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Author Wikström, Gunilla
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Ordinary Differential Equation ♦ Parameter Occurring Linearly ♦ Linear Appearance ♦ Saddle Point ♦ Initial Guess ♦ Parameter Estimation ♦ Several Local Minimum ♦ Used Iterative Optimization Method Converges ♦ Integral Equation ♦ Differential Equation ♦ Independent Variable ♦ Nonlinear Function ♦ Wanted Minimum ♦ Truncation Erro ♦ Spaced Value ♦ Chosen Dynamic Model ♦ Big Problem ♦ Algebraic Equation ♦ Negligible Measurement Error ♦ Model Parameter ♦ Approximate Parameter
Abstract A big problem when minimizing the sum of squares of nonlinear functions, is the existence of several local minima and saddle points. Because of this, it is necessary to find an initial guess in the vicinity of the solution for the parameters to be estimated, so that the used iterative optimization method converges to the wanted minimum. When the parameters appear linearly in the chosen dynamic model, it is possible to estimate approximate parameters by transforming the differential equations into integral equations, approximating these integrals by use of given data and then solving the resulting algebraic equations for the parameters. Methods based on this approach are analyzed and tested in the case of negligible measurement errors and equally spaced values of the independent variable. It is shown that the methods work well and in agreement with the theory. Keywords : parameter estimation, ODE-systems (with linear appearance of model parameters), linear least squares, truncation erro...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study