Related papers: SVD-based Kalman Filter Derivative Computation

Applications such as face recognition that deal with high-dimensional data need a mapping technique that introduces representation of low-dimensional features with enhanced discriminatory power and a proper classifier, able to classify…

Lossy image compression is essential for efficient transmission and storage. Traditional compression methods mainly rely on discrete cosine transform (DCT) or singular value decomposition (SVD), both of which represent image data in…

Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…

Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally…

Motivated by filtering tasks under a linear system with non-Gaussian heavy-tailed noise, various robust Kalman filters (RKFs) based on different heavy-tailed distributions have been proposed. Although the sub-Gaussian $\alpha$-stable…

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…

In this project, we propose a Variational Inference algorithm to approximate posterior distributions. Building on prior methods, we develop the Gradient-Steered Stein Variational Gradient Descent (G-SVGD) approach. This method introduces a…

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically…

A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…

This paper continues the research devoted to the design of numerically stable square-root implementations for the maximum correntropy criterion Kalman filtering (MCC-KF). In contrast to the previously obtained results, here we reveal the…

Conventional Kalman filtering (KF) approaches exhibit significant limitations in addressing nonlinear state estimation problems contaminated by non-Gaussian noise disturbances. To overcome these challenges, this work proposes a robust…

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

Due to the iterative nature of most nonnegative matrix factorization (\textsc{NMF}) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many initialization schemes…

This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to…

The randomized singular value decomposition (R-SVD) is a popular sketching-based algorithm for efficiently computing the partial SVD of a large matrix. When the matrix is low-rank, the R-SVD produces its partial SVD exactly; but when the…

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…

Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (2019b) for exploratory Item Factor Analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for…