The real-time estimation of (particularly first and second) derivatives of motion from position data has many applications in automatic control. Errors in such estimates at high sampling rates arise from noise or quantization of the data and from the presence of high-order derivatives of motion at low rates.
This paper presents a generalized method to allow estimation of derivatives of orbitary order from position data, with minimum overall error, for a given signal-to-noise ratio and sampling-to-signal frequency ratio. Experimental results included in the paper show that the theory is borne out in practice.
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