## Form of the statistics

The general form of the statistics of interest is

 (8.1)

and is the -by-1 real input data vector

are real symmetric8.1-by- matrices, are -by- vectors, and are scalars.

The challenge is to determine the joint PDF of under a specified Gaussian hypothesis, that is,

where mean vector

and covariance matrix

Note that there is no loss of generality in assuming that and , where is the -by- identity matrix and is the -by-1 vector of zeros. Call this the white Gaussian noise (WGN) assumption . This is because we can write

where

 (8.2)

 (8.3)

 (8.4)

and is the Cholesky decomposition of ,

Baggenstoss 2017-05-19