Optimal horizons for a one-parameter family of unbiased FIR filters |
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Authors: | Yuriy S Shmaliy Jorge Munoz-Diaz Luis Arceo-Miquel |
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Affiliation: | aGuanajuato University, FIMEE, 36730, Salamanca, Gto., Mexico |
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Abstract: | In this paper, we find the optimal horizons and sampling intervals, both in the sense of the minimum mean square error (MSE), for a one-parameter family of the discrete-time unbiased finite impulse response (FIR) filters. On a horizon of Nl points in the nearest past, the FIR and the model k-state are represented with the l-degree and m-degree polynomials, respectively. The noise-free state space model is observed in the presence of zero-mean noise of an arbitrary distribution and covariance. The approach is based on the following. The FIR filter produces an unbiased estimate if l m. In order to reduce the noise, Nl needs to be increased. The model fits the increased horizon with a higher degree polynomial, m>l. Minimization of the mean square error for m>l gives the optimal horizon and sampling interval. Justification is provided for the global positioning system (GPS)-based measurements of the first state of a local crystal clock provided in the presence of uniformly distributed sawtooth noise induced by the GPS timing receiver. |
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Keywords: | State estimation Unbiased FIR filter Optimal horizon |
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