Joint denoising and delay estimation for the extraction of pulse-width of signals in rf interference

Abstract

A feature detection system, the system comprising: at least one processor in operative communication with a signal source, said processor further comprising at least one non-transitory storage medium, wherein at least one non-transitory storage medium contains instructions configured to cause the processor to: apply a joint group sparse denoising and delay estimation approach to a signal received from said signal source; and output statistics regarding the signal, wherein the joint group sparse denoising and delay estimation approach comprises; using the following equation: where: ϕare regularization functions; ∥y−x∥is a data-fidelity term and, in embodiments, is chosen as the least-square term; lare real numbers; Dare operators, which may be linear filters that can be written in matrix form; λare regularization parameters; and x*,τ* represent estimates of at least one transmitted pulse and associated delay, and solving the equation for multiple values of ϵ; choosing a vector, x, such that a cost function comprising the data fidelity term and regularization function is minimized; determining the ϵ that corresponds to the x that minimizes the cost function; and calculating the pulse width of the received signal, which corresponds to the desired estimate of the vector, x.