This paper considers the construction of minimal state space models of linear time-invariant systems on the basis of system representations in terms of generalized orthogonal basis function expansions. Starting from the classical Ho-Kalman algorithm that solves the problem using Markov parameter expansions, a generalization is obtained by analysing the matrix representations of the Hankel operators in generalized orthonormal bases. Using the so-called Hambo-domain techniques an efficient algorithm is given to implement the proposed method.