This technology is available from Temarex Corporation.

Title: **METHOD FOR PREDICTING FUTURE FUNCTION VALUES
UTILIZING**

**DERIVATIVE SAMPLES**

Inventors: D. Mugler, Y. Wu

Disclosure 306 U.S. Patent not yet issued

For any system which is oscillatory in nature, the present invention addresses industry's need for improved accuracy and/or larger stability regions in system simulations and in prediction of function values from function and derivative samples. The invention is essentially a new "Predictor-Corrector" integrator. Particularly useful for system simulations, the new method builds on past polynomial-based methods such as Adams-Bashforth (AB) for predictors and Adams-Moulton (AM) for correctors in the sense that the new method includes the old polynomial-based methods as a special case. Based on a Nyquist-type criterion which involves the highest frequency of the solution, the invention provides coefficients different than the AB or AM methods would dictate, and the result allows for an increase in the size of the time step in a simulation, resulting in a faster calculation of the solution.

Work in the digital domain is assumed for the calculations, but data may be samples of a continuous time signal such as in the case of uniform sampling of a signal from a sensor. With an appropriate estimate of the highest frequency in the data, just as for the standard Nyquist criterion, coefficients in the new predictor-corrector formulas are determined and may be stored in a lookup table without recalculation. The result may be applied to functions of even polynomial growth which are oscillatory in nature, and the new computations will provide better accuracy. If the highest frequency in the data is near zero, then the data is essentially polynomial-like in nature and the new method simplifies to the standard AB and AM methods. For truly oscillatory functions, the new approach increases accuracy and reduces computation time.

In addition to system simulations, applications of the invention include any area where the prediction of a future function value from past derivative samples is needed. For example, such information could be used to more accurately deploy airbags (i.e. smart airbags), based on the new approach applied to estimate velocity from accelerometer data. Other instances of where prediction of future velocity values may be implemented is in controlling the operation of a moving object or in regulating the spacing of moving vehicles (i.e. inter-vehicle spacing) on an automated highway system (AHS). Further applications suitable for this technology include aircraft's enhanced ground proximity warning systems (EGPWS), traffic collision and avoidance systems (TCAS) and the like. Other applications include predictive filters, signal prediction and the like. For commercial applications, these new formulas and methods could be hardwired into computer circuitry.