Robust M-estimates of the frequency and amplitude of a complex-valued harmonic

A maximum likelihood type nil-estimates of the time-invariant amplitude and time-varying frequency are developed for observations of a complex-valued harmonic contaminated by impulse random errors having an unknown heavy-tail ed error distribution. The M-estimates are different from the standard shor t-time periodogram by a nonquadratic loss function minimized in order to ob tain the estimates. A choice of this loss function on the base of the Huber 's minimax robust statistics enables the M-estimates to be robust with resp ect to the error distribution. Asymptotic analytical results are given for the variance and bias of the estimates; The l(1)-periodogram is introduced as a special class of the robust periodogram where the loss function is a s um of absolute values of real and imaginary parts of residuals. The simulat ion demonstrates an effectiveness of the proposed robust estimates. (C) 199 9 Elsevier Science B.V. All rights reserved.