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This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
Reconstructing urban scenes is challenging due to their complex geometries and the presence of potentially dynamic objects. 3D Gaussian Splatting (3DGS)-based methods have shown strong performance, but existing approaches often incorporate…
Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…
An important preliminary procedure in multi-sensor data fusion is \textit{sensor registration}, and the key step in this procedure is to estimate sensor biases from their noisy measurements. There are generally two difficulties in this bias…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…
Maximum likelihood estimation (MLE) is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the MLE converts to a nonlinear least squares (NLS) problem. Efficient solutions to NLS…
Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency…
In the field of localization the linear least square solution is frequently used. This solution is compared to nonlinear solvers more effected by noise, but able to provide a position estimation without the knowledge of any starting…
Analysis of line-of-sight and non-line-of-sight (LOS/NLOS) visibility conditions is an important aspect of wireless channel modeling. For statistical channel models the Monte Carlo simulations are usually used to generate spatially…
Global Positioning System (GPS) plays a critical role in navigation by utilizing satellite signals, but its accuracy in urban environments is often compromised by signal obstructions. Previous research has categorized GPS reception…
Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to efficiently search for the global minimum of a black-box computational model. Gaussian processes have limited applicability in…
Optimizing robot poses and the map simultaneously has been shown to provide more accurate SLAM results. However, for non-feature based SLAM approaches, directly optimizing all the robot poses and the whole map will greatly increase the…
The maximum-marginal-a-posteriori success rate of statistical decision under multivariate Gaussian error distribution on an integer lattice is almost rigorously calculated by using union-bound approximation and Monte Carlo integration.…
Despite the advancements in quality and efficiency achieved by 3D Gaussian Splatting (3DGS) in 3D scene rendering, aliasing artifacts remain a persistent challenge. Existing approaches primarily rely on low-pass filtering to mitigate…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…