The role of abstract algebra in structured estimation theory

An attempt is made to formalize both structured covariance estimation and autoregressive process parameter estimation in terms of the underlying abstract Jordan algebra, an algebra that differs from the usual noncommutative but associative matrix algebra. The investigation puts one on a firm footing from which to attack future problems in statistical signal processing, rather in the same manner that the introduction of Lie algebra and Lie groups in control theory made a variety of new ideas and developments possible