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Numerical experiments with a new differentiation filter.

H R Busby, D M Trujillo

    Journal of Biomechanical Engineering
    |November 1, 1985
    PubMed
    Summary
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    This study numerically investigates a dynamic programming filter for estimating derivatives from displacement data. The filter utilizes weighted least squares, offering a new approach compared to existing techniques.

    Area of Science:

    • Numerical analysis
    • Data processing
    • Signal processing

    Background:

    • Empirical displacement data often requires accurate derivative estimation for analysis.
    • Existing methods for derivative estimation may have limitations in certain applications.
    • Dynamic programming offers a robust framework for optimization problems.

    Purpose of the Study:

    • To numerically investigate a dynamic programming filter for estimating first and second derivatives.
    • To evaluate the filter's performance using weighted least squares criteria.
    • To compare the filter's results with established derivative estimation techniques.

    Main Methods:

    • A dynamic programming filter was developed and implemented.
    • The filter employs a weighted least squares approach for derivative estimation.

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  • Numerical examples from existing literature were used for validation.

    • Main Results:

    • The dynamic programming filter successfully provided estimates of first and second derivatives.
    • Numerical examples demonstrated the filter's applicability.
    • Performance was assessed against previously published methods.

    Conclusions:

    • The dynamic programming filter is a viable method for estimating derivatives from empirical displacement data.
    • The weighted least squares criterion enhances derivative estimation accuracy.
    • This filter presents a competitive alternative to existing derivative estimation techniques.