Correlation matrix estimation of ordered data using sketches

Non-linear methods are usually used to analyze and process random sequences with outliers or in presence of impulsive noise. One of these methods is based on order statistics, which includes rank information by increasing the problem size. In this article we use a rank one quadratic measurement model based on sketches and apply it to order statistics. We introduce a method to estimate the correlation matrix from a reduced number of measurements, based on a convex relaxation problem that exploits the structure for a sequence of ordered data. We provide simulations to illustrate the behavior of these estimators and show their robustness when uniform noise is present.