On Effectiveness of Complex Kalman Filter to Real Kalman Filter for Estimation of Discrete Frequency Spectrum.

概要

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In general, it seems to be considered that use of complex Kalman filter instead of real Kalman filter complicates a computation of the algorism and it is of no worth. In this paper, some advantages of complex Kalman filter to real Kalman filter for estimation of discrete frequency spectrum is discussed. The results, firstly, clarify the following advantages of complex Kalman filter in comparison with real Kalman filter using only real part of complex signal. (1) Procedure of computing frequency spectrum is simple, and components with negative frequency can be easily taken into account in estimation, (2) sampling interval is over twice as wide as that in real Kalman filter, (3) the estimate converges about two times as quickly as that in real Kalman filter, (4) amount of multiplication to obtain the desirable estimate is reduced to about 1/4, and etc. Secondary, in comparison of real Kalman filter using both real and imaginary parts of complex signal, (1) amount of multiplication to obtain the desirable estimate is reduced to about 1/2, and etc. In addition, from a view of probability density function and covariance matrix of estimate error, it is indicated that the complex Kalman filter is a reduced form of real Kalman filter.
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