A note on the limitations of lattice least squares

This paper quantifies the known limitation of lattice least squares to ARX models in terms of the dynamic properties of the system being modeled. This allows determination of the applicability of lattice least squares in a given situation. The central result is that an equivalent ARX model exists for an ARMAX system if and only if the ARMAX system has no transmission zeros from the noise port to the output port. The technique used to prove this fact is a construction using the matrix fractional description of the system. The final section presents two computational examples.