New Robust Estimators of Correlation and Weighted Basis Pursuit

The autocorrelation function is a commonly used tool in statistical time series analysis. In this paper we examine the robustness of two estimators of correlation based on memoryless nonlinear functions of the observations, the Median-of-Ratios Estimator (MRE) and the Phase-Phase Correlator (PPC), which are applicable to complex-valued Gaussian random processes. We show that they are robust to impulsive noise from a bias perspective at the expense of statistical efficiency at the Gaussian distribution. Additionally, we develop iterative versions of these estimators named the IMRE and IPPC, realizing an improved bias performance over their non-iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). We use robust Mahalanobis distances generated by the IMRE and IPPC to improve the performance of impulsive noise suppression through the use of weighted basis pursuit methods. These estimation and data-cleaning techniques are applied to both synthetic and actual collected data using an Ettus Research USRP to perform robust spectral estimation on signals from the digital television band in the presence of additive impulsive noise. Finally, the analysis reveals that if the time series is highly correlated and the contamination rate is low, the MRE outperforms the PPC estimator from a variance and bias perspective. However, the PPC is the estimator of choice when the correlation is lower and is better suited to time critical applications due to lower computation costs.