Related papers: Perturbed Initial Orbit Determination
We present an algorithm to compute the minimum orbital intersection distance (MOID), or global minimum of the distance between the points lying on two Keplerian ellipses. This is achieved by finding all stationary points of the distance…
Accurate robot odometry is essential for autonomous navigation. While numerous techniques have been developed based on various sensor suites, odometry estimation using only radar and IMU remains an underexplored area. Radar proves…
The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of…
We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedure relies on polynomial optimization to construct nonnegative…
State estimation is a crucial component for the successful implementation of robotic systems, relying on sensors such as cameras, LiDAR, and IMUs. However, in real-world scenarios, the performance of these sensors is degraded by challenging…
Millimeter wave radar can measure distances, directions, and Doppler velocity for objects in harsh conditions such as fog. The 4D imaging radar with both vertical and horizontal data resembling an image can also measure objects' height.…
An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…
This study concentrates on advancing mathematical and computational methodology for radar tomography imaging in which the unknown volumetric velocity distribution of a wave within a bounded domain is to be reconstructed. Our goal is to…
Radar odometry is crucial for robust localization in challenging environments; however, the sparsity of reliable returns and distinctive noise characteristics impede its performance. This paper introduces geometrically-constrained…
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
Autonomous radar has been an integral part of advanced driver assistance systems due to its robustness to adverse weather and various lighting conditions. Conventional automotive radars use digital signal processing (DSP) algorithms to…
Radar offers unique advantages for localization in unstructured environments, including robustness to weather, lighting, and airborne particulates. While most prior work has studied radar odometry in urban, largely planar settings, its…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
Due to the importance of satellites for society and the exponential increase in the number of objects in orbit, it is important to accurately determine the state (e.g., position and velocity) of these Resident Space Objects (RSOs) at any…
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by PDEs. The goal is to find a placement of sensors, at which experimental data are collected, so as to minimize the uncertainty in…
The estimation of origin-destination (OD) matrices is a crucial aspect of Intelligent Transport Systems (ITS). It involves adjusting an initial OD matrix by regressing the current observations like traffic counts of road sections (e.g.,…
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm,…
In recent years, the development of the Lunar Gateway and Artemis missions has renewed interest in lunar exploration, including both manned and unmanned missions. This interest necessitates accurate initial orbit determination (IOD) and…
Given a set of astrometric observations of the same object, the problem of orbit determination is to compute the orbit and to assess its uncertainty and reliability. For the next generation surveys, with much larger number density of…
Positioning is a prominent field of study, notably focusing on Visual Inertial Odometry (VIO) and Simultaneous Localization and Mapping (SLAM) methods. Despite their advancements, these methods often encounter dead-reckoning errors that…