# Regensburg 2013 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 7: Poster I

### DY 7.17: Poster

### Montag, 11. März 2013, 17:30–19:30, Poster C

**A Parameter Estimation Method for Ordinary Differential Equations** — •Oliver Strebel — Launitzstr. 21, 60594 Frankfurt

Estimating parameters for ordinary differential equations (ODE) is an active field of research. Prominent methods are least square and Kalman methods [1]. While the former suffer from various convergence problems [2], the latter face frequently the "loss of lock" problem of nonlinear filtering [3].

In this contribution a method is presented, which first determines the tangent slope and coordinate for given data of the solution of the ODE. With these values the ODE is transformed into a system of equations, which is linear for linear appearance of the parameters in the ODE. In this case no initial guess of the parameters is necessary. For nonlinear parameter dependence of the ODE nonlinear equations must be solved, using parameter guesses as initial values for the Newton iteration. In both cases the equations are solved repeatedly using randomly selected data points and the averaged results yield the estimates. For numerically generated data of the Lorenz attractor good estimates are obtained even at large noise levels.

[1] B. P. Bezruchko et al: Extracting knowledge from time series, Springer 2010.

[2] B. P. Bezruchko et al:, Chaos, Solitons & Fractals 29, p. 82, 2006.

[3] Z. Schuss: Nonlinear Filtering and Optimal Phase Tracking, Springer 2012.