Robust Localization Based On Difference Frequency For Long-Range Source In Deep-Water

Passive source localization has been one of the research hotspots in acoustic array signal processing.Matched field processing(MFP)is the most popular method to address this problem.Unfortunately,MFP techniques are not always successful and may be limited by noise,receiving array sparsity,or incomplete knowledge of the acoustic environment between the source and recording arrays.Worthmann et al.proposed the frequency difference matched field processing(FDMFP),which uses the frequency-difference processing to downshift the frequency of the signal to obtain the frequency-difference signal.The working principle of FDMFP is to correlate frequencydifference signals and the low frequency replicas to determine how well they match for different locations.However,FDMFP cannot localize correctly in the deep-sea long-range environment.David et al.improved it and proposed the frequency difference source localization(FDSL),which was successfully applied to long-range localization of experimental data in the Philippine Sea.In addition to generating the frequency-difference signal,the frequency-difference processing will also generate additional cross-terms,which will lead to the degradation of the FDSL performance.This paper is devoted to propose a tolerant source localization method for deep-sea long-range environment.We first analyze the correlation between measured and predicted fields when the MFP and the FDMFP are mismatched in different degrees,and verify that the frequency-difference processing is tolerant of the mismatch.However,in the deep-sea long-range environment,the localization errors of the FDMFP will occur even when the parameters are completely matched.Through mathematical derivation and simulation analysis,it is shown that caustics is the cause of the error: caustics phase shift exists in the predicted field,but not exist in the frequency-difference signal.Therefore,FDSL also performs frequency-difference processing on the predicted field.we analyze the influence of receiving array aperture and different mismatch scenarios on the source localization performance of FDSL.The results show that the FDSL can successfully localize the source localization in the deep-sea and long-range environment,and has good tolerance for mismatch.Despite is found to be robust to uncertain ocean enviroments,it is found that the source localization prediction provided by FDSL is more inaccurate than that of traditional MFP,providing lower PBR and ambiguity surface peak values.This phenomenon is caused by the additional cross-terms generated by the frequency-difference processing.By analyzing the properties of the cross-terms,we use Robust Principal Component Analysis(RPCA)and Low-rank Representation(LRR)to suppress the cross-terms.After suppressing the cross-terms,the FDSL is used to localize the source,so the two methods are called FDSL-RPCA and FDSL-LRR respectively.The simulation results show that the suppression of cross-terms,instead of affecting the localization accuracy,will effectively improve the localization performance of the FDSL.Finally,we use FDSL,FDSL-RPCA and FDSL-LRR to localize the source of the South China Sea trial data.The results show that the three methods can localize the source within a certain error range when the experimental parameters cannot be precisely obtained.However,the localization performance of FDSL-LRR is superior to the other two methods in terms of ambiguity surface peak and PBR,and has better performance.