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Towards a mathematical foundation of minimum-variance theory

The minimum-variance theory which accounts for arm and eye movements with noise signal inputs was proposed by Harris and Wolpert (1998 Nature 394 780–4). Here we present a detailed theoretical analysis of the theory and analytical solutions of the theory are obtained. Furthermore, we propose a new version of the minimum-variance theory, which is more realistic for a biological system. For the new version we show numerically that the variance is considerably reduced.