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Statistically optimal null filter based on instantaneous matched processing

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A novel approach is proposed for solving the problem of enhancement/suppression of narrowband signals of short-record length based on combining the maximum signal-to-noise ratio (SNR o) and the least-squares (LS) optimization criteria. This two-fold optimization is implemented by scaling the output of an instantaneous matched filter used for the maximization of theSNR o, over a variable-time observation interval, with the locally generated function λ(t) whose gain is optimized through the LS procedure. The intrinsic property of the proposed statistically optimal null filter (SONF) is its ability to track rapidly, leading to a more practical processing of short duration signals (transients). The theoretical analysis and simulation studies show that the SONF, based on this proposed two-fold optimization procedure, is closely related to the Kalman filter. On the other hand, the design of the SONF does not require the solution of a nonlinear equation of the Ricatti type that is necessary in finding the gains of the Kalman filter. Consequently, the proposed algorithm may be considered as an alternate approach to Kalman filtering. The paper also presents some simulation results illustrating the application of the proposed SONF.

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This work was partially supported by Micronet, a Candidan Network of Centre of Excellence, by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by Fonds Pour la Formation de Chercheurs et L'Aide a la Recherche (FCAR) of Province of Quebec, Canada.

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Agarwal, R., Plotkin, E.I. & Swamy, M.N.S. Statistically optimal null filter based on instantaneous matched processing. Circuits Systems and Signal Process 20, 37–61 (2001).

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