Abstract
The paper considers the problem of generating derivatives of measured data when appropriate transducers and/or observers are not available. Six methods or schemes for estimating acceleration (or generally the second derivative of one parameter with respect to another), by central finite-difference methods, are described. Each scheme is subject to two principal sources of error: noisy or quantized data and the presence of ignored high-order derivatives of motion. The first of these increases with sampling frequency, and the second decreases. There is thus an optimal frequency of sampling for each scheme, dependent on the system signal/noise ratio, the signal- frequency content and the order of the derivative modelled by the scheme. Tables are given that enable the investigator to select the most accurate scheme for a given signal/noise ratio and a desired sampling-frequency I signal-frequency ratio, together with estimates of the resulting combined mean absolute error from the two sources. The results are confirmed experimentally.
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