Robust error‐in‐variables estimation using nonlinear programming techniques

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Abstract
For systems described by algebraic or differential equation models where all variables are subject to error, the error‐in‐variables method (EVM) for parameter estimation has been shown to be superior to standard least‐squares techniques. Previous EVM algorithms were developed assuming linear (or linearized) model equations. Unfortunately, many chemical engineering processes operate in strongly nonlinear regions where linear approximations may be inaccurate. In this paper, new algorithms using nonlinear programming techniques for the error‐in‐variables methods are proposed. In addition, a method for discerning when these methods are necessary is discussed. The proposed algorithms are compared to the least‐squares method and traditional error‐in‐variable approaches. Improved parameter estimates for several steady‐state nonlinear processes are demonstrated.