The Sparse-grid based Nonlinear Filter: Theory and Applications

Filtering or estimation is of great importance to virtually all disciplines of engineering and science that need inference, learning, information fusion, and knowledge discovery of dynamical systems. The filtering problem is to recursively determine the states and/or parameters of a dynamical system from a sequence of noisy measurements made on the system. The theory and practice of optimal estimation of linear Gaussian dynamical systems have been well established and successful, but optimal estimation of nonlinear and non-Gaussian dynamical systems is much more challenging and in general requires solving partial differential equations and intractable high-dimensional integrations. Hence, Gaussian approximation filters are widely used. In this dissertation, three innovative point-based Gaussian approximation filters including sparse Gauss-Hermite quadrature filter, sparse-grid quadrature filter, and the anisotropic sparse-grid quadrature filter are proposed. The relationship between the proposed filters and conventional Gaussian approximation filters is analyzed. In particular, it is proven that the popular unscented Kalman filter and the cubature Kalman filter are subset of the proposed sparse-grid filters. The sparse-grid filters are employed in three aerospace applications including spacecraft attitude estimation, orbit determination, and relative navigation. The results show that the proposed filters can achieve better estimation accuracy than the conventional Gaussian approximation filters, such as the extended Kalman filter, the cubature Kalman filter, the unscented Kalman filter, and is computationally more efficient than the Gauss-Hermite quadrature filter

Quadrature filters for one-step randomly delayed measurements

In this paper, two existing quadrature filters, viz., the Gauss–Hermite filter (GHF) and the sparse-grid Gauss–Hermite filter (SGHF) are extended to solve nonlinear filtering problems with one step randomly delayed measurements. The developed filters are applied to solve a maneuvering target tracking problem with one step randomly delayed measurements. Simulation results demonstrate the enhanced accuracy of the proposed delayed filters compared to the delayed cubature Kalman filter and delayed unscented Kalman filter

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

Examinar a ampliação do uso de TICs por organizações sociais e governamentais na gestão da cidade é o objetivo do presente estudo. Nossa intenção é entender de que forma as tecnologias da informação e comunicação podem ser uma via alternativa que redefine as relações entre Estado e sociedade, substituindo políticas urbanas tradicionais por formas colaborativas de interação dos atores sociais. Entre os resultados alcançados pela pesquisa, é possível destacar a elaboração de uma metodologia capaz de mapear os princípios de organização, articulação, conexão e interação que constituem a existência de redes tecnossociais. A aplicação da metodologia nas cidades do Rio de Janeiro e de São Paulo demonstrou indicadores, gráficos e práticas políticas. A análise desses dados revela como as redes se constituem por uma arquitetura móvel, fluída, flexível, organizadas em torno de políticas comuns de ação e formadas por uma identidade coletiva que aproxima os atores das redes tecnossociais. Os princípios que mediam esta coesão são de compartilhamento, confiança e solidariedade, que redefinem as formas da organização do poder em direção a alternativas de organização política e desenvolvimento social

Adaptive Sparse-grid Gauss-Hermite Filter

In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss–Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid Gauss–Hermite filter (SGHF) and Gauss–Hermite filter (GHF) with a considerable reduction in computational load. Further, in the conventional GHF and SGHF, any increase in the accuracy level may result in an unacceptably high increase in the computational burden. However, in ASGHF, a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter. This enables the online estimator to operate near full efficiency with a predefined computational budget

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF3), and the fifth-degree cubature Kalman filter (CKF5) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF

Regularized EM algorithm for sparse parameter estimation in nonlinear dynamic systems with application to gene regulatory network inference

Parameter estimation in dynamic systems finds applications in various disciplines, including system biology. The well-known expectation-maximization (EM) algorithm is a popular method and has been widely used to solve system identification and parameter estimation problems. However, the conventional EM algorithm cannot exploit the sparsity. On the other hand, in gene regulatory network inference problems, the parameters to be estimated often exhibit sparse structure. In this paper, a regularized expectation-maximization (rEM) algorithm for sparse parameter estimation in nonlinear dynamic systems is proposed that is based on the maximum a posteriori (MAP) estimation and can incorporate the sparse prior. The expectation step involves the forward Gaussian approximation filtering and the backward Gaussian approximation smoothing. The maximization step employs a re-weighted iterative thresholding method. The proposed algorithm is then applied to gene regulatory network inference. Results based on both synthetic and real data show the effectiveness of the proposed algorithm