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This paper compares between several parameter estimation methods (Classical Gramm-Schmidt (CGS), Modified Gramm-Schmidt (MGS), Householder Transform (HT), and Givens Rotation (GR)) for Nonlinear Autoregressive with Exogenous Inputs (NARX) system identification of a DC motor model using Binary Particle Swarm Optimization (BPSO) by (Kennedy and Eberhart, 1997) as the structure selection method. First, we describe the application of BPSO for model structure selection, by representing its particles' solutions as probabilities of change in a binary string. The binary string was then used to select a subset of regressor columns from the regressor matrix. The parameters (linear least squares solution) were then estimated using CGS, MGS, GT and GR. One-Step Ahead (OSA) and correlations tests performed on the DC motor dataset show that: 1) The BPSO-based selection method has the potential to become an effective method to determine parsimonious NARX model structure, and 2) The CGS, HT and GR algorithms were the best choices for parameter estimation of the model.