Search results
Results From The WOW.Com Content Network
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
When the two random vectors are the same, the cross-covariance matrix is referred to as covariance matrix. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable.
Here the location parameter is a n-dimensional complex vector; the covariance matrix is Hermitian and non-negative definite; and, the relation matrix or pseudo-covariance matrix is symmetric. The complex normal random vector Z {\displaystyle \mathbf {Z} } can now be denoted as Z ∼ C N ( μ , Γ , C ) . {\displaystyle \mathbf {Z} \ \sim ...
A vector's components change scale inversely to changes in scale to the reference axes, and consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including rotation and ...
Returning to the example above, when the covariance is zero it is trivial to determine the location of the object after it moves according to an arbitrary nonlinear function (,): just apply the function to the mean vector. When the covariance is not zero the transformed mean will not generally be equal to (,) and it is not even possible to ...
The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R p×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. [1]
Items of information a and b are known and are to be fused into information item c.We know a and b have mean/covariance ^, and ^, , but the cross correlation is not known. The covariance intersection update gives mean and covariance for c as