Periodic Fisher-Scoring Algorithm with Applications for DOA Estimation in Seismic Arrays

In many practical parameter estimation problems, such as phase, frequency, and direction-of-arrival (DOA) estimation, the observation model is periodic with respect to the unknown parameters, and thus, the appropriate estimation criterion is periodic in the parameter space. However, iterative estimation methods, such as the Fisher-Scoring method, do not take into consideration the periodic information in order to improve the accuracy of the estimation. In this paper, we present a new iterative method - periodic Fisher-Scoring, which takes into account the signal’s periodic properties through the utilization of the cyclic Cramér-Rao bound (CRB). The cyclic CRB is a lower bound on the mean cyclic error (MCE) of unbiased estimators and, thus, is more appropriate for the derivation of the iterative method. In addition, the periodic Fisher-Scoring method uses the modulo $2 \pi$ operator at each iteration. Simulation results for DOA estimation in seismic arrays show that the proposed periodic Fisher-Scoring estimator has a lower MCE compared to the conventional Fisher-Scoring estimator. The performance improvement is more significant around the edges of the range $[-\pi,\pi]$ and under the misspecified model, i.e. under the mismatched assumption of white noise. We also show that the periodic Fisher-Scoring estimator achieves the cyclic CRB much faster than the CRB.