The covariance matrices specified by the COV and COV1 options in the STATE statement must be positive semidefinite. When these matrices are of general form and are not user-specified, they are internally parameterized by their Cholesky root. Suppose that , an positive semidefinite matrix of rank , is such a covariance matrix. Then, can always be written as
where the (generalized) Cholesky root, , is an lower triangular matrix with nonnegative diagonal elements (that is, and ). The SSM procedure parameterizes by the elements of its Cholesky root, which adds elements to the parameter vector .