The paper deals with a problem of numerical conditioning of basic J-lossless factorisations associated with suboptimal H_∞ norm estimation of discrete-time processes described in the so-called delta-domain. State space formulae for dual J-lossless factorisations of a chain scattering representation of the estimated process are given. Solutions (estimators) are obtained via solving two coupled algebraic Riccati equations. A relative condition number of the delta-domain algebraic Riccati equation is developed as a measure of numerical conditioning of these equations. A numerical example is given to show that solutions obtained for the delta-operator approach are much better-conditioned than its counterpart versions based on the common forward shift operator.