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An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities
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An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems based on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES), which eliminates the need to derive sensitivity equations.Abstract:
An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.read more
Citations
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References
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The Nelder-Mead Simplex Procedure for Function Minimization
Donald M. Olsson,Lloyd S. Nelson +1 more
TL;DR: The Nelder-Mead simplex method for function minimization is a direct method requiring no derivatives as mentioned in this paper, where the objective function is evaluated at the vertices of a simplex, and movement is away from the poorest value.
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Dud, A Derivative-Free Algorithm for Nonlinear Least Squares
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Journal ArticleDOI
Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations
N. K. Gupta,Raman K. Mehra +1 more
TL;DR: Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined and new results on the calculation of state sensitivity functions via reduced order models are given.
Determination of Airplane Model Structure From Flight Data by Using Modified Stepwise Regression
TL;DR: In this paper, the problem of determining airplane model structure is addressed using linear and stepwise regressions, and the MSR was constructed to force a linear model for the aerodynamic coefficient first, then add significant nonlinear terms and delete nonsignificant terms from the model.
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