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There are a variety of Gaussian sigma-point Kalman filters (GSPKF) existing in the literature which are based on different quadrature rules. Their performances are always compared with each other on accuracy and robustness from the numerical-integration perspective, where the number of the sigma points and their corresponding weights are the main reasons resulting in the different accuracy. A new perspective on the GSPKF is proposed in this paper, which is the Mahalanobis distance ellipsoid (MDE). From the MDE perspective, GSPKFs differ from each other on accuracy and robustness mainly because they enclose different probability concentrations. This characteristic is evident when using the high-degree GSPKFs to filter the low-dimensional nonlinear systems. Two classical nonlinear system examples are used to demonstrate the proposed point of this paper. Moreover, some suggestions are given on how to select an appropriate GSPKF for a given nonlinear system. [ABSTRACT FROM AUTHOR]

Integrated global positioning system (GPS)/strap-down inertial navigation system (SINS) systems are widely used for positioning and attitude determination applications. Kalman filtering is the most common method to combine both sensors. A standard Kalman filter (SKF) relies on the correct definition of the measurement and process models and cannot handle measurements with outliers. The H∞ filter can achieve better robustness performance based on minimising the worst-case estimation error. Different to other adaptive KFs, the H∞ filter controls its robustness by a restriction parameter γ. The γ parameter is usually set and fixed by experience. In this paper, an adaptive strategy to gain a time-varying γ is proposed. The construction of the time-varying parameter is based on a two-segment function of an approximate ratio of the traces of the calculated predicted residual's covariance and the theoretical covariance. The test results indicate that the proposed filtering can achieve the expected robustness performance and efficiency more comprehensively when compared with other filtering methods. [ABSTRACT FROM AUTHOR]

In position control of mechatronic devices, velocity feedback is important for injecting additional damping to avoid low-frequency fluctuation around desired trajectories. In practice, velocity signal is often obtained by finite difference of position signal from an optical encoder. However, such a numerical differentiation produces high-frequency noise by magnifying quantization error contained in the position signal. As a result, the controller may produce high-frequency vibration. This paper presents a new noise-reduction discrete-time filter based on sliding mode and adaptive windowing. The presented filter is an improved version of a sliding mode filter by Jin et al. (2012), with including adaptive windowing of which the window size is determined in a similar way to that of a discrete-time adaptive windowing differentiator by Janabi-Sharifi et al. (2000). The presented filter is then applied to a position control of a mechatronic device for improving velocity feedback. Experimental results show that the presented filter provides better velocity feedback than its previous version, Janabi-Sharifi et al.’s differentiator, and combinations of these two filters. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to nonlinear filtering utilizing on-line quantization. We develop performance bounds for the algorithm. We also present an example which illustrates the performance of the method. [ABSTRACT FROM PUBLISHER]

The problem of classification of finite-dimensional estimation algebras was formally proposed by Brockett in his lecture at International Congress of Mathematicians in 1983. Due to the difficulty of the problem, in the early 1990s Brockett suggested that one should understand the low-dimensional estimation algebras first. In this article, we extend Yau and his coauthors' work of the Mitter conjecture for low-dimensional estimation algebras in nonlinear filtering problem. And, we apply the results to give classification of estimation algebras of dimension six. [ABSTRACT FROM PUBLISHER]

Using a measure change, an exact estimate and an approximate recursive estimate are obtained for the conditional density of a hidden signal and a parameter in a state space model, where the hidden signal has deterministic dynamics and it is observed in fractional Gaussian noise. [ABSTRACT FROM AUTHOR]

Various switching-based median filters have been proposed in the literature for restoration of extremely corrupted images and video sequences by impulsive noise. Among these, switching median filters with boundary discriminative noise detection (BDND) are very effective and outperform all the previously proposed median-based filters. However, the calculation is very time-consuming. Hence, in this paper, a median filter with an efficient BDND (EBDND) is proposed for denoizing image and video sequences corrupted by impulsive noise. The proposed EBDND uses a faster sorting algorithm both in noise detection and adaptive filtering stages for the restoration of image and video sequences contaminated by impulse noise. For motion estimation of the video sequence, block-matching technique is used. The performance of the proposed EBDND is demonstrated through computer simulations in comparison with the BDND method. [ABSTRACT FROM AUTHOR]

We provide a comparative study between two different approaches to construct nonlinear filter estimators: on the one hand grid methods using zero-order and first-order quantization schemes, and on the other hand particle filtering algorithms using sequential importance sampling or resampling. For each method, numerical implementation is explicited in addition to convergence arguments and algorithmic complexity. Numerical examples are then given over three state space models: the Kalman filter case, the canonical stochastic volatility model and the infinite dimension explicit filter introduced in [Genon-Catalot, V., 2003, A non linear explicit filter. Statistics and Probability Letters, 61, 145-154] [ABSTRACT FROM AUTHOR]

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]