Name
Abstract | ||
|---|---|---|
New defition of circularity and properness for quaternion random variables.Description of covariance matrices symmetries for quaternion proper random variables.Generalization of the Gaussian proper quaternion random variable.Connection between properness of 4D random variables and rotations in 4D. Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal processing (detection, filtering, estimation). Just like in the complex case, circularity for a quaternion-valued random variable is related to the symmetries of its probability density function. As a consequence, properness of quaternion random variables should be defined with respect to the most general isometries in 4D, i.e. rotations from SO(4). Based on this idea, we propose a new definition of properness, namely the (1, 2)-properness, for quaternion random variables using invariance property under the action of the rotation group SO(4). This new definition generalizes previously introduced properness concepts for quaternion random variables. A second order study is conducted and symmetry properties of the covariance matrix of (1, 2)-proper quaternion random variables are presented. Comparisons with previous definitions are given and simulations illustrate in a geometric manner the newly introduced concept. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.sigpro.2017.03.017 | Signal Processing |
Keywords | Field | DocType |
Quaternion random variables,Properness,4D rotation group,Second order moments,Symmetries,Structured covariance matrix | Random variable,Algebra,Quaternion,Multivariate random variable,Covariance matrix,Geometry,Sum of normally distributed random variables,Rotation group SO,Probability density function,Mathematics,Covariance | Journal |
Volume | Issue | ISSN |
138 | C | 0165-1684 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicolas Le Bihan | 1 | 254 | 23.35 |