An adaptive and computationally efficient algorithm for parameters estimation of superimposed exponential signals with observations missing randomly

In this paper, we consider the parameters estimation of a model of superimposed exponential signals in multiplicative and additive noise when some observations are missing randomly. The least squares estimators (LSEs) and asymptotic Cramer–Rao low bound (ACRLB) for the considered model are studied and the asymptotic distributions of the LSEs for parameters of frequencies, phases and amplitudes of the considered model are also derived and obtained. An adaptive and computationally efficient iterative algorithm is proposed to estimate the frequencies of the considered model. It can be seen that the iterative algorithm works quite well in terms of biases and mean squared errors and the refined estimators by three iterations are observed to be asymptotically unbiased and consistent. The statistics for iteration are designed to change adaptively according to different missing distributions of time points so as to keep the estimators of frequencies to be asymptotically unbiased. Moreover, the proposed estimators attain the same convergence rate and asymptotic distribution as those of LSEs which are used to obtain the confident intervals and coverage probabilities of the frequencies for finite sample. Since the iterative algorithm needs only three iterations to work, it saves much computation time. So the proposed estimators are LSEs equivalent while avoid the heavy computation cost of LSEs. Finally, several simulation experiments are performed to verify the effectiveness of the proposed algorithm. To examine the robustness of the proposed algorithm, we also test the algorithm on the dual tone multi-frequency (DTMF) signal with observations missing in block and symmetric α-stable (SaS) noise condition, as well as on sinusoidal frequency modulated signals.