Related papers: Particle Filtering for Attitude Estimation Using a…
This paper presents theory, application, and comparisons of the feedback particle filter (FPF) algorithm for the problem of attitude estimation. The paper builds upon our recent work on the exact FPF solution of the continuous-time…
All quaternion methods for static attitude determination currently rely on either the spectral decomposition of a 4 x 4 matrix (q-Method) or finding the maximum eigenvalue of a 4th-order characteristic equation (QUEST). Using a spectral…
There are several attitude estimation algorithms in existence, all of which use local coordinate representations for the group of rigid body orientations. All local coordinate representations of the group of orientations have associated…
A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the…
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…
Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…
This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
We introduce an auxiliary technique, called residual nudging, to the particle filter to enhance its performance in cases that it performs poorly. The main idea of residual nudging is to monitor, and if necessary, adjust the residual norm of…
Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration.…
Particle filtering is a powerful approximation method that applies to state estimation in nonlinear and non-Gaussian dynamical state-space models. Unfortunately, the approximation error depends exponentially on the system dimension. This…
This paper presents solutions to the following two common quaternion attitude estimation problems: (i) estimation of attitude using measurement of two reference vectors, and (ii) estimation of attitude using rate measurement and measurement…
Particle filtering is a recursive Bayesian estimation technique that has gained popularity recently for tracking and localization applications. It uses Monte Carlo simulation and has proven to be a very reliable technique to model…
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
This paper is concerned with the applications of local features of the quaternion Hardy function. The feature information can be provided by the polar form of the quaternion Hardy function, such as the local attenuation and local phase…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
The ability to track a moving vehicle is of crucial importance in numerous applications. The task has often been approached by the importance sampling technique of particle filters due to its ability to model non-linear and non-Gaussian…