setting of hyperparameters and to block the propagation of the accumulated error, we propose two rules, estimation and lower bound consistencies, to conduct the hyperparameters' initialization at the beginning of iteration at each sampling time and also derive an optimization method to update hyperparameters during iteration. Finally, the performance of our proposed method is demonstrated in the nonlinear orbital estimation problems. [ABSTRACT FROM AUTHOR]

• A variational Bayesian based cubature Kalman filter (VBCKF-R) is derived. • An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation). • The VBCEECKF algorithm is developed by applying the CEE criteria to the proposed adaptive robust nonlinear filtering framework. • The proposed VBCEECKF algorithm has high precision in target tracking under non-ideal measurement situations. An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation) to simultaneously handle the outliers and uncertain measurement noise covariance matrix (MNCM) for state estimation. This framework utilizes the cubature criterion to solve nonlinear integration problems. By embedding GM estimation in the VB method, the uncertain MNCM is modified while robust estimation is performed. The modified MNCM also provides more accurate model parameters for GM estimation, achieving the unity of adaptability and robustness. The VBCEECKF algorithm was obtained by applying the strong robust centered error entropy criterion to the adaptive robust nonlinear filtering framework. The simulation results of target tracking under different noise conditions verify the superiority of the adaptive robust filter compared to existing methods. [ABSTRACT FROM AUTHOR]

In many practical applications, the initial alignment of the strapdown inertial navigation system (SINS) must be performed under large misalignment angles. However, the error model of SINS in this situation is nonlinear, making it hard to obtain an accurate initial alignment result. Aiming at solving this problem via nonlinear filtering, an improved Markov chain Monte Carlo (MCMC)-based particle filter (PF) algorithm is designed in this article, which uses a square-root cubature Kalman filter (SCKF), PF, and MCMC algorithm synthetically. The algorithm is dedicated to extract particles from the posterior distribution of the state by the improved MCMC algorithm and avoid the particle degeneration and the particle impoverishment in a PF. This can effectively improve the performance of particle filtering for nonlinear systems. Furthermore, to solve the problem caused by the fixed number of iterations in the typical MCMC algorithm, a novel adaptive approach is introduced according to the maximum mean discrepancy. The simulation and experimental results of GPS-aided SINS in-motion initial alignment show that the proposed algorithm can provide good filtering accuracy and have good real-time performance. [ABSTRACT FROM AUTHOR]

The recovery of an unknown (or minimally known) physiological signal embedded in noise has been an indispensable topic drawing the attention of many researchers. Restoration of these signals through conventional linear filtering schemes induces oversmoothing effect at jump discontinuities, and most of the nonlinear filters do not perform well at large noise level. In this paper, we propose a new nonlinear filtering approach, which incorporates the majorized version of a class of nonsmooth functions integrated with Moreau envelope-based regularization. By relaxing the strict sparsifying penalty, the new algorithms balance the smoothness property and the piecewise characteristics of biosignals. We provide the optimality criterion for the proposed algorithms. These algorithms recover the source signals from their noisy measurements. The algorithms outperform the state-of-the-art methods for piecewise synthetic and real-world physiological signals corrupted by additive noise. [ABSTRACT FROM AUTHOR]

In order to control the orientation of a satellite, it is important to estimate the attitude accurately. Time series estimation is especially important in micro and nanosatellites, whose sensors are usually low-cost and have higher noise levels than high end sensors. Also, the algorithms should be able to run on systems with very restricted computer power. In this work, we evaluate five Kalman-type filtering algorithms for attitude estimation with 3-axis magnetometer and sun sensor measurements. The Kalman-type filters are selected so that each of them is designed to mitigate one error source for the unscented Kalman filter that is used as baseline. We investigate the distribution of the magnetometer noises and show that the Student's t-distribution is a better model for them than the Gaussian distribution. We consider filter responses in four operation modes: steady state, recovery from incorrect initial state, short-term sensor noise increment, and long-term increment. We find that a Kalman-type filter designed for Student's t sensor noises has the best combination of accuracy and computational speed for these problems, which leads to a conclusion that one can achieve more improvements in estimation accuracy by using a filter that can work with heavy tailed noise than by using a nonlinearity minimizing filter that assumes Gaussian noise. [ABSTRACT FROM AUTHOR]

As an alternative to the Kalman filter and the particle filter, the particle flow filter has recently attracted interest for solving the curse of dimensionality of the particle filter. Compared with the particle filter, the particle flow filter can obtain a better performance in high-dimensional state spaces with fewer samples. However, for some unobservable state dimensions, the flow operation wastes computational resources. In this paper, we propose a marginalized particle flow filter to handle the unobservable sub-state estimation. In contrast to the standard particle flow filter, we only migrate those observable dimensions of each particle according to homotopy theory and estimate the unobservable dimensions using the Kalman filter. The proposed algorithm can enhance the estimation quality of the unobservable state space and reduce the runtime of the particle flow filter. We evaluate the performance of the proposed algorithm through a multi-target tracking simulation. [ABSTRACT FROM AUTHOR]

Noise reduction of micrographs is often an essential task in high resolution (scanning) transmission electron microscopy (HR(S)TEM) either for a higher visual quality or for a more accurate quantification. Since HR(S)TEM studies are often aimed at resolving periodic atomistic columns and their non-periodic deviation at defects, it is important to develop a noise reduction algorithm that can simultaneously handle both periodic and non-periodic features properly. In this work, a nonlinear filtering algorithm is developed based on widely used techniques of low-pass filter and Wiener filter, which can efficiently reduce noise without noticeable artifacts even in HR(S)TEM micrographs with contrast of variation of background and defects. The developed nonlinear filtering algorithm is particularly suitable for quantitative electron microscopy, and is also of great interest for beam sensitive samples, in situ analyses, and atomic resolution EFTEM. [ABSTRACT FROM AUTHOR]

Cultural artworks that are not properly cared for, degrades over time. However modern image processing techniques proves to be a boon for such artworks. Various techniques have been developed time to time for different aspects of image processing like noise removal, improving brightness and image quality, etc. One of such techniques is PSO (Particle Swarm Optimization) that can be used for image restoration. In this paper a combination of median filter and PSO has been used for the quality improvement of the distorted tribal artworks and the results are compared with few HE (Histogram Equalization) techniques like the CLAHE, BBHE and DSIHE. The comparison is done on the basis of various image quality assessment parameters, namely PSNR, AMBE, NMSE, CPP and MSE. [ABSTRACT FROM AUTHOR]

A novel optical flow estimation is proposed in this paper, which addresses some issues including the credible estimation of optical flow and the prevention of over-smoothing across motion boundaries. Our main contribution is that we estimated the optical flow by a nonlinear filtering process instead of an energy minimizing process, the latter often needs the corresponding smoothing constraint to be restricted to some form of convex and differentiable entity. In this way, it avoids some restrictions needed by the regularization. So we can choose a nonlinear filter from more flexible forms, which can help to deal with flow discontinuities more efficiently in some sense. We modified and extended a scalar 2D bilateral filter to optical flow field as the wanted nonlinear filter. Qualitative and quantitative results show that the new method can produce a reliable result. [ABSTRACT FROM AUTHOR]

The fundamental voltage, current, and phase angle are required for a wide variety of power system applications. An algorithm that is capable of calculating or estimating these quantities in real time, in the presence of distorted waveforms, finds application in diverse areas of power systems. Techniques to detect voltage sag include the root mean square (rms), Fourier transform, and peak voltage detection methods. The problem with these methods is that they use a windowing technique and can therefore be too slow when applied to detect voltage sags for mitigation since they use historical data. Recent work in the field of signal processing has led to an algorithm that can extract a single non-stationary sinusoidal signal out of a given multi-component input signal. The algorithm is capable of estimating the amplitude, phase and frequency. In this paper, the algorithm is compared to existing methods of sag detection. [ABSTRACT FROM AUTHOR]

Abstract: Stack filters are a class of non-linear filters for suppressing the noise that is uncorrelated with the signal. Their design is formulated as a highly nonlinear optimization problem. A modified immune clonal selection algorithm, called immune memory clonal selection algorithm, is employed to perform the configuration of filters design. The new algorithm has the advantage of preventing from prematurity and fast convergence speed. As an experiment, the stack filters are used to restore images corrupted by uncorrelated additive noise with the level from 10% to 50%. The filters are trained on the small regions of the noise-free and noisy image and then applied to the whole image. The new algorithm has faster convergence speed than that of genetic algorithm. The results are compared with that using the median filter. It turns out that, with our proposed algorithm, a smaller MAE for all noise levels is achieved and much detailed information of the images is preserved. The results show that the new algorithm is effective and feasible. [Copyright &y& Elsevier]

In this paper, we propose a new approach to study the stability of the optimal filter w.r.t. its initial condition in introducing a "robust filter," which approximates the optimal filter uniformly in time. This approach allows us to prove, in some cases, when the signal is nonergodic. the stability of the optimal filter in mean over the observations and the uniform convergence in mean over the observations of a special interacting particle filter to the optimal filter. [ABSTRACT FROM AUTHOR]