Shrinkage sinusoidal phase estimation based on spherical simplex unscented transform and bootstrap method

Abstract

This paper presents novel shrinkage-based sinusoidal phase estimation algorithms. The main contributions of this paper are two-fold. First, the shrinkage factor is found using the spherical simplex unscented transform (SSUT) and the combination of bootstrap and SSUT to reduce the computational complexity of the Monte Carlo method. The computational burden of the proposed methods is relatively low due to the use of SSUT, resulting from the carefully selected sigma points. Second, the accuracy of the novel shrinkage estimator is better than that of the maximum likelihood estimator (MLE) and existing shrinkage estimator under the low signal-to-noise ratio (SNR) and small sample number conditions. It is demonstrated that the resulting accuracies of the proposed shrinkage-based phase estimation methods are superior to those of existing shrinkage algorithm and MLE in low SNR and small sample number conditions.