State Estimation—Beyond Gaussian Filtering

This dissertation considers the state estimation problems with symmetric Gaussian/asymmetric skew-Gaussian assumption under linear/nonlinear systems. It consists of three parts. The first part proposes a new recursive finite-dimensional exact density filter based on the linear skew-Gaussian system. The second part adopts a skew-symmetric representation (SSR) of distribution for nonlinear skew-Gaussian estimation. The third part gives an optimized Gauss-Hermite quadrature (GHQ) rule for numerical integration with respect to Gaussian integrals and applies it to nonlinear Gaussian filters. We first develop a linear system model driven by skew-Gaussian processes and present the exact filter for the posterior density with fixed dimensional recursive representation, i.e., the skew-Gaussian filter (SGF). The SGF not only has an analytical recursion of a small dimension akin to the Kalman filter, but also possesses an efficiency comparable to the Kalman filter. The minimum mean-square error (MMSE) estimator based on our proposed skew-Gaussian filter is demonstrated via a simulation study. Next, we propose a skew-symmetric presentation of the posterior density to handle the discrete-time filtering problem for a nonlinear system driven by non-Gaussian processes. The skew-symmetric representation of distributions, which has a product form of a symmetric pdf (known as the base pdf) times a perturbation function (known as the skewing function), is employed in this dissertation. Based on a first-order skew-symmetric representation of Gaussian distribution, we propose the first-order skew-Gaussian filter (FOSGF) and demonstrate it by applications to the radar tracking problem. For the filtering problem where Gaussian integrals are adopted in the state update, we propose a new set of Gauss-Hermite quadrature rules using an optimized proposal density. The optimized GHQ rule, proposed in this dissertation, finds an optimized way to improve GHQ-based Gaussian integration when the integrand is not close to a polynomial by transforming it to one approximated by a polynomial. The solution is formulated as a nonlinear least-squares problem with linear constraints. Several numerical examples based on the optimized GHQ rule are studied and compared with the traditional methods

Estimation of the Handwritten Text Skew Based on Binary Moments

Binary moments represent one of the methods for the text skew estimation in binary images. It has been used widely for the skew identification of the printed text. However, the handwritten text consists of text objects, which are characterized with different skews. Hence, the method should be adapted for the handwritten text. This is achieved with the image splitting into separate text objects made by the bounding boxes. Obtained text objects represent the isolated binary objects. The application of the moment-based method to each binary object evaluates their local text skews. Due to the accuracy, estimated skew data can be used as an input to the algorithms for the text line segmentation

An analysis of skewness and skewness persistence in three emerging markets

This paper reports an investigation into the extent and persistence of skewness in stock returns in three emerging markets, namely the Czech Republic, Kenya and Poland. The study is undertaken using the extended skew normal distribution and an asymmetric version of the generalised error distribution. The motivation for this paper is the hypothesis that skewness is a particular feature of returns in emerging markets; it may lack persistence and may decline in absolute terms as time passes and the market matures. When daily returns are considered, the majority of stocks in all three markets exhibit a significant degree of skewness. The value of the skewness parameter is often different in each of the three estimation periods considered. Little evidence has been found to support the view that skewness is an artifact of emerging or evolving markets. Over the period covered by the study, the number of stocks with a significant degree of skewness has remained more or less the same. For weekly returns, the same conclusions apply to the Czech Republic and to Kenya, but there is far less evidence of skewness in weekly returns on Polish Stocks. There is consistent evidence of short-term reversion in daily returns; increases (decreases) in mean return and volatility imply that there will be a decrease (increase) in skewness in the next month. This effect does not persist over longer time horizons