Orthogonal Representations for Output System Pairs
Abstract
A new class of canonical forms is given proposed in which $(A, C)$ is in Hessenberg observer or Schur form and output normal: $\bf{I}  A^*A =C^*C$. Here, $C$ is the $d \times n$ measurement matrix and $A$ is the advance matrix. The $(C, A)$ stack is expressed as the product of $n$ orthogonal matrices, each of which depends on $d$ parameters. State updates require only ${\cal O}(nd)$ operations and derivatives of the system with respect to the parameters are fast and convenient to compute. Restrictions are given such that these models are generically identifiable. Since the observability Grammian is the identity matrix, system identification is better conditioned than other classes of models with fast updates.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.06571
 Bibcode:
 2018arXiv180306571M
 Keywords:

 Statistics  Methodology;
 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Statistics Theory
 EPrint:
 Work done in 200. Minor Revision 2001