A method for computing least squares estimates for transient nonlinear gas path analysis is derived. The solution to the optimal estimation problem is found by solving a system of nonlinear equations. A single iteration of the equation system requires integrating an extended set of nonlinear ordinary differential algebraic equations (ODAE). The additional differential equations originate from the differentiation of the least squares expression used to define optimality. The numerical efficiency of the extended ODAE algorithm is assessed by comparing it to an optimization based method. To illustrate the derived estimation technique a complete model of the Frank Whittle W1 engine is given within the paper. An example of the implementation of the extended ODAE method is demonstrated in the framework of this model. The performance of the method is also discussed and evaluated on a full nonlinear transient model of the RM12 fighter engine.

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