TDOA/FDOA Estimation In Passive Emitter Localization

Passive localization means that the system localizes a target by passively receiving signals reflected or emitted from the target,instead of emitting signals itself.For dual-satellite passive localization systems,two satellites are used as the platform and emitter is localized by estimating the time difference of arrival(TDOA)and the frequency difference of arrival(FDOA)between two received signals of the two satellites.The dual-satellite passive localization system can be used not only for satellite interference localization,but also for military targets localization,such as Radar,communication base stations and so on.The passive localization system has the advantages of strong concealment and strong survival ability in electronic warfare.Thus,the passive localization system plays a more and more important role especially with the development of the technology of signal processing and electronic measuring.The fast and precise estimation of the TDOA and FDOA between two received signals is the basis of the passive localization technology.Most of the existing algorithms of TDOA and FDOA estimation have the problem of large computation complexity.The speed for TDOA and FDOA estimation for long signals is hard to meet the needs for real time localization.Thus,the research on the algorithms for TDOA and FDOA estimation is of important significance.The work in this dissertation is carried out with the needs for fast and precise estimation of TDOA and FDOA between two signals in dual-satellites passive localization technology.Ambiguity function is one of the most common tools for TDOA and FDOA estimation,which can be seen as the 2-dimensional correlation function in time and frequency domain.And the coordinates of the peak in the image of ambiguity function correspond to the values of TDOA and FDOA between the two signals.After analyzing the problems existed in algorithms for TDOA and FDOA estimation,this dissertation proposes several new algorithms through different ideas.In addition,the dissertation generalizes the definition of ambiguity function to the fractional Fourier domain and proposes a fast algorithm for Radon-ambiguity transform(RAT)based on the fractional Fourier transform(FrFT)of the signals.The main work and contributions of this dissertation are listed as follows.(1)For passive localization technology based on TDOA and FDOA,this dissertation studies the principle of the parameters of TDOA and FDOA and establishes the signal model for the problem of TDOA and FDOA estimation.This dissertation draws forth the concepts of ambiguity function and FrFT and studies the common algorithms for realizing discrete ambiguity function and discrete fractional Fourier transform(DFrFT).And also,the Cramér-Rao bound of TDOA and FDOA estimation is introduced in this dissertation.(2)Because the velocity between a satellite and a target is limited in practice,the FDOA between two received signals is also limited and usually much smaller than the sampling frequency f_s.However,by taking fast Fourier transform(FFT)on the mixing product of the signals,the values of the discrete ambiguity function on the entire frequency region[-f_s2,f_s2]will be calculated.The region[-f_s2,f_s2]is usually much larger than the range of FDOA,which means a waste of computing resource.In order to avoid unnecessary calculations,the zoom fast Fourier transform(ZFFT)is used to narrow the range of the spectrum of the mixing product.As a result,the calculations of the values of discrete ambiguity function on the frequencies not interested are avoided.And also this dissertation proposes the implementation architecture equivalent to the algorithm for calculating the values of discrete ambiguity function based on ZFFT with high efficiency.To further improve the computational efficiency for calculating the values of discrete ambiguity function by ZFFT,the range of TDOA and FDOA is narrowed with the coarse estimation of TDOA and FDOA which is obtained in this dissertation by calculating the decimated finite ambiguity function.And the simulations show that the algorithm based on ZFFT can estimate the TDOA and FDOA of signals accurately and rapidly and the root mean square error gets close to Cramér-Rao bound with the increase of signal noise ratio.(3)In the figure of ambiguity function of linear frequency modulate(LFM)signals,a ridge passing through the peak point with slope as chirp rate is existed,With the use of the character,a novel algorithm for estimating TDOA and FDOA between LFM signals by searching the peak along the ridge is proposed in this dissertation.The proposed approach first estimates the location of the ridge of the ambiguity function of two LFM signals and then calculates values of the discrete ambiguity function along the ridge through1-dimensional correlation in the fractional Fourier domain.Because the peak point of the ambiguity function is searched 1-dimensionally along the ridge and the values of the ambiguity function along the ridge are calculated through FFT-based processing,the proposed algorithm is computational efficient.For multi-component LFM signals,the proposed algorithm can also estimate the TDOA and FDOA of different components according to different ridges.Simulation results show that the proposed algorithm can estimate the TDOA and FDOA of LFM signals accurately and the root mean square error gets close to Cramér-Rao bound with the increase of signal noise ratio.(4)This dissertation also generalizes the definition of ambiguity function by deriving the generalized definition based on the signals in the fractional Fourier domain,and also proves the property that the coordinate-rotated ambiguity function by an angle is equivalent to the generalized ambiguity function on that angle.An analytic expression for RAT directly based on the FrFT of signals,instead of the ambiguity function,is deduced in this dissertation.With the use of the analytic expression,the RAT can be realized without calculating the values of ambiguity function and taking coordinate rotation of the ambiguity function,and also the discrete RAT can be realized through FFT-based processing.Thus the fast algorithm for RAT proposed in this dissertation is computationally efficient.Simulation results validate the rotational property of generalized ambiguity functions and also demonstrate the performance of the fast algorithm for RAT proposed in this dissertation.(5)A fast method for joint estimation of the TDOA and FDOA for LFM signals based on the RAT is also proposed in this dissertation.According to peak positions of the RAT of a LFM signal on different angles,a set of equations with the TDOA and FDOA as the unknowns can be established.In order to eliminate the noise,the least square method is used to solve the equation and estimate the TDOA and FDOA.Because the proposed algorithm does not need to calculate the values of the 2-dimensional ambiguity function and the discrete RAT can be realized rapidly by the fast algorithm proposed previously in this dissertation,the computational cost of the proposed method is relatively low.Simulation results show that the proposed algorithm can ensure the accuracy of the estimation of TDOA and FDOA as well as is computationally efficient compared with common algorithms based on peak searching of the ambiguity function.A comprehensive study of the fast and precise estimation of the TDOA and FDOA between two signals is carried out in this dissertation.Since the research in this dissertation is under the assumption of narrowband signals,the study does not apply any more when the target emits wideband signals.The passive localization technology for emitters of wideband signals and the estimation of corresponding parameters will be further studied in our future work.