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Passive localisation with high accuracy is attractive in numerous fields. Beam-space direct position determination (BS-DPD) using antenna arrays is a promising positioning method which possesses both excellent performance and moderate complexity. Optimised beam-space design is a vital ingredient for practical BS-DPD systems. In this work, BS-DPD schemes using receiving arrays with random shape errors have been investigated. Performance limits are derived by using Fisher information analysis. Besides, robust formulation based on the compressed Taylor approximation is proposed to counter the randomness existing in antenna positions. Simulation results are provided to reveal the information loss induced by the non-idealities in receiving arrays and also to validate the robustness of the proposed BS-DPD algorithm.