System and method of use for non-parametric circular autocorrelation for signal processing

摘要

A computer-implemented method to characterize a signal structure is provided. The method may receive a first set of time-dependent data vectors; select a sample size of data vectors; determine a minimum number of lags to process to characterize the first set of data vectors; calculate a cross-product term for each data vector in the sample size for each lag, a mean value and a variance value based on the sum of the cross-product term for each lag; calculate a circular correlation function for each lag; determine an upper and a lower correlation bound for the circular correlation based on the mean value, the variance value, and a desired false alarm rate; and characterize the signal structure based on the number of calculated circular correlation functions that exceed the upper or lower correlation bounds so as to generate a signal characterization data signal.

主权项

1. A computer-implemented method to characterize a signal structure of an environmental signal received at a receiver comprising:
receiving a first set of data vectors of the environmental signal from the receiver on a first data channel, each data vector, x1, x2, . . . xn, having a length n and an associated amplitude, and said first set of data vectors being time-dependent; selecting a sample size of data vectors from the first set of data vectors utilizing a data processor; determining a minimum number of lags to process to characterize the first set of data vectors based on the selected sample size utilizing a data processor; calculating a cross-product term for each data vector in the selected sample size for each determined lag utilizing a data processor; summing each data vector used in the cross-product term for each determined lag by a data processor to give sums, S1, S2, S3 and S4 of the calculated cross-product term wherein:Si=∑i=1n⁢⁢xij; calculating a mean value μ=E(R) utilizing a data processor based on the data vector length n and sums, S1 and S2, of the calculated cross-product term for each determined lag in accordance with:E⁡(R)=S12-S2n-1; calculating a variance value σ2=var(R) utilizing a data processor based on the sums of the calculated cross-product term for each determined lag in accordance with:var⁡(R)=S22-S4n-1+S14-4⁢S12⁢S2+4⁢S1⁢S3+S22-2⁢S4(n-1)⁢(n-2)-(S12-S2)2(n-1)2; calculating a circular correlation function for each determined lag utilizing a data processor; determining an upper and a lower correlation bound for the calculated circular correlation function utilizing a data processor based on the calculated mean value, the calculated variance value, and a predetermined, desired false alarm rate; characterizing the signal structure utilizing a data processor based on the number of calculated circular correlation functions that exceed one of the determined upper and lower correlation bounds to generate a signal characterization data signal characterizing the environmental signal as one of “signal” or “noise”; and providing the generated signal characterization data signal on a second data channel.