An improved method for estimating the number of signal sources by combining fourth-order cumulants and Gail circles

Abstract

The invention discloses a signal source number estimation method improved through combination of a fourth-order cumulant and gerschgorin circles and aims to improve source number estimation performance under the colored noise environment when a source number is close to an array element number of an array. The method comprises steps that firstly, array elements of the array are utilized to receive signals to construct a fourth-order cumulant matrix, and redundancy elimination is carried out; secondly, the fourth-order cumulant matrix after redundancy elimination is taken as a gerschgorin circle method to receive a covariance matrix of the information, after unitary transformation, the circle center information of the gerschgorin circles is utilized to carry out compression and descending sort of radiuses of the gerschgorin circles, and source number estimation is accomplished lastly through gerschgorin circle criteria. The method is advantaged in that the method is applied to the technical field of source number estimation in spatial spectrum researches.

Description

technical field [0001] The invention relates to the technical field of signal source estimation in space spectrum research, in particular to an improved signal source number estimation method combining fourth-order cumulants and Gail circles. Background technique [0002] The direction of arrival (DOA) estimation algorithm is a hot issue in the field of spatial spectrum research at present. However, in actual situations, the number of signal sources is often unknown when estimating the direction of arrival. Accurately obtaining the number of signal sources is the key to improving the DOA An important prerequisite for estimating the correct rate. At present, methods for estimating the number of signal sources have been derived from different mathematical criteria, including AIC, MDL, and KIC methods based on information theory criteria, BIC methods based on Bayesian probability, and PET methods based on hypothesis testing. Under the assumption of statistically independent Ga...

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Problems solved by technology

At present, methods for estimating the number of signal sources have been derived from different mathematical criteria, including AIC, MDL, and KIC methods based on information theory criteria, BIC methods based on Bayesian probability, and PET methods based on hypothesis testing. Under the assumption of statistically independent Gaussian white noise, but for the actual color noise environment, the estimation performance of the above method will decrease or even fail

[0003] For the color noise environment, the Gail circle method (GDE) has the advantages of estimating consistency and small amount of calculation. The article "A New Gerschgorin Radii based Method for Source Number Detection[C / / Proc10thIEEE Work Shop on Statistical Signal] by H.T.Wu et al. and Array Processing, 2000: 104-107" further proposed a heuristic criterion about the Gael circle, which can better distinguish the signal disk from the noise disk, but still cannot avoid "the structure of the Gale disk itself Among them, the loss of the degree of freedom of the covariance matrix, when the number of sources is close to the number of array elements, the degree of freedom of the system is not enough, resulting in a decrease in estimation performance"

On the other hand, the fourth-order cumulant can also suppress the Gaussian color noise in the signal very well, and the article "Fourth-Order Cumulant based SourcesNumber Estimation from Mixtures of Unknown Number of Sources[c]2014 SixthInternational Conference on .IEEE, 23-250ct.2014: 1-6.”, through the fourth-order cumulant to generate virtual array elements to improve the degree of freedom of the system, it provides a theoretical basis for the fourth-order cumulant combined with the source number estimation algorithm, but the fourth-order cumulant The calculation of the cumulant is complex, and the noise characteristic value diverges seriously in the actual environment

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