The CRB of direction estimation for underwater wideband sources

The Cramer-Rao Bound (CRB) expression of direction estimation for underwater wideband sources is deduced. According to the expression,the characteristics of wideband CRB and the factors relating to the performance of direction estimation are shown:the wideband CRB of single source can be divided into two items,and one depends on signal characteristics,which include the second moment in frequency and SNR etc.The other one lies on the array geometry composed of array manifold,the source direction,the position of reference point and so on.As for two mutually independent sources,the CRB of each source is equaled to the one of single source.When the included angle of two mutually dependent sources is larger than beam-width,the CRB of each source is approximate to the one of single source.Because of mistaken estimation of sources number,one source is mistaken for two sources,and then the CRB of each source close to infinity.According to the wideband CRB expression,not only the best performance of the wideband direction estimation algorithms is presented,but also useful guidance is provided from the point to improve the performance of direction estimation.