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The estimation of time varying parameters in nonlinear dynamic systems remains as an open problem. In this work, we propose a new approach to addressing this problem by using dynamic optimization. The system is described by a rigorous model which is a set of nonlinear differential and algebraic equations with unknown parameters. The sequential quadratic programming and the orthogonal collocation methods are used to solve the dynamic nonlinear optimization problem. An efficient procedure is presented for calculation of the sensitivity coefficients, gradients and optimization. The effectiveness of the approach is illustrated by estimating tray efficiencies of a pilot distillation column.